In this study, we performed multi-objective model-based optimization of a potato-frying process balancing between acrylamide production and a quality parameter (yellowness). Solution analysis revealed that, for most of the Pareto solutions, acrylamide levels exceeded the EFSA recommendation. Almost equivalent optimal solutions were found for moderate processing conditions (low temperatures and/or processing times) and the propagation of the uncertainty of the acrylamide production model parameters led to Pareto fronts with notable differences from the one obtained using the nominal parameters, especially in the ranges of high values of acrylamide production and yellowness. These results can help to identify processing conditions to achieve the desired acrylamide/yellowness balance and design more robust processes allowing for the enhancement of flexibility when equivalent optimal solutions can be retrieved. Food engineering has become an increasingly important field, as evidenced by the growth of mathematical models devoted to understanding and improving food-processing operations . One impOptimization is the process of finding the best possible solution to a problem. This usually involves finding the best compromise among several conflicting demands. To optimize a process, one must find the set of decision variables which, for example, maximize profitability while meeting a set of constraints. Several model-based optimization methods can be used to improve food processing. These methods are more rigorous than other empirical approaches and are thus more likely to find the best possible solution .In general, optimization can be applied effectively to food processing if the changes during the process can be predicted mathematically. Heat, mass, and momentum transfers (as well as kinetics) are major mechanisms in food processing, and mathematical models describing these phenomena are essential for further mathematical-based optimization procedures .Optimal operating conditions in the food industry are usually sought to ensure maximum profits and product quality, subject to constraints arising from food-safety issues and often environmental regulations. However, the dynamic, nonlinear and highly constrained nature of food-processing models can make the optimization of these processes a daunting task .Achieving optimization in food processing requires some way of describing the potential alternatives and of choosing the best alternative. In the design, construction and maintenance of any engineering system, different technological and managerial decisions are required to be given at different stages of the process to either minimize the effort required or maximize the benefit desired. The formal description of any optimization problem has three parts :A set of variables that the optimization method can control and use to specify the alternatives .A set of requirements  that the optimization method must achieve or satisfy.A measure of performance to compare one alternative to another (the objective function). The objective function, which may be continuous or in some cases discrete, is the function to be optimized (maximized or minimized). This can be accomplished by using either a mathematical model or by fitting an equation through the experimental data.For most industrial processes in food, simultaneous optimization of multiple objectives  is the more realistic and desirable approach, but since these criteria are often opposing, the optimal solution is not unique. The multi-objective optimization (MOO) approach is used to find the best set of solutions for a problem with multiple objectives. In food engineering, MOO is used to optimize processes where conflicting objectives such as e.g., process economy, quality parameters or environmental indexes appear. These solutions are known as nondominated or Pareto optimal solutions . Each ofMulti-objective approaches have been used to solve optimization problems in the food engineering industry. For instance, Vilas et al. sought to maximize food quality and safety by developing smart active packaging systems that optimize food-packaging design and prediction of the expected shelf life along the food chain . AbakaroUncertainty propagation has been extensively studied in the fields of physics and mathematics ,19,20,21In this study, the propagation of uncertainty to the MOO approach was assessed by propagating the uncertainty of model parameters to the solutions shown in the Pareto front. Parameter uncertainty can affect the shape of the Pareto optimal front in multi-objective optimization, and this can have important implications for decision-making .Different methods can be used to propagate uncertainty in food engineering. Each method has its strengths and weaknesses, and the choice often depends on the type of data being studied. Some of the most common methods of uncertainty propagation include Monte-Carlo simulation , linear Specifically, this article applies the Monte-Carlo method which is a powerful tool for studying the propagation of uncertainty . The metThis study analyzed the potato-frying process to optimize food safety and culinary quality. Specifically, the impact of the heat treatment on the amount of acrylamide produced and the yellowness and moisture content were studied. The whole study was based on mathematical model simulations. We used the Maillard model (Equations (1)–(5)) to simulate the acrylamide formation using the fitted model provided by Knol et al.  and the w/v. The concentration of hydrogenated cotton seed oil in total (refined plus hydrogenated) oil was considered as 50%  min for time and  °C for temperature.Multi-objective optimization aims at finding the best possible solutions to a set of conflicting objectives, Equations (12)–(16) define the mathematical formulation applied to our case study.D is defined as t is the processing time, T is the temperature, and X is the moisture content. For every value *b of yellowness within the interval , which corresponds to the minimum and maximum yellowness values in the ranges of times and temperatures considered, we calculate the level curveThere are several methods for solving the problem. In the first approach, we used a systematic complete search using the nominal values for the model’s parameters to obtain not only the Pareto front but also the whole feasible region. The procedure is described as follows: A set The described complete search procedure is computationally intensive since it evaluates all the solutions in the feasible regions. As stated above, this was only applied using the nominal parameter values. For assessing the uncertainty propagation, where 1000 Pareto fronts were calculated by simulating different values for the model parameters see , the heuUncertainty propagation was applied to the estimation of the equilibrium constants of the differential equations describing acrylamide production (Equations (1)–(5)). The model considers up to six equilibrium constants for which confidence intervals are given in . The MonThe multi-objective approach using the nominal values for the kinetic parameters provided in  led to aThe first relationship was, as expected, that the higher the yellowness, the lower the moisture content and the higher the amount of acrylamide. All of this was positively correlated with the treatment severity . On the other hand, given the problem boundaries and constraints, the yellowness was limited to values between 22 and 27, while the acrylamide did not exceed 1300 µg/kg which is 26 times higher than the EFSA recommendation.A temperature–time representation of the Pareto front is shown in As shown in During the optimization process, the existence of multiple quasi-equivalent solutions in the Pareto front was found for the ranges of low acrylamide production and low yellowness . The existence of these multiple solutions was caused by the flatness of the objective functions in areas of low temperatures and processing times . Table 1In this section, we analyze the uncertainty propagation from the kinetic parameters of the Maillard equation characterized by Knol et al.  to the PThis paper addresses the problem of food safety combined with product quality. It uses a multi-objective approach, which has been widely used in the literature ,13,14,15The MOP’s solutions  show thaThese results are influenced by all the premises taken such as the potato variety and the type of thermal process, among others. Therefore, any change in these assumptions may influence the results, although the procedure and analysis is useful for studying this type of problem. For example, Johnson determined that, given their composition, not only can the potato variety modify the balance between the variables, but the way they are grown can also have an influence .On the other hand, these solutions are not unique since at the practical level equivalent solutions appear. Therefore, two frying processes with different conditions (time or temperature) can produce the same amount of acrylamide while maintaining equivalent quality (yellowness and moisture content). This existence of equivalent solutions in the Pareto front was recently observed by Ortiz-Martínez et al.  in the mThe study of the propagation of the uncertainty associated with the parameters complements a study that provides an additional tool to take into account other possible scenarios. The presented analysis shows that, when performing multi-objective optimization for design purposes, the model parameters variability and their propagation must be taken into account to find sets of design options  that account for every possible scenario. In this particular application, it was also shown that the propagated variability is not the same in every part of the objectives space, being lower with soft operating conditions  was addressed in this study. The results show that most of the optimal solutions (the Pareto front) considering the usual temperature and processing time ranges provide higher acrylamide amounts than the limit recommended by EFSA (50 μg/kg). In addition, multiple solutions for some areas of the Pareto front  have been identified. The existence of these multiple solutions can be anticipated by a previous analysis of the objective function and their sensitivities to changes in the decision variables (temperature and processing time) in different areas of the search space. In our case, both objective functions showed flat areas in the ranges of low temperatures and processing times, which allows the existence of multiple optimal solutions. These multiple solutions are not equivalent from a mathematical point of view but they are from a practical point of view, allowing us to slightly change the processing conditions to obtain the same results for the objective function within a given tolerance.The uncertainty of the kinetic parameters for acrylamide production has been propagated to the Pareto front using a Monte-Carlo simulation, showing that the uncertainty with respect to the Pareto front using the nominal values increases as the values of the objective functions do. This uncertainty must be taken into account when designing the frying process to make the design more robust and avoid undesirable solutions .We recommend, if possible, performing these analyses when performing model-based multi-objective optimization to design food processes. This type of methodology is of course not specific to food processes but, given their nature, where multiple objectives must be optimized simultaneously, it should be applied to them. Other objectives could be included  or other types of food/processes where acrylamide production may be an issue can be considered by applying the methodologies presented here. These methodologies can help in making optimal decisions where there are unexpected conditions deviations or in re-designing the processes.


