N = 66,110) to obtain evidence and explore the extent to which an imitation strategy affects firm growth. Moreover, by further examining the moderating effects of industry conditions, country-specific factors, and performance time horizons, this research also aims to address a complementary research question: in which context is imitation strategy more beneficial for the firm growth? We found that an imitation strategy is more effective in promoting firm growth in low-tech industries than in high-tech industries and in non-OECD countries than in OECD countries. It fosters the short-term performance rather than the long-term performance of a firm. Our research findings are meaningful for enterprises to choose an appropriate imitation strategy according to their unique attributes, enabling sustainable growth in a dynamic environment.The increasing number of successful latecomer enterprises has led to a growing research interest in the area, but there is a lack of consensus in academic circles on the relationship between imitation strategy and firm growth. While some enterprises achieved sustainable growth based on an imitation strategy, others withdrew from the market soon after their initial market entry. In this context, this meta-analysis synthesizes empirical findings including 23 independent samples ( Recently, a large number of latecomer firms, such as Lyft  or Hellobike and Mobike , have been able to maintain their market position even in the face of fierce market competition in rather dynamic environments. The increasing number of successful latecomer firms has attracted great attention in the academic and managerial community. However, scholarly knowledge has been limited with respect to the extent to which an imitation strategy can promote the sustainability of firm growth in dynamic environments. On the one hand, the imitation strategy is likely to boost firm growth . For exaThe mixed results of these studies might be due to the fact that diverse attributes have been investigated in the different studies. However, these attributes seem to have a rather different impact and might cause high variability and uncertainty in cases when an imitation strategy is implemented . In thisOrganizational learning theory reveals the dynamic and phased characteristics of the firm learning process . As a foTo fill the above research gaps, the objective of this research is to contribute several new insights to the literature. First, the authors of this paper aim to identify more general patterns in the relationship between imitation strategy and firm growth by providing a quantitative empirical aggregation of prior empirical studies regarding imitation strategy and firm growth. A single empirical study might face sampling, measurement, stochastic, and external validity problems. However, a comprehensive and systematic analysis of the imitation strategy–firm growth relationship, to our best knowledge, has not been undertaken. Meta-analysis has a rigorous and systematic calculation procedure to aggerate prior empirical studies, so it can overcome limitations in a single empirical study . The maiThe remainder of this paper is organized as follows: In section “Theoretical Framework and Hypothesis Development”, the theoretical framework derived from the literature is constructed, and different hypotheses are developed. In section “Method and Data”, the different samples, data, and research methods are illustrated, followed by the description of the findings in section “Findings”. In section “Discussion”, the paper discusses the key findings, limitations, and implications for future research. Finally, the conclusions are presented in section “Conclusion”.Within their respective traditions, resource-based theories of the firm, neo-institutional approaches, and theories on organizational learning have extensively been used in the past to analyze the relationship between the imitation strategy and firm growth. From the perspective of the resource-based theory of the firm, firm-internal resources and assets are the basis for an enterprise to survive. If an enterprise adopts appropriate development strategies to make full use of their valuable and rare resources and assets, it will be able to improve its long-term performance . For exaFrom the perspective of organizational learning, an imitation strategy is a type of organizational learning used by firms based on observation and learning leading to similar actions . With anHowever, empirical studies have shown that the results of some of these predictions are rather mixed. Some studies have indicated that an innovative strategy can lead to more technological strengths and size-related flexibility leading to a higher firm performance . In addiAlthough research has also shown that an imitation strategy may negatively influence the innovative performance of a firm, a large number of latecomer enterprises catch up with first movers in the market by implementing an imitation strategy as demonstrated by enterprises like Lyft or Hellobike. In dynamic environments, firms facing high uncertainty may use an imitation strategy to gain from advertising spillovers from the first movers of the market, enjoy the new markets pioneered by these companies, and reduce their own market development costs and marketing expenses. At the same time, an imitation strategy can utilize the knowledge