Autism spectrum disorder is the most used umbrella term for a myriad of neuro-degenerative/developmental conditions typified by inappropriate social behavior, lack of communication/comprehension skills, and restricted mental and emotional maturity. The intriguing factor of this disorder is attributed to the fact that it can be detected only by close monitoring of developmental milestones after childbirth. Moreover, the exact causes for the occurrence of this neurodevelopmental condition are still unknown. Besides, autism is prevalent across individuals irrespective of ethnicity, genetic/familial history, and economic/educational background. Although research suggests that autism is genetic in nature and early detection of this disorder can greatly enhance the independent lifestyle and societal adaptability of affected individuals, there is still a great dearth of information to support the statement of proven facts and figures. This research work places emphasis on the application of automated machine learning incorporated with feature ranking techniques to generate significant feature signatures for the early detection of autism. Publicly available datasets based on the Q-chat scores of individuals across diverse age groups—toddlers, children, adolescents, and adults have been employed in this study. A machine learning framework based on automated hyperparameter optimization is proposed in this work to rank the potential nonclinical markers for autism. Moreover, this study aimed at ranking the AutoML models based on Mathew's correlation coefficient and balanced accuracy via which nonclinical markers were identified from these datasets. Besides, the feature signatures and their significance in distinguishing between classes are being reported for the first time in autism detection. The proposed framework yielded ∼90% MCC and ∼95% balanced accuracy across all four age groups of autism datasets. Deep learning approaches have yielded a maximum of 92.7% accuracy on the same datasets but are limited in their ability to extract significant markers, have not reported on MCC for unbalanced data, and cannot adapt automatically to new data entries. However, AutoML approaches are more flexible, easier to implement, and provide automated optimization, thereby yielding the highest accuracy with minimal user intervention. Developmental disorders are chronic disabilities and in recent years autism has gained importance across the globe owing to the increasing count of families facing a dilemma while raising affected children . This haDetecting autism sans delay is pivotal to choosing the most appropriate course of therapy, deciding on the level of attention and personal care for the child, managing patient expenses, and prioritizing the nature of schooling and education. The societal stigma associated with Autism Spectrum Disorders (ASD) has escalated the mental trauma faced by families. Early detection of this neurological condition is expected to assist in timely therapy and nurturing for the affected child and family . CompletArtificial intelligence (AI) solutions are influencing every sphere of life ranging from finance and education to the field of medicine and defense. Machine learning, one of the major building blocks of AI, has been studied and diverse techniques have been proposed in the recent past for computer-aided diagnosis of autism –8. InterMachine learning techniques have been proposed in the past for autism classification from clinical datasets obtained by collating real-time questionnaires from parents and healthcare workers. These have been made publicly available as four different nonclinical ASD datasets. Recent research has now delved into the use of deep learning techniques for image classification and text analysis. Many recent reports in the literature, have compared the performance of conventional and deep learning approaches for autism classification –18. PresAutism needs to be initially identified by the caretakers of the infant/child. Hence, nonclinical marker detection plays a crucial role in enabling parents/family members to easily identify the level of developmental delay in the child –3. The dThe organization of the research article is planned as follows: this section is followed by the state-of-the-art on the recent research findings in the sphere of computational classification of ASD. Later, the article describes the materials and proposed methods carried out in this work, which is followed by a detailed description of the experimental results and analysis. Discussions on the findings of this research are presented after the results followed by the conclusions from the work.Autism Spectrum Disorders have been studied by researchers for ages and the findings indicate that ASD diagnosis adopted two main approaches—categorical and dimensional. Volkmar et al.  stated tAhmed et al.  proposedMohanty et al.  reportedAlsaade et al.  proposedSeveral studies were undertaken on classifying ASD from images through traditional machine learning models, hybrid models that infuse feature selection with classification, deep learning models, and AutoML models , 23–27. However, thus far in research, there have been only comparisons of different ML models based on their performance in classifying autism using the UCI ML and Kaggle toddler datasets –31. BothThis research work contributes to the current state of autism classification through machine learning models by aiming at the following three main objectives: (i) Design of a hybrid AutoML-based machine learning framework that interprets the role of potential attributes (feature signatures) for detecting autism. (ii) Automation of algorithmic parameters during execution such that in the event of new data being added to the training set, the use of AutoML approaches would optimize the model parameters and tune the functions to yield the highest performance. (iii) Compare the performance of traditional, deep, and AutoML approaches in autism classification on all 4 datasets employed in this study by utilizing metrics suitable for both balanced and unbalanced datasets.This study concentrates on four autism datasets (i) the child autism dataset—UCI, (ii) the adolescent autism dataset—UCI, (iii) the adult dataset—UCI, and (iv) the toddler dataset—Kaggle. Thabtah , 30 provThe authors noted that most of the predictor attributes were similar in all four datasets. The type of data is diverse across the datasets. All datasets have missing values. The UCI dataset incorporates one additional feature of including individuals who have already used the screening app. One of the objectives of this research is to find the most crucial questions/observations that could lead to early and accurate detection of autism in a noninvasive and less stigmatic manner.The number of instances and attributes for all the datasets included in this study is graphically represented in The software platforms and machine learning models based on automated machine learning are described in the following subsection.https://www.jadbio.com) is an AutoML technology that is very flexible and user-friendly with a highly interpretable interface that generates exhaustive reports on every machine learning task [The software suite utilized in this research is JadBio Automated Machine Learning Platform . AutoML ing task . They arTo the best of our knowledge, no other AutoML platform can identify small-size feature signatures or generate such accurate interpretable results in less time.The AutoML framework proposed in this article is portrayed in Figures The transformed data were then loaded onto the AutoML software suite, and the analysis commenced after the software acquired certain user inputs such as the option to choose between interpretable models or the best-performing models. The users can also choose to perform feature selection or aggressive feature selection. The choice of evaluation metric to rate the performance of the models, and the number of CPU cores for large data was also available. In this work, the authors chose to analyze using the best-performing model with feature selection and aggressive feature selection. Aggressive feature selection differs from feature selection as it places focus on generating the most crucial and small-sized feature signature even at the loss of predictor performance.The proposed framework commenced with the data preprocessing phase, and as is evident from The analysis of the model began with feature selection. AutoML in JADBio implemented the SES  and LASSO (least absolute shrinkage and selection operator) methods. The SES algorithm works on the principle of Bayesian networks' constraint-based learning .The SES method manages to unearth multiple predictive feature subsets whose performances are statistically equivalent .aj is the coefficient of the jth feature. The final term is called the L1 penalty and α is a hyperparameter that tunes the intensity of this penalty term. The higher the coefficient of a feature, the higher the value of the cost function.LASSO is a linear model that uses the following cost function:α hyperparameter value is automatically selected by a cross-validation approach. Hence, when the coefficient of any feature is 0, it is discarded. The model fits a lasso regression on a scaled version of the data and retains only those features whose coefficient is different from 0.LASSO feature selection aims to optimize the cost function by minimizing the absolute values of the coefficients . This feFeature selection is followed by classification and the best performing model was SVM of type C-SVC using a linear/polynomial/radial basis function kernel with cost and gamma hyperparameters set to 1 . The detThe results of this work are reviewed in three sections. The first section elaborates on the performance metrics and the evaluation methods that were adopted in this study. The second section depicts the feature selection and classification results based on the selected metrics. The third section describes the comparative performance of AutoML classifiers with previously reported records on the same autism datasets.The standard metrics for unbalanced data were adopted to rate the AutoML models in this study. It can be noted from the graph in Both these metrics are computed using the confusion matrix that calculates the number of true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN). In this study, if the subject is nonautistic, it is considered a positive case. Based on these terms, the MCC and balanced accuracy were calculated as follows , 44:(2)∝The performance evaluation method adopted in this work was, a repeated 10-fold cross-validation technique, wherein the training dataset was divided into 10 groups (folds) and during each epoch, 9 folds were used for training the model, and one fold was used to test the trained model. This was repeated 10 times and the average MCC and balanced accuracy have been reported. This is a standard statistical method used in data mining and machine learning for evaluating classifier performance. The standard confidence interval was set to 95% while performing the experiments.Feature signature is the combination of features from the original dataset that are highly predictive of the target class. The cumulative results of the proposed AutoML framework are tabulated in The feature signature is generated by AutoML predictors in the order of increasing importance. It is to be recorded based on the tabulated performance metrics in To ascertain the contribution of each individual component to the feature signature, the authors attempted to identify the role of each feature in enhancing predictive performance. Since the aggressive feature selection methods try to minimize the feature signature size at the cost of the model's predictive performance, as witnessed from the results in The feature signature on the toddler and child dataset denotes that there is very little space for improving the performance as both graphs indicate a maximum reduction of ∼0.2% on the predictor performance.The country of residence is a new attribute added to the feature signature in the age groups over 11 as noted from Figures It is evident from the feature signatures generated across all age groups that the questions in the Q-chat alone will suffice to detect autism in young children based on observation of behavior with more than 90% accuracy. Moreover, the use of the autism screening apps, ethnicity, or the existence of autism in the family has not surfaced as a ranked feature in any of the four feature signatures that generated high predictive performance.Recent work in the literature that has reported on the use of the JadBio AutoML framework on other biological datasets has recorded only the training estimates. The authors in this work proceed to validate the performance metrics generated by JADBio using validation data. Four metrics to test the validity of the generated AutoML models across all four datasets have been utilized as seen in The OUT OF SAMPLE TESTING (OOST) metrics have been recorded for the first time on Autism data. This is a measure of how the model predicts a sample that it has not been trained on, that is, totally new test data. The lesser false predictions (FP and FN) in OOST, the more robust the model.The tabulated results clearly reveal that the OOS metrics have very few misclassifications across all age groups. Even aggressive feature selection models have depicted a classification performance comparable to feature selection-based models on the validation data.Since no previous literature is available on AutoML models for autism classification from nonclinical data and most of the existing literature has reported only on the accuracy using traditional and deep learning models, the authors make a comparative performance based on the accuracy of the AutoML models on the ASD datasets.The comparative study of results in Autism-affected individuals irrespective of their age, gender, social status, and educational backgrounds, are subjected to intense social stigma and this affects not only the individual but also their families and the society at large. This research work was undertaken to identify the exact combination of features that could enable early detection of autism, based on questionnaires to caretakers of infants/toddlers who are at high-risk. Research has suggested possible links towards certain high-risk factors like premature gestation delivery, adopting improper delivery mechanisms, unprescribed medical dosages during pregnancy, increased maternal age, and genetic factors , 46.The feature signatures generated for autism detection across all age groups clearly reveal that questions on social interaction and general behavior would suffice to identify the possibility of autism development. This would surely enable caretakers and physicians to ensure that every child is monitored during regular clinic visits and general health checks for behavioral and social interaction abilities.  The feature signature for toddlers: A9, A7, A2, A6, A5, A4, A8, A1, and A3  The feature signature for children: A10, A4, A9, A5, A8, A1, A3, A6, A7, and A2This discussion is restricted to identifying the feature signatures for toddler and child datasets since adolescents and adults, by general behavior, reveal their neurodegenerative status. However, those datasets were included in this study for validating the AutoML classifier performance. It is also to be noted that although multiple signatures could be generated for a single dataset, the proposed AutoML models generated only a single distinct signature for each of the four datasets.The feature signatures indicate that all questions of the Q-chat as described in the attribute description section are required for detecting autism. Besides, the authors also tried including the Q-chat score result as a predictor in the data. In that case, the AutoML model selected only that 1 predictor as a feature signature. The result is depicted in The graph and histogram are shown for the class probability “Yes” which indicates the probability of autism based on the Q-chat score. When the score value is above a certain threshold (∼30%), all subjects are classified as autistic. This is valid proof that the AutoML model is robust in its performance and auto updates itself as per the changes in the training dataset. The graph showing the class distribution based on the Q-chat score is portrayed in The authors also elaborate on the difference between the feature selection, aggressive feature selection, and the basic classification model. Feature selection works by repeated epochs where the focus is placed by the AutoML model only on achieving a high-performance metric.Aggressive feature selection concentrates more on the minimal signature size and reveals the most reduced signature with a reasonable performance above a certain threshold as decided by the AutoML model itself. Feature selection is crucial to this study as the proposed work has identified that ethnicity/jaundice/exposure to app/country of residence are not potential nonclinical markers for autism, especially during the infancy stages and early years of growth.Besides, the authors confirm the effectiveness of the signature markers identified by the AutoML hybrid technique for feature selection and classification by visualizing the projection of the data using principal component analysis , 47 and Probability values should be close to 1 for the positive class and close to 0 for the negative class when plotted according to the predictors with high performance . It is iThe authors also explored the performance of traditional learning models on all four datasets to further establish the superior performance of AutoML models in terms of time, performance, and minimal expert inputs. The comparative performance using the ORANGE data mining tool  is depicIt is to be recorded here that the previous work has reported the accuracy using different performance evaluation methods like train-test ratio, cross-validation, and real-time test datasets. This result is reported using the standard 10-fold cross-validation method and clearly reveals the higher performance of AutoML models in classification. Furthermore, the authors also highlight the role of feature signatures in classification using conventional learning methods. The FCBF (fast correlation-based filter) algorithm uses the idea of identifying features that are highly indicative of the target and highly independent of the other variables as well. The algorithm relies on a metric called Symmetrical Uncertainty (SU) that uses information theory . The difIt is evident from the results in Research in the field of autism and its causes, symptomatic variations, and therapy has been one of the extensively researched spheres in the recent past. Owing to the adverse effects caused by this neurodevelopmental condition, parents and caretakers are keen to ascertain the predictive features of this disorder. Machine learning and computational intelligence have influenced several healthcare areas providing solutions in the form of predictive and diagnostic models, computer-aided assistantships to physicians, and recommender systems for therapeutic guidance. This research work fuses the competence of automated machine learning and computational intelligence to discover highly predictive features for autism that would enable possible early detection of the disorder. As the globe soars towards automated solutions for everyday living, exploring the possibility of automating the diagnostic procedure for diseases through Artificial Intelligence solutions is a great step forward in the field of science and technology. The authors believe the work undertaken in this research provides an informative insight into autism prevalence irrespective of the subject's ethnic, social, or family status. The authors in the future would focus on biosignature detection for autism based on genomic data and the possibility of automatically extracting image-based feature signatures for autism diagnosis.


The dynamic functional connectivity (dFC) in functional magnetic resonance imaging (fMRI) is beneficial for the analysis and diagnosis of neurological brain diseases. The dFCs between regions of interest (ROIs) are generally delineated by a specific template and clustered into multiple different states. However, these models inevitably fell into the model-driven self-contained system which ignored the diversity at spatial level and the dynamics at time level of the data. In this study, we proposed a spatial and time domain feature extraction approach for Alzheimer’s disease (AD) and autism spectrum disorder (ASD)-assisted diagnosis which exploited the dynamic connectivity among independent functional sub networks in brain. Briefly, independent sub networks were obtained by applying spatial independent component analysis (SICA) to the preprocessed fMRI data. Then, a sliding window approach was used to segment the time series of the spatial components. After that, the functional connections within the window were obtained sequentially. Finally, a temporal signal-sensitive long short-term memory (LSTM) network was used for classification. The experimental results on Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Autism Brain Imaging Data Exchange (ABIDE) datasets showed that the proposed method effectively predicted the disease at the early stage and outperformed the existing algorithms. The dFCs between the different components of the brain could be used as biomarkers for the diagnosis of diseases such as AD and ASD, providing a reliable basis for the study of brain connectomics. Hemodynamics is inextricably linked to neuronal activation. Previous studies have demonstrated that the interactivity among brain regions is a powerful tool to study the working mechanisms of the brain . Restinga priori knowledge or preexisting assumptions. The spatial independent brain networks acquired by ICA could capture the complex nature of the fMRI time course  . Howevere course . The ICAa priori information about fMRI and identify common components of the group in the analysis of group data. Moreover, ICA is used for signal decomposition and feature extraction as an integral part of machine learning (ML) disease diagnosis. Study has shown that the selection of the subset ICA features can significantly improve the performance of the classifier compared to ML alone  approach for early diagnosis of the AD and ASD which investigated the feasibility of dynamic temporal properties of spatially independent brain function sub networks as potential disease biomarkers. Specifically, the spatial independent component analysis (SICA) method was applied to the rs-fMRI data to obtain several components that were spatially maximally independent of each other. The sliding window method was used to obtain the dynamic functional connectivity (dFC) status between different ICs. Then, the dynamic characteristics of the functional connectivity values between each pair of ICs were obtained as features. Finally, the features with temporal characteristics were used as the input to the LSTM network for disease prediction. The highlights of the method include the following: (i) The ICA method is used to partition the spatial domain of the brain map automatically and capture the multivariate features which are more targeted than that from the traditional ROI template. The data-driven approach overcomes the dependence on established templates while avoiding the self-contained nature of model-driven approaches. (ii) The dynamic fMRI specifically depicts the process of functional connectivity between spatial patterns in the brain over time, allowing even small changes that occur within a short period of time to be identified. The dynamic properties in this method solve the problem of the potential kinetic properties ignorance in the traditional ICA methods and static FC studies, providing methodological support for parsing the higher cognitive functions of the human brain and mapping the connectivity of the human brain. (iii) The LSTM network is specific to temporal signals in the field of deep learning. We applied the LSTM to fit with the extracted dynamic temporal features which solve the problem that traditional classifiers are insensitive to temporal signals. We applied the method to two separate databases, Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Autism