spillovers by the first mover, reduce the uncertainty surrounding the technology choice, and minimize the “trial and error” cost of business management through low-cost imitation and learning. Therefore, the imitation strategy will effectively allow to reduce the business risks of the enterprise, and consequently, achieve greater efficiency with respect to technological innovation and performance improvement.From the theoretical discussion, we derived the following hypotheses:Hypothesis 1. An imitation strategy has a positive impact on firm growth.Organizational learning theory emphasizes the dynamic and phased nature of the learning process of a firm . EnterprWithin the external environment of enterprises, industry conditions exercise an important influence on the relationship between imitation strategy and firm growth. The industry conditions of enterprises are heterogeneous, and the technological opportunities and interaction patterns in different industries are also different. While high-tech sectors emphasize research and development (R&D), low-tech sectors tend to rely on technology acquisition. Therefore, enterprises need to choose effective development strategies to adapt to specific industry conditions . CompareHypothesis 2. As the relationship between an imitation strategy and firm growth is moderated by industry conditions, the relationship will be stronger in low-tech industries than in high-tech industries.In the process of implementing an imitation strategy, country-specific effects play an important role in promoting firm growth . For exaEven if From the aspect of local economic development, the living standards of the general public are higher in OECD member states as the local economy in these countries is well developed. When the basic living conditions of people in countries are covered, companies also provide high-tech products of high-quality features in these markets. High-end consumer demand is rather difficult to satisfy for companies with a simple imitation strategy. Moreover, companies in OECD member countries are more likely to have sufficient economic strength to take on possible risks surrounding R&D investment. As a result, they might pay more attention to their own innovation ability rather than blindly imitate other companies. In contrast, in non-OECD countries where the economies are relatively underdeveloped, the basic needs of people are often not fully satisfied. A company will be more likely to use an imitation strategy in order to copy firms that already provide products that fill the local market demand at a low cost and sell these products at a low price. In this way, the imitation strategy can help non-OECD countries obtain feedback from the consumers in the market and promote their growth in the local market. From the aspect of sectoral belongings, the industrial structure and the pillar industries are often different in OECD member countries and non-OECD countries, and non-OECD countries tend to have more low-tech enterprises than OECD member countries . ImitatiHypothesis 3. As the relationship between an imitation strategy and firm growth is moderated by country-specific factors, the relationship will be stronger for non-OECD countries than for OECD member countries.“History friendly modeling,” introduced by One of the salient advantages of enterprises adopting an imitation strategy is that they are able to enter markets and penetrate them rapidly . For exaHypothesis 4. As the relationship between an imitation strategy and firm growth is moderated by the time under consideration, the relationship will be stronger for the short term compared to the long term.The scientific measurement rules of meta-analysis enable scholars to explore in more detail the relationships between different variables, which is beneficial if a more complex conceptual model is tested. Due to this benefit, scholars have widely used the meta-analysis method in business management research . CombiniAdditionally, the meta-analysis method can also be used to test whether the results of existing research in a certain area are consistent. If the research results are inconsistent, the meta-analysis method can further test the moderating effects of the relationship between the independent variable and the dependent variables through different scientific calculation procedures to generate a reasonable explanation for the apparent inconsistencies of the research results . TherefoThe analysis was undertaken in the following way. First, we collected the existing quantitative literature with a focus on imitation strategy and firm growth from different academic databases. Second, after importing the collected quantitative research data into the meta-analysis software, we tested the publication bias of the data set derived from the literature search to ensure the validity and reliability of the data. Third, we conducted the main effect test to explore the relationship between imitation strategy and firm growth. The strength of the overall relationship between the imitation strategy and firm growth is reflected in the overall weighted average correlation coefficient , and firm growth . Then, we manually retrieved information from high-quality journals in the area of business management including Management Science, Strategic Management Journal, and the Journal of Business Venturing. In addition, we also retrieved data by searching on Google Scholar for unpublished papers in this area. In this way, we could test for publication bias and the accuracy and effectiveness of the meta-analysis results. By using these three retrieval methods, the different articles for the final dataset were collected.t-test.To undertake the meta-analysis, we had to extract the relevant data from each collected article to further explore the relationship between the independent variable and the dependent variables. In the process of screening for these data, the study adopted the following criteria: first, the literature should focus on the theme of imitation strategy and firm growth; second, the literature should be quantitative by nature; third, the literature should also report statistical criteria such as sample size, the correlation coefficient between variables, or the value for the After using the above principles to screen the studies collected, we obtained 23 articles that met all requirements. The 23 articles provided 66,110 independent samples in total. The meta-analysis method requires at least 10 articles . TherefoThe collected quantitative research was standardized by using the following procedure. First, we recorded the basic information of each study, including the name of the author followed by the year of publication, the sample size of the variable names, and the country . Furthermore, we coded the industry condition of the investigated enterprises (high-tech or low-tech) and the length of time covered to measure the variable related to firm growth. Second, the overall correlation coefficient of each study was calculated and recorded. If a multidimensional scale for imitation strategy or firm growth was adopted in a study, the mean of the correlation coefficients would be calculated and then recorded as the overall correlation coefficient.To improve the accuracy of the meta-analysis results, the coding process was independently performed by the three co-authors. Comparing the respective coding results finished by the three co-authors, we found that 95.65% of the initial coding results were consistent. Conflicting coding results were also resolved by agreement after the detailed discussion and negotiation by the research team. The final coding results are presented in Firm growth manifests itself as a fundamental characteristic of the gradual expansion of scale, the maturity of the company, and its stable operation . To measImitation strategy refers to the extent to which an enterprise will grow based on observational learning and hands-on learning to replicate and develop products that are new to the organization but not necessarily new to the market . The scaThe research included three moderating variables, namely industry conditions, country-specific factors, and performance.In order to study the effects of industry conditions on the implementation of an imitation strategy, we utilized the distinction developed by This moderating variable refers to the country in which the analysis has been undertaken. The literature has shown that these country-specific differences are also likely to play an important role in promoting the growth of firms when they adopt an imitation strategy . Taking This moderating variable refers to the time-period over which the firm performance was measured. The literature has shown that an imitation strategy might have differential effects on achieving competitive superiority over the long term compared to the short term because an imitation strategy might be more challenging to maintain a long-term competitive advantage . ConsistAs meta-analysis enables a researcher to combine a variety of published and unpublished studies while allowing to conduct a comprehensive analysis of these studies. A publication bias test is required to ensure the accuracy and validity of the meta-analysis results.Publication bias refers to the phenomenon that in similar studies, papers with positive results  are more likely to be accepted and published in accredited journals than papers with negative results  . The colp-value is obtained based on several studies, but a few studies may be missed. If these missed studies are included in the meta-analysis, then the p-value of the main effect may no longer be statistically significant. Therefore, the meta-analysis approach can calculate how many missing studies are needed to the main effect size statistically insignificant. If only a few studies are needed to reverse the significance of the main effect, then we would suspect that the actual main effect size is statistically insignificant. Conversely, if it takes a lot of research to reverse the statistical significance of the main effect, there is no reason to suspect that the true effect is insignificant. Conversely, if the FSN is larger, it would be less likely for publication bias to exist, and the meta-analysis results would be more consistent. According to the criterion proposed by Suppose that a significant Q test was used to test for statistical heterogeneity, and then I2-heterogeneity was used to quantify the results. In this way, the heterogeneity of the research results was tested.The main effect test and moderating effect tests are shown in the correlation analysis. Through the main test, the strength of the overall relationship between imitation strategy and firm growth could be verified. Based