Brain Imaging Data Exchange (ABIDE).The proposed dICA-LSTM disease classification framework based on rs-fMRI is composed of three modules shown in : individThe standard preprocessing and feature matrix construction methods were used for all rs-fMRI data in ADNI and ABIDE datasets to achieve reliable and reproducible solutions. Data preprocessing procedure was carried out by using the Data Processing Assistant for Resting-State fMRI (DPARSF)  and StatThe SICA can identify event-related and spatially independent sub networks of brain functions in multivariate data without restricting the time domain. In this study, the 10-fold cross-validation was performed in the ICA process. Specifically, all subjects were divided into 10-fold. Onefold was used as the testing set, and the remaining ninefold was used as the training set. The process was repeated 10 times until each fold was used as the testing set. At the training stage, the SICA in Group ICA Of fMRI Toolbox (GIFT)  was perfThe GICA methods consisted of three parts: data reduction, independent component computation, and reverse reconstruction. First, the PCA was used to reduce the data for the dimension reduction. Here, the number of principal components was reduced to 20 by using two times of PCA based on 95% variance of the original data. Next, ICA with the Infomax algorithm was performed to decompose the data into 20 independent components and obtain group-level independent components (GLIC). Specifically, the ICASSO algorithm was used to run the ICA decomposition 10 times to ensure the reliability and stability of the evaluated components . The relmth subject, where w was the number of windows, wth sub-time series of the mth subject which was a two-dimensional matrix of 50 (Width of the window)×15 (Number of the RSN). Then, let Tm. The wth sub-functional connectivity matrix of the mth subject, where the size of 15×15. Here,We selected 15 meaningful RSNs after removing the noise components from the estimated 20 stable ICs shown in . The timcorr was the Pearson correlation coefficient. If A and B, respectively. We kept the sign of the Pearson correlation coefficient, thenwhere E(A)andE(B) were the means of the variables A and B. The σAandσB were the standard deviations of A and B. Since 105 elements in mth subject could be represented as w, where w referred to the number of windows in the sliding process, that was, the change of the feature at w time points. In this way, the time-varying multidimensional features of each subject were obtained. Let the set of subjects was denoted as S = {S1;S2;……;SN}, where N represented the number of subjects. Then, the feature characteristics of all subjects were combined as X =  which was used as the input of the subsequent LSTM network.where mth subject was denoted as w, where w referred to the number of windows in the sliding process and the dimension of the feature was 6670. Finally, the features of all subjects were combined as Y = .The dFC matrix at the ROI level was also computed to cross-verify the effectiveness of temporal properties of fMRI and the validity of ICA. Specifically, the AAL template  was usedThe static functional connectivity matrices at the ICA and ROI level were also conducted to illustrate the reliability of dynamic features as potential biomarkers. The specific process was expressed as a direct correlation analysis of the obtained time series at the ICA and ROI levels, thus obtaining the functional connectivity matrix of the entire time course as features without taking a sliding window. Then, the upper triangular elements of the functional connectivity matrix were tiled into a one-dimensional vector as the feature vector. Finally, two representative classifiers, SVM and RF, were applied for classification. Compared with the dynamic features based on sliding windows, the features lacked information about the time dimension which was therefore called static features.The LSTM network has mostly been applied to the prediction of signals with strong temporal characteristics such as speech and text but is little used in neuroimaging . The aimThe recurrent neural network (RNN) is prone to stop learning when the gradient disappears during backpropagation and thus has short-term memory. As the variant of RNN, the LSTM network overcame this problem. The LSTM is composed of several identical components, called hidden cells, where multiple hidden cells are connected first and last. It can pass and forget information through gate structures and cell states. The information in all cells is sent to the fully connected layer to obtain the final diagnostic results. In this study, the structure of the proposed network includes the input layer, LSTM layer, fully connected layer, activation function layer, softmax layer, and classification output layer. The LSTM network was a multiple-input single-output model whose input was the product of the feature count time-step matrices and the output was a categorical type categorical column vector. The architecture of the LSTM network in the study consisted of 30 hidden cells, and each cell is made up of three controlled structures: input gate, forgetting gate, and output gate. The LSTM layer maintained the values that were determined in the previous period by these gates which controlled the data transmission in the cell . The mecThe forgetting gate was structured as the single-layer neural network as shown in equation (4). If the output was one, the forgetting gate was activated.The input gate consisted of two parts including the current sequence and the memory sequence which were represented by the following equations:X(t)andh(t) were the input and output of the current cell. The C(t−1) and h(t−1) were the state and output of the previous cell. The σ denoted the logical sigmoid function. The ωo,ωf,ωi,andωcwere different weighting factors. The bo,bf,bi,andbc were corresponding to different biases.where The rs-fMRI data from two independent databases ADNI and ABIDE  were appThe 10-fold cross-validation was utilized to evaluate the performance of the model. The data were randomly divided into 10-fold. In each loop, the 9-fold was applied for training, while the remaining 1-fold was used for testing. The average of the ten loops was used as the final classification result. Four evaluation metrics were used in the experiments including accuracy (ACC), sensitivity (SEN), specificity (SPE), and F1 score (F1) .where the true positive (TP) was the number of correctly predicted patients in the patient sample. The true negative (TN) was the number of correctly predicted in a normal control. The false positive (FP) was the number of normal controls predicted to be patients. The false negative (FN) was the number of patients predicted to be normal.We also performed multi-classification to predict the AD, LMCI, EMCI, and NC on the ADNI database. The Kappa coefficient and Jaccard similarity score were introduced as evaluation metrics in the quadratic classification.po was the overall classification accuracy, ytest was the set of sample labels, ypred was the set of prediction results, s was the sample size of category, c was the number of samples correctly classified, and T was the total number of samples.where The classification results based on dynamic features at the ROI level and the ICA level are shown in The experimental results of the static features methods are presented in We compared our method with the previous research studies, and the results are indicated in In this study, we proposed a dynamic ICA combined with LSTM network to detect the possible dFC biomarkers from the rs-fMRI data which were applied to the disease identification aspects of AD and ASD. Specifically, the ICA was utilized to obtain maximally mutually independent states. Then, the dynamic connectivity networks were constructed from the time series of each independent component through sliding windows. The approach allowed for overlap between the time windows which had explicit temporal dynamic interpretability. The independent components were usually combined and categorized into some existing specific RSN templates in the established studies, for example, the visual network, auditory network (AN), and default mode network (DMN). However, the potential discriminated information may be excluded in this process. In this study, we used all components after eliminating the obvious noisy parts. We hypothesized that there were certain subjective factors in the categorization process that could affect the experimental results. The group-level independent component decomposition method was utilized which ensured that the activation components at the same sites were obtained in all subjects and avoided the component mismatch in the individual independent component decomposition process. The number of independent components was one of the important factors for ICA results. The few components may result in non-independence of the ICs, while more components may lead to excessive decomposition of the independent individuals. In this study, the number of ICs was set to be 10, 20, 30, and 40 to investigate their effects on the results. The issue of sliding window settings of dFC networks has been widely emphasized and discussed . The twoThe LSTM network is effective for capturing the depth features of temporal signals. In this study, we used LSTM to verify the effectiveness of dFC in fMRI data and achieved rewarding classification results. Previous studies have applied LSTM to fMRI data for disease prediction. The ICA-based dynamic connectivity reflects the inherent functional interactions among different brain sub networks. The characteristic abnormal features in AD or ASD may be presented. The brain disorder-specific insights on the dynamic connectivity could serve as features for early disease classification which are helpful for the investigation of the pathogenesis.To investigate the deep features that are related to AD or ASD, we compute the most discriminative features in the deep learning process. We found the abnormal dynamic connectivity of the DMN in AD. The abnormal dynamic connectivity between DMN and hippocampus plays a key role in the classification. The DMN is involved in the coordination of cognitive behavior. The hippocampus is inextricably linked to the production of memories. Thus, abnormal dynamic connectivity between the DMN and hippocampus may lead to decreased conscious responsiveness and memory capacity. Moreover, we found that abnormalities of the dynamic connectivity in attention network (AN) and sensorimotor network (SMN) in ASD were important for the classification. AN is responsible for perceiving external stimuli and directing attention. SMN is responsible for activity participation awareness and awakening maintenance. The anomaly of the connectivity may have contributed to the lack of awareness of participation in ASD and thus the inability to communicate properly in public places.This study proposed a dynamic ICA-LSTM approach for the fMRI disease classification which investigated the feasibility of dynamic temporal properties of functional connectivity among independent sub networks at the spatial level of the brain as potential disease biomarkers. The independent brain networks of subjects were obtained using group spatial ICA. Then, the dynamic FC features from RSNs were captured by using sliding windows. Finally, the LSTM networks were used to extract deep temporal features for disease prediction. The method exploited the dynamic temporal properties of spatial brain mapping of fMRI data by using the data-driven entry point, which solved the problem of difficulty in extracting deep temporal features by traditional machine learning methods and the self-limiting problem of model-driven. The results demonstrated that spontaneous brain activity on a time scale of seconds could be used as the distinguishable measures of brain activity.https://ida.loni.usc.edu.Publicly available datasets were analyzed in this study. This data can be found here: JQ and ZW: conceptualization, resources, and supervision. JQ and RW: writing and methodology. RW, HL, and GX: data analysis. All authors contributed to this study and approved the submitted version.


The use of advanced chemometrics tools in food authenticity research is crucial for managing the huge amount of data that is generated by applying state-of-the-art analytical methods such as chromatographic, spectroscopic, and non-targeted fingerprinting approaches. Thus, this review article provides description, classification, and comparison of the most important statistical techniques that are commonly employed in food authentication and traceability, including methods for exploratory data analysis, discrimination, and classification, as well as for regression and prediction. This literature revision is not intended to be exhaustive, but rather to provide a general overview to non-expert readers in the use of chemometrics in food science. Overall, the available literature suggests that the selection of the most appropriate statistical technique is dependent on the characteristics of the data matrix, but combining complementary tools is usually needed for properly handling data complexity. In that way, chemometrics has become a powerful ally in facilitating the detection of frauds and ensuring the authenticity and traceability of foods. The authenticity of foods and beverages is an issue of utmost importance for all actors participating in the food chain . WhereasThe large and complex datasets that state-of-the-art analytical methods usually generate make the implementation of advanced chemometric techniques, aimed at extracting as much valuable information as possible from the raw data, mandatory. Thus, chemometrics refers to the application of statistical and mathematical tools for identifying the underlying relationships between variables. This enables the construction of statistical models able to interpret the characteristics of the system on the basis of available chemical data, which can subsequently be employed for classification, discrimination, and prediction purposes. In this review article, we provide a description, classification, and comparison of the most commonly employed chemometric techniques in food authentication and traceability. Furthermore, we also discuss some relevant issues that are sometimes underestimated in this field, such as the importance of data preprocessing and further validation of the models obtained.Two complementary analytical strategies are available nowadays for food authentication and traceability, namely targeted and non-targeted approaches ,7. TargeChromatography coupled with spectroscopic or spectrometric detection has been proven to be a suitable tool for determining and quantifying individual components or compound classes in food samples . Liquid 18O) and deuterium (δ2H) are strongly impacted by hydrological factors, so they can serve to differentiate food samples according to their origin. The carbon isotopic ratio (13C/12C) is affected by climatic conditions, plant type, and agricultural practices. Finally, nitrogen isotopic analysis (δ15N) allows the differentiation of conventional from organic farming because the nitrogen isotope content in synthetic fertilizers is much lower than in organic ones [As minerals are mainly absorbed by plants and animals through soil and water resources, multi-elemental techniques have demonstrated great utility for assessing geographical origin, environmental conditions of the growing/breeding area, and crop management ,19. Furtnic ones . Regarding non-targeted fingerprinting, it should be noted that various analytical platforms have been proposed over recent years for analyzing complex metabolomes. However, as each one of these techniques has their own advantages and limitations, the combination of various approaches is nowadays the common practice for performing comprehensive analysis . The useFinally, a variety of molecular biology approaches are also well-established for the analysis of nucleic acids, proteins, and peptides as markers of adulteration and authenticity. In particular, as the DNA sequence is unique to each living organism, DNA-based methods have traditionally been employed to track raw materials across the whole industry process. These molecular techniques range from traditional molecular marker-based methods  to more recent single region approaches  and next-generation sequencing-based methods  . HoweverAs a result of the large amount of data that the abovementioned analytical techniques generate, the use of advanced multivariate chemometric tools is mandatory for extracting as much valuable information as possible . MultivaPrior to performing any statistical analysis, the application of preprocessing tools is usually mandatory for enhancing the quality of the data matrix via removing unwanted variability sources . This is typically accomplished by applying various sequential steps, including data cleaning , scaling, and transformation . MissingExploratory data analysis (EDA) is normally employed as a first step to visualize the main characteristics of the dataset. For this purpose, unsupervised pattern recognition techniques are normally applied to reduce the dimensionality of complex data matrices without losing information. This enables projecting samples into a low-dimensional space  with the aim of inspecting sample groupings, detect outliers, etc.Principal component analysis (PCA) is a powerful and commonly used tool for reducing the dimensionality of vast sets of data . AccordiCluster analysis (CA) enables the grouping of similar observations into a number of clusters based on the observed values of several variables for each individual. These subclasses may reveal patterns related to the phenomenon under study. To conduct CA, similarity measures must be first computed between observations and between clusters once observations begin to be grouped into clusters. The clustering procedure is usually based on Euclidean distance (d), although other metrics may also be adopted to measure distances between objects, such as the squared Euclidean distance, the Manhattan distance, the Pearson coefficient of correlation, or user-defined distances. Clustering methods can in turn be categorized into four subtypes: hierarchical, optimizing, density-seeking, and clumping techniques. In hierarchical methods, classes are subclassified into groups by repeating the modeling in iterative steps to yield a tree, where study groups are represented as branches. Optimizing techniques are based on the construction of clusters by selecting the optimal grouping criteria. The obtained classes must be mutually exclusive, where the observations are plainly divided in different sets. In density-seeking , the clusters are detected and generated by searching areas on a graphical representation containing concentrations of data measures. Finally, clumping methods use a modification of the density-seeking approach based on weighting specific variables to assign the clusters in a manner where obtained groups can be overlaid on graphic projections. Among them, the most common form of analysis is the hierarchical cluster analysis (HCA) tool , for whiDiscrimination and classification methods are employed for predicting an object’s belonging to a given category based on its characteristics . For thiIn this respect, it should be noted that supervised methods that are normally employed for classification and discrimination purposes are prone to overfitting, especially when the number of variables exceeds the number of observations, which makes the implementation of validation tools mandatory . ExternaLinear discriminant analysis (LDA) is a supervised tool where a number of orthogonal discriminant functions (DF) equal to the number of categories minus one are generated. Discriminant functions are computed as linear combinations of the predictor variables and used to differentiate study groups by controlling the within-class and between-class ratios. The discriminant capacity of DFs can be assessed through the measurement of the Wilks’ lambda parameter, which is calculated for the global model after excluding the selected variable. Afterward, a forward stepwise algorithm is applied to retain the functions that must be considered in the final model. Accordingly, the assessment F values are regarded as suitable criteria for including or removing predictors in LDA. Furthermore, Wilks’ lambda and F values can be employed for testing the importance of each variable in the model. Once the DFs are computed, the groups can be differentiated by hyperplanes contained inside the space defined by DFs, and samples can be classified depending on their belonging to these subspaces (classification rule).Y2, RX2, and Q2. RY2 and RX2 are the proportion of Y and X variances explained by the model, respectively. Q2 is a measurement of the model prediction capacity. Furthermore, PLS models also enable obtaining an indicator of the discriminant ability of each variable by computing the variable importance for the projection (VIP) parameter. This is a weighted sum of squares of the PLS loadings that considers the proportion of Y-variance that is described by each component. Those variables showing VIP values larger than 1 can be regarded as the most discriminant ones, whereas values below 0.5 indicate little influence in the model.Partial least square discriminant analysis (PLS-DA) is a pattern recognition tool that relies on identifying an adequate number of latent variables/components with the aim of discriminating between previously established groups . This teSoft independent modeling of class analogy (SIMCA) calculates significant PCs to classify samples based on their distance from the model representing each category. For this purpose, a training set is used to determine the number of PCs needed to describe the structure and boundaries of each class. Accordingly, objects are included within a certain class if they fall into the n-dimensional class-box limited by these boundaries. As each category is modeled independently of the rest, it is common to find overlapping between the spaces of each class. Therefore, three situations are possible: (1) the object falls within the boundaries of only one class, so it is unequivocally classified into that class; (2) the object is not located in any of the class boxes, so it is considered as an outlier; (3) the object falls in the overlapped region, so it is assigned as belonging to the overlapping classes (Massart). The classification results can be assessed by Coomans’ plots, a graphical tool for visualizing pairwise groupings, in which the axes depict the normalized orthogonal distance of the objects with respect to each individual model.K-nearest neighbors (kNN) is a simple method that does not require any distribution assumption and can be used when the number of samples is small. This algorithm is based on calculating the distances  from each object to the rest of the samples within a training set to select the k nearest neighbors. This kNN algorithm enables classifying new objects, considering that an increased k value reduces the impact of errors whereas its decrease worsens classification.The support vector machine (SVM) is a non-parametric machine learning tool that can be applied for both classification and regression purposes . This teDecision trees are powerful machine learning algorithms based on the use of a tree-like model of decisions and their possible consequences, which can be applied for both classification and regression tasks . Some ofIn recent years, modern variations of these classical approaches based on decision trees have been developed, RF being the most widely employed. RF is a non-parametric and non-linear tool that relies on a learning strategy known as ensemble learning, which is based on generating decision trees by combining individual trees that are determined by the values of a random vector sampled independently and with the same distributions for all the trees in the forest . These tAn artificial neural network (ANN) is a nonlinear pattern recognition technique based on imitation of the functioning of biological nervous systems, which is capable of predicting categorical and quantitative variables . In geneMultivariate calibration techniques, based on statistical regression and prediction, are aimed at determining relationships between response and independent variables . To this2), an estimate of the proportion of the global variation in the data that is explained by the model, is used as an indicator of the goodness of fit.Multiple linear regression (MLR) is commonly employed for calibration and regression in chemistry. The association between the response and the input variables is measured by standardized regression coefficients that are obtained by the method of least squares. The application of MLR requires the following conditions: dependent and independent variables must be linearly inter-related, the observations must be independent, normality and homoscedasticity of the residuals, absence of influential points , and no multicollinearity. Multicollinearity occurs when the explanatory variables are highly intercorrelated, which may consequently provoke imprecision or instability during the estimation of the model parameters, thereby affecting the accuracy of the model prediction. This can be evaluated by computing the correlation between pairs of independent variables or by calculating the variance inflation factor (VIF). The VIF parameter is indicative of the variance increase of an estimated regression coefficient with respect to the ideal situation where the explanatory variables are strictly independent. Therefore, a high VIF value denotes the presence of multicollinearity, being usually employed a threshold equal to 5 or 10, depending on the domain. A simpler way to minimize the VIF parameter is to discard highly intercorrelated variables or, eventually, to standardize the data. To confirm the statistical validity of the model, the coefficient of determination , based on classical PCA, applies linear regression modeling to predict the outcome on the basis of the covariates, for which the PCs of the explanatory variables are employed as regressors. Accordingly, PCR transforms a set of correlated variables into a set of uncorrelated PCs. Therefore, one major application of PCR is to solve multicollinearity issues. PCR overcomes the collinearity problem by excluding low-variance PCs in the regression step.2) and the residual predictive deviation (RPD).This is a widely used multivariate statistical technique whose objective is to find latent variables by projecting the X and Y variables in a new space where their covariance is maximized. A PLS model will try to find the multidimensional direction in the X space able to explain the maximum variance direction in the Y matrix. PLS regression is of particular utility in avoiding overfitting when the number of explanatory variables is large and they are intercorrelated. This is because during PLS modeling most of the variance is explained by the first latent variables, whilst the remaining variance mostly describes random noise or linear relationships between dependent and independent variables. The optimal number of components is usually obtained using cross-validation tools by calculating a statistic for lack of prediction accuracy called prediction residual sum of squares (PRESS). Thus, the optimum number of components will be the one that produces the lowest PRESS value. Furthermore, their predictive ability can also be evaluated by calculating the regression correlation coefficient  is a supervised method that is commonly employed to find the relationship between a set of predictor variables (X) and one or more responses (Y). Basically, OPLS is intended to extract the maximum information that reflects the variation in the original dataset, while assuming the existence of a small subset of hidden variables able to predict the response variables. These subsets are formally known as latent variables. The OPLS method uses orthogonal signal correction to maximize the explained covariance between X and Y on the first latent variable, while the remaining components capture variance in X orthogonal to Y.To contextualize the above-provided overview on the application of chemometrics in food authenticity and traceability research, in this section we review some recent literature considering olive oil as an example. Using an LC-MS platform, Becerra-Herrera et al. characterized the phenolic profile of extra-virgin olive oil (EVOO) samples and then applied various chemometric approaches to discover chemical descriptors to differentiate between different PDOs . An explMulti-elemental analysis, in combination with advanced chemometric techniques, has also demonstrated great utility in evaluating the geographical origin of Spanish EVOO samples . PrelimiAs a complement to conventional chromatographic profiling approaches, metabolomics stands out as a very powerful tool to comprehensively characterize the phytochemical profile of olive oil. In this vein, Senizza et al. recently applied untargeted LC-MS-based metabolomics to 408 Italian EVOO samples, corresponding to different varieties, origins, and blends . MultivaMultiple factors  may influence the chemical composition of foods and therefore have a considerable impact on their organoleptic, nutritional, and bioactive properties. For this reason, reliable, cost-effective, and powerful analytical methods are needed to ensure the authenticity and traceability of food products. However, the importance of properly addressing data processing and analysis steps is often underestimated in this field. In this respect, the use of advanced chemometric tools is mandatory in building multivariate models for classification, discrimination, and prediction, and for identifying candidate authenticity and traceability markers. The choice of the most appropriate statistical tool to apply depends on several factors related to the nature of the dataset, including the definition of the class criteria, the homogeneous distribution of the sample, the number of input variables, and the number of samples. However, it is common practice to apply various classification techniques and evaluate their fitness for the problem under study . This is


Detecting high-speed and maneuvering targets is challenging in early warning radar applications. Modern early warning radar has many functions such as detection, tracking, imaging, and recognition which need a high signal-to-noise ratio (SNR). Thus, long-time coherent integration is a necessary method to realize high SNR requirements. However, high-speed and maneuverable motion cause range and Doppler migration, which brings about serious coherent integration loss. Traditional integration methods usually have the drawbacks of model mismatching and high computational complexity. This paper establishes a novel long coherent processing interval (CPI) integration algorithm that detects maneuvering and weak targets which have a low reflection cross-section (RCS) and low echo SNR. The range and Doppler migration problems are solved via a layer integration by blending the association in a tracking-before-detection (TBD) technique. Compact SNR gain is achieved with a target information transmission mechanism and an updated constant false alarm ratio (CFAR) threshold. The algorithm is applicable in multiple target scenarios by considering different velocity ambiguities and maneuvers. A simulation and real-measured experiments confirm the effectiveness of the algorithm. With the development of aerospace technology, the detection of space targets has attracted much attention in recent years. Small space targets, including missile shrapnel and precision-guided weapon seekers, pose a considerable threat to defense security. If these targets are detected, it will significantly reduce threats to our safety. Thus, detecting small space targets greatly challenges our early warning radar. Space targets are usually characterized by a low reflection cross-section (RCS), which results in a low SNR. Therefore, coherent or incoherent integration in a long CPI is an effective way to obtain a high SNR gain. However, space targets usually have high-speed and maneuverable motion, leading to range and Doppler migration and causing severe performance loss of integration gain ,2,3. EstIn recent years, many methods have been proposed to realize coherent or incoherent integration of high-speed and maneuverable targets. Generally, they can be divided into three categories: (1) Incoherent integration method. A Hough transform (HT) ,5,6 is aExcept for signal domain processing, recently, the tracking-before-detection (TBD) methods ,34,35,36Based on the weak target detection consideration, there are two critical problems: model mismatching and high computational complexity. The problem of model mismatch arises because the target cannot keep the same motion model in a long CPI, and it needs a higher-order model to fit the motion model. Given these problems, we propose a robust and efficient layer integration algorithm to detect weak and maneuvering radar targets with a long CPI for narrowband radar. This paper uses the piecewise way to simplify the complex motion over a long time. First, the echoes over a long time are divided into several echo segments over a short time. The complex motion over a long time can be regarded as combining several different uniform motions in a short time. Then, the coherent integration for every signal segment is carried out, and a low detection threshold is used to obtain the rough detection results in every signal segment. Because of every segment’s short coherent integration time, many false alarms are in the detection results. A target association and signal integration between segments using the H-PMHT are proposed to increase SNR gain and exclude false alarms. The high-order motion parameter is estimated based on the velocity variation between target association results. Because the target can be associated and the target’s signal can be integrated between segments, and as the false alarms are hardly integrated, the false alarms can be excluded. The target can be detected with the segment fusion layer by layer. In addition, to avoid the target glint problem, the target information transmission policy is also designed to prevent the loss of target information. Compared with traditional methods, the proposed method mainly has three advantages:(1) It uses piecewise integration and TBD between slow-time segments to increase model adaption and decrease computational complexity;(2) The layer integration detection mode, updated CFAR threshold, and target-alarm transmission association mechanism are designed so that the glint targets can be detected effectively;(3) It uses coherent integration processing and compensates for the motion parameters which are estimated by associating between segments, helping to detect the low SNR targets effectively.The rest of paper is organized as follows: In (1). Preprocessing: The pulse compression and segment division are based on radar parameters in slow time. To detect all targets, we must select a certain number of pulses to obtain enough of an SNR and ensure that the target cannot have Doppler migration in every segment. The specific method of segment determination is discussed in the following sections.(2). Noise power estimation and low-threshold detection: Range migration is corrected using the keystone transform in every slow-time segment. The noise power is estimated, and the CFAR threshold is set to detect targets based on noise power. To make sure that all targets can be detected, the threshold should be low, which means that many false alarms may be involved; thus, the increased threshold with layers is necessary to exclude false alarms and preserve the target.(3). Target association and interaction: Combined with the TBD method, targets can be associated between segments. The target usually has the case of glint RCS, which means that the targets cannot be detected in a specific segment, and the target information cannot be transmitted into the following layer. The problem can be solved by designing a target-alarm information transmission mechanism to preserve targets and alarm information in every layer so that the information on the glint target would not be discarded as the layers increase.(4). Compensation and integration: Compensate for the range and Doppler phase of the associated targets using the estimated parameters and coherently integrate them. Then, the integrated segments are transmitted to the next layer and processed using the same steps.(5). CFAR threshold updating: With the increasing layers, the targets are integrated, and the alarms are not. Thus, the CFAR threshold needs to be increased based on the integration gain.The algorithm was summarized above, and the specific algorithm is described in the next section.In Suppose that radar transmits an LFM signal:The echo in the range frequency-slow time domain given by :(5)sr,c(From Equation (5), we can see that the phase is nonlinear due to maneuverable motion. We use the piecewise concept to adapt to high-order complex motion models, which use several uniform motions in continuous slow time to approximate high-order motions. This way, we divide the long CPI into several segments, thus the phase can be approximately regarded as linear and integrated using the keystone transform. Moreover, the assumption of the piecewise segmental method is reasonable since narrowband radar usually has a low pulse repetition frequency (PRF) to reduce range ambiguity. Combined with dividing several segments of slow time, every segment’s velocity resolution is low. Thus, it can be regarded as a constant velocity with a low-velocity resolution. Moreover, the acceleration error can be compensated for by using the estimation parameter of the segment association. We use the long CPI to integrate signals to get a high SNR gain. However, it will bring substantial computational costs if we process the signal during the slow time. For example, suppose the keystone transform is used to correct the range migration. In that case, the computational complexity is proportional to the square of the slow-time number using the discrete Fourier transform (DFT) method. Therefore, if we use the long CPI to obtain coherent integration results, the computational burden usually is unacceptable. On the contrary, the segment division decreases the complexity affected by the number of pulses, and parallel computing can be used in every segment to increase calculation efficiency. Then, we derive the signal model based on the segment division.Suppose that there are Further, in order to ensure the maximum energy integration, the pulse number of one segment can be determined by:Suppose that the radar maximum non-ambiguous velocity is Thus, the signal model in the In this way, we use the segment division method to realize model matching and reduce the computational burden problem. Thus, the signal can be decoupled and integrated in every segment using the keystone transformation as subsection B.After segmentation division and piecewise approximation using the method in subsection A, the nonlinear phase can be regarded as a linear phase coupled with the range frequency in a short time period. The keystone transformation modifies the slow time axis to decouple the range frequency and slow time from the coupling phase; this specific method references . Note thThe ambiguous channel of the keystone signal model unfolding Equation (10) is:The signal after the ambiguity compensation is:By applying the keystone transformation, and substituting The keystone transformation can be processed by the chirp Z-transform-inverse Fourier transform (CZT-IFFT) or scaled Fourier transform-inverse Fourier transform (SFT-IFFT) method to improve operational efficiency. Therefore, the signal can be integrated by moving the target detection (MTD) after the keystone transformation.After integrating the first layer, the CFAR detection threshold should be determined based on noise power. The high speed and maneuvering target detection are usually applied in detecting space targets such as missiles and aircraft. The space target detection usually has these characteristics: (1) the clutter has little effect on echo; (2) the echo is mainly affected by the thermal noise of the transmitter and receiver; (3) the distribution of noise with different ranges and Doppler cells is usually homogeneous. In this case, the influence of clutter on the detection is small, and only Gaussian white noise is considered. Assuming that all the measurement cells share the same noise distribution, based on the CFAR detection theory, the adaptive threshold corresponding with the constant false alarm rate and statistical noise power should be applied to the detector. As for this condition, the white Gaussian noise obeys duced as :(19)Pfa=In this way, with the layer increasing, the targets can exceed the increased threshold and false alarms cannot since the false alarms have a low probability of being associated with the layer detector passing by; therefore, the false alarms will be excluded and the target will be integrated and detected in the last layer.After segment division, integration, and target detection in every segment, the signals need to be integrated between segments. The targets have a high-speed and maneuverable motion, resulting in the range and velocity change in the adjacent segment. Based on the detection and integration result, the problem becomes associating targets between segments, compensating for the phase caused by the maneuverable motion, and integrating them. Combined with the TBD concept, we use the H-PMHT method to associate targets. The H-PMHT method quantizes the amplitude of measurement cells as a synthetic histogram with several shots. The shot is treated as a measurement, and the sum of shots is treated as the total number of acquiring measurements. The shot distribution of a segment obeys multinomial distribution, where the probability of each cell can be considered as a superposition of targets and noise. Moreover, successive scans are associated with the state transformation function. Thus, the joint probability distribution can be obtained, and parameters can be estimated using the expectation maximization (EM) method. Moreover, ,38 derivSuppose that targets have constant acceleration between segments; then, the state transformation function in the Based on the H-PMHT, the distribution of the mean cell value is given by :(24)PPk, the signal can be coherently integrated.The signal can be integrated using the above method in long coherent periods; however, there is an additional question to consider regarding glint target integration and detection. The glint target usually has a low RCS in a specific segment, and the echo cannot be integrated effectively. Based on the layer detection framework, the false alarms which cannot exceed the increased threshold will be discarded and result in missing the detection of the glint target, which is not integrated and treated as a false alarm. Considering this question, if we preserve the false alarm information and design the mechanism of information transmission and interaction, the glint targets could be detected. From the target detection analysis, According to the above analysis, false alarms are unlikely to be associated between segments. Even though they can be successfully associated with a specific layer, they are not likely to pass by the final layer and exceed the threshold. Therefore, only the cases of the targets’ association and detection should be considered to avoid missing detection. The association and detection of targets can be divided into four issues as follows:(1) Targets are well associated and exceed the threshold . It is an ideal condition, and the target can be detected in the last layer;(2) Targets are well associated and do not exceed the threshold (weak targets). The target is unstable and the integration gain is less than the increased threshold, thus the target’s information should be preserved and transmitted into the following layers;(3) Targets are not associated and exceed the threshold (strong glint targets). Although the target is glint, the power is strong enough in a specific segment, and the target also can be detected in the following layers;(4) Targets are not associated and do not exceed the threshold (glint targets). If the target is glint and weak, the target will not be associated and exceeds the threshold. Thus, it cannot be detected in the following layer, and the information should be preserved.As for these four types of targets, the target and false alarm pursuit mechanism is designed as shown in As for computational complexity, the LVD method is an effective way to solve the maneuvering motion integration problem. It needs a correlation process and keystone transformation in every range cell. Suppose that Nv2logNv . The pro® CoreTM i7-7700 CPU and Matlab 2017 to compare the proposed method with the LVD method for calculation efficiency. The LVD method uses 31.779885 s on average to calculate one range cell. However, the total calculation time of the proposed method is 5.344031 s. The results show that the proposed method is more efficient than the correlation method, such as LVD.Therefore, our method is more efficient compared with the LVD distribution method. Compared with parameter searching methods such as the Radon Fourier transform , our appA. The threshold of the first layer determination. The first layer threshold should be determined by the lowest signal power in a single pulse. Assume that the lowest SNR of a target after pulse compression to be detected is B. The number of pulses in the first layer segment determination. The number of pulses in the first layer is determined by two aspects: Doppler migration and the SNR requirement in the first layer detector. The Doppler migration limitation makes sure that the target echo satisfies the piecewise assumption. The SNR requirement makes sure that the target which has the lowest power requirement can be detected. Based on these two criterions, the number of pulses can be determined as follows:(1) Doppler migration limitation. Based on the uniform motion assumption, the target cannot cross the Doppler cell in the segment. The Doppler migration is caused by an equivalent acceleration, and the maximum equivalent acceleration is defined as Simplify it, and the limitation can be derived as:(2) The SNR requirement in the first layer detection. The SNR can be increased by Therefore, the The number of pulses The experiment comprises three parts to prove that our method is effective for multiple targets, especially glint target integration and detection. First, a scenario of multiple targets with different range velocity accelerations and ambiguity numbers is set to prove that our method is valid. Second, a glint target scenario is set to verify that our approach has better performance for glint target integration compared with the traditional method. An integration comparison experiment uses our technique and traditional techniques to analyze integration and detection performance. Third, Monte Carlo experiments are designed to quantitatively compare the detection probability and integration SNR.In order to make a reference to integration performance, first we derive the upper limit of the pulse compression and coherent integration signal. Suppose that the length of transmitting sampling is We assume that the noise power spectral density is If we coherently integrate the Whatever integration method we use, the integration SNR output cannot exceed Equation (34); thus, we can use the SNR upper limit to evaluate the integration method performance.2, 60 m/s2 and 20 m/s2, respectively. Based on the radar parameters shown in To prove that our algorithm is effective in the aspects of multi-targets, multi-ambiguity channels, glint targets, and low SNR detection, the scenario that includes three targets is set to evaluate the multi-target detection performance. The ranges of target1, target2, and target3 are in the 2000th, 1000th, and 300th cells, and the velocities are 600 m/s, 1600 m/s, and 2300 m/s, respectively. The accelerates of the targets are 60 m/sUsing the proposed method of integration and detection to obtain the visualized integration and detection result in every layer, a three layer detector is set. In other words, the original signal can be divided into four segments. 2. A random simulation shows the target glint in the 251st–500th slow-time period. The proposed method and LVD distribution method integration results are shown in The target-alarm information transmission mechanism is designed as above. In this subsection, we design a comparison experiment with the LVD distribution method to prove that the proposed method has good integration performance with the glint target. Suppose that the target has a weak RCS in a specific segment, the glint case obeys binomial distribution with a probability of 0.25, and the radar parameters are set as shown in From 2, and 100 Monte Carlo trails are implemented. The results of output SNRs with different input SNRs are shown in In this subsection, we analyze a quantitative experiment’s integration and detection performance because the proposed method mainly solves the problem of SNR integration loss and the high complexity of the correlation method. In addition, the proposed method uses the TBD concept to realize association and integration. Therefore, it is necessary to compare the proposed method with traditional correlation and TBD detection methods. This subsection uses the traditional correlation method of LVD and the traditional TBD method of DP as comparative methods. The radar parameters are set as shown in The real-measured data of the space target are used to verify that the proposed method effectively completes signal integration for weak targets. The radar parameters are listed in The recorded echoes are shown in For this target, we use the proposed detection method of segment division to realize coherent integration. The detection false alarm rate in the first layer is set as From the results, we can see that the energy of the target is integrated layer by layer, and the false alarm cannot be integrated and excluded. In order to verify that the target is integrated gradually in every layer, the statistical SNR is calculated in Finally, the estimation results of range, velocity, and acceleration are also given in Using the piecewise approximation mindset and segment integration method, the proposed method has advantages in increasing SNR gain and computational efficiency for small and weak targets. As seen in the simulated and real-measured experiments, the proposed method has more than 1 dB of SNR integration gain compared with traditional methods such as LVD. In addition, the computational speed increases almost 6 times more than in LVD. However, the proposed method relies on the robust detection results in the first layer, and a more complex motion will lead to the performance degradation of the proposed method. In addition, the target association is not considered good; thus, we will focus on robust initial detection and target association in future works.


The popularity of action recognition (AR) approaches and the need for improvement of their effectiveness require the generation of artificial samples addressing the nonlinearity of the time-space, scarcity of data points, or their variability. Therefore, in this paper, a novel approach to time series augmentation is proposed. The method improves the suboptimal warped time series generator algorithm (SPAWNER), introducing constraints based on identified AR-related problems with generated data points. Specifically, the proposed ARSPAWNER removes potential new time series that do not offer additional knowledge to the examples of a class or are created far from the occupied area. The constraints are based on statistics of time series of AR classes and their representative examples inferred with dynamic time warping barycentric averaging technique (DBA). The extensive experiments performed on eight AR datasets using three popular time series classifiers reveal the superiority of the introduced method over related approaches. The automatic interpretation of actions performed by the human body is both challenging and desired. Well-designed action recognition (AR) algorithms could be put into practice in the detection of aggressive behavior, video surveillance, interaction with humans and robots, or advanced control over virtual reality avatars. In recent years, many methods for human action recognition have been developed . HoweverSuboPtimAl Warped time series geNEratoR) algorithm  [33]bc a [33]bc aux frame :(7)u=bcuations  , UTD MulAccording to the original paper introducing the MSRA dataset, there are seven subjects performing actions. However, the larger version, consisting of 10 subjects, is publicly available and can be downloaded from the authors’ website . This veIn this study, two types of validation were performed. For MSRA, SYSU, UTD-MHAD, and KARD, 50-50 validation tests were used, in which the training and testing sets were split in half based on the subjects performing actions. The protocol for UTD-MHAD and FLORENCE is 10-fold cross-validation. For each dataset, the validation protocols proposed by the authors were used. In the case of KARD, 50-50 validation was used instead of the 10-fold cross-validation due to excessive computation time. All performed tests were subject independent, which means that in each test, the training set contains actions performed by subjects not present in the testing set. Such tests simulate the behavior of a recognition application in practice, where people performing actions do not participate in the creation of the training data.Actions from all datasets were recorded using a Microsoft Kinect sensor. In this work, only skeletal joints were used to characterize human actions. The skeletons for actions present in all datasets except FLORENCE and KARD consist of 20 joints, while the skeletons used to capture actions in the FLORENCE and KARD datasets consist of 15 joints see .The same subsets of joints and bones cannot be used for 20-joint datasets and 15-joint datasets. Furthermore, FLORENCE and KARD do not have identical joint sets despite having the same number of joints. Therefore, for the experiments, three groups of joint subsets and bone subsets were selected separately for the Distance Descriptor and the Bone Pair Descriptor. They are listed in The subsets of joints and bones were selected experimentally as a part of the previous work on the subject of human action recognition . DiffereTo show exemplary time series, in Among classification methods, the classical Dynamic Time Warping (DTW) and two recent methods were used: LogDet Divergence-based Metric Learning with Triplet constraints (LDMLT)  and TimeIn The feature vectors used in the experiments are concatenations of the DD and BPD features without ARSPAWNER generates new data based on a pair of input time series, and therefore, the number of generated examples by other methods is aligned with the number of returned samples. This ensures a fair comparison of algorithms.In this study, four augmentation methods are compared using the classification accuracy obtained for each dataset and classifier. Due to the randomness of the augmentation algorithms and TCK classifier, each accuracy is calculated for 10 runs and averaged. Then, the following values are calculated: average accuracy, average rank, geometric average rank, and a number determining how many times a method achieved the best accuracy (count best). These values are considered as the comparative criteria. To compare the methods, ranks from 1 to 5 are used, where a lower rank means a method has greater accuracy. The compared approaches are: SPAWNER, ARSPAWNER, Window Slicing , and WinThe experimental results reveal that the proposed ARSPAWNER is the most effective augmentation method and outperforms the non-augmentation case according to all comparative criteria. The method shows the greatest advantage over the others when used with DTW. However, in the case of the other two classifiers, ARSPAWNER and SPAWNER have close average effectiveness. They both significantly outperform the other methods, as well as the results of the non-augmentation case.The LDMLT classifier yielded better results than the other two methods for all datasets, and its suitability for the action recognition problems was proven in the previous study . The stuOverall, it can be seen that the introduced ARSPAWNER outperforms the remaining data augmentation methods on action recognition datasets, since it considers the specificity of such data collections, with many similar and overlapping action classes.To show the areas in which new samples are generated by the augmentation methods from the MSRA I dataset, Kruskal’s nonmetric MDS  is emploThe recognition problems can also be highlighted by showing testing examples together with training data and augmented data. Therefore, in https://www.mathworks.com (accessed on 13 March 2022)) [Since there are approaches based on GAN architecture to augment time series in different domains, the performance of ARSPAWNER is compared with those of Conditional GAN on three MSRA datasets. Due to the lack of Matlab implementations of GAN-based approaches designed to augment action recognition time series in the literature, the available Matlab CGAN example designed to generate synthetic time series was adapted ) . The empThe network was adapted to perform the augmentation of action recognition MSRA datasets that contain time series of different lengths, belonging to 8 classes and composed of 69 features. Specifically, due to the ability to generate two class time series, it was run eight times with input samples divided into two classes . Additionally, since it is not designed to process multivariate time series and to avoid time-consuming computations, the PCA technique was applied to reduce the feature dimensionality from 69 to 5 and CGAN was run for each new feature independently with the concatenation of data to form synthesized five-dimensional vectors. Furthermore, since time series in MSRA datasets are of different lengths, they were interpolated to the same length, imposed by the network architecture. The finally obtained augmented examples were added to the original samples and employed by the nearest neighbor classifier with the DTW distance. The parameters of the network were set as recommended by the network designers, with the reduced number of iterations since the model converged earlier, allowing for the reduction in the training time. Important parameters of CGAN: number of iterations = 1000, learning rate = 0.0002, the Adam optimizer, batch size = 256, latent dimension = 100, and embedding dimension = 100. In experiments with CGAN, a PC with Nvidia Quadro RTX 4000 MAX-Q GPU, i9-10885H CPU, and 64 GB RAM was used. To ensure a fair comparison, ARSPAWNER was also run on the same five-dimensional feature vectors resulting from PCA.The accuracy of the classifier for three augmented MSRA datasets after PCA feature reduction is presented in The next experiment concerns the impact of the ARSPAWNER parameters The To determine the capability of the introduced ARSPAWNER to augment small datasets, composed of a small number of training examples per class, it was tested using the MSRA I-III datasets varying the number of input time series. This experiment also indicates problems with small benchmark datasets in which class boundaries cannot be easily established due to an insufficient amount of available data and a relatively large number of classes . In the experiment, 3 to 15 input examples per class were randomly selected and used by ARSPAWNER to generate synthetic data. Then, the average accuracy of the nearest neighbor classifier with the DTW distance based on ten draws is reported in In this paper, a novel method for the augmentation of datasets with time series representing human actions has been presented. The introduced ARSPAWNER improves the original SPAWNER by introducing action recognition-related constraints addressing problems present in this domain. The approach identifies data samples, i.e., time series, that are far enough from input samples and still do not cross the boundaries of other classes. Additionally, data samples that are in the proximity of the input time series, and consequently do not introduce new knowledge, are rejected. The constraints are based on distances between a new sample and an input sample and a sample generated as a representative time series characterizing a class. It has been shown that the introduced constraints provide to the augmentation leading to the improved performance of classifiers. The method has been experimentally compared with related approaches using three classifiers on eight action recognition datasets.Future work will involve an application of optimization techniques to select a suitable set of generated time series based on data clustering quality indices. Such an approach can be seen as an extension of the study presented in this paper since constraints that remove augmented samples may be replaced with a step in which their suitability is assessed based on the quality criteria describing clusters of generated samples. Another interesting research direction is to employ augmentation methods like ARSPAWNER to augment small datasets and train time-consuming deep learning classifiers.www.marosz.kia.prz.edu.pl/ARSPAWNER.html (accessed on 13 March 2022). The scripts for Distance Descriptor and Bone Pair Descriptor are also publicly available and can be downloaded [To facilitate the reproducibility of the approach, the Matlab implementation of the introduced ARSPAWNER is available at wnloaded .