on the suggestions of The heterogeneity of test results also determines whether further moderating effect tests are required. If the heterogeneity test results indicate that there is considerable heterogeneity among the correlation coefficients in the collected studies, then subsequent analysis of potential moderator variables is beneficial for explaining which factors cause this heterogeneity .k + 10 . Besides, we further checked the publication bias among the collected studies by applying a funnel diagram. The results are shown in The publication bias test is applied to characterize the effectiveness and accuracy of the results of the meta-analysis. The publication bias test is based on the FSN, which is 1476 for this meta-analysis, larger than 5The authors used meta-analysis software to test the main effect of the relationship between imitation strategy and firm growth. The test results are displayed in p = 0) with 0.232 as the upper limit of the 95% confidence interval and 0.112 as the lower limit. Therefore, we could conclude that the imitation strategy is positively correlated with firm growth. Thus, Hypothesis 1 was verified.A total number of 66,110 articles were used to investigate the relationship between imitation strategy and firm growth. Thus, the weighted Q-value was 661.729 (p = 0) revealing significant heterogeneity among the 23 collected research results in the different studies.The results for the homogeneity test are displayed in I-squared value of 96.675, which showed that 96.676% of the observed variation in the relationship between imitation strategy and firm growth are caused by the variety of correlation coefficients in the collected studies. The demarcation point concerning the I-squared value of different heterogeneity degrees was 75/50/25. If the I-squared value was larger than 75%, it indicated that the correlation coefficients in the studies were characterized by high heterogeneity. By further testing for the moderating effects within the relationship between the imitation strategy and firm growth, we found that the high heterogeneity of the studies also indicated that the random effect model should be selected for correlation analysis when applying meta-analysis.Additionally, we found an The moderating effect test was conducted in an attempt to explain why there were inconsistent results in the collected studies. More specifically, we analyzed the moderating effects to examine whether the industry conditions, the country-specifics, and the performance measure affect the strength of the relationship between imitation strategy and firm growth. The results of the moderating tests have been as follows:p < 0.05). The influence of an imitation strategy for firms in a low-tech industry was also significant with a weighted p < 0.01). The results reflected that the imitation strategy had a more statistically significant impact in a low-tech industry compared to a high-tech industry.The moderating effect test results for industry conditions are shown in In addition, the weighted To further explore how country-specific differences influenced the relationship between imitation strategy and firm growth, the authors tested the moderating effect of the country-specific conditions.p < 0.05). In non-OECD countries, the imitation strategy was also a significant predictor of firm growth, with a weighted p < 0.05). These results verified Hypothesis 3 stating that the relationship between an imitation strategy and firm growth is moderated by country-specific factors, with a stronger relationship in non-OECD countries compared to OECD countries.As shown in To further explore how the performance dimension influences the relationship between imitation strategy and firm growth, we tested the moderating effect of performance over time.p < 0.01). In the short term, the imitation strategy also had a significant impact on firm growth, with a weighted p < 0.01). These results verified Hypothesis 4, which argued that the relationship between an imitation strategy and firm growth is moderated by the time period over which performance is measured. This relationship is stronger for companies over the shorter term rather than in the longer term.As shown in In line with previous research, the paper demonstrated that an imitation strategy has a positive impact on firm growth (see Hypothesis 1). This conclusion is consistent with the research results by We were able to show that the relationship between an imitation strategy and firm growth is moderated by industry conditions. This relationship will be stronger in low-tech industries compared to high-tech industries (see Hypothesis 2). From the perspective of the contingency theory, this result echoes the view by To a certain extent, this conclusion can enlighten macro-level innovation policymakers. The commercial innovation encouragement policy for small and young enterprises in the low-tech industry needs to be designed and enforced to support these enterprises in technological R&D. These small and young firms are often unable to embark on innovation activities because of insufficient R&D resources. As a result, they sometimes have to adopt imitation strategies to deal with the temporary thorny business survival issues. However, innovation is the driving force for the long-term development of an enterprise, and R&D expenditure is the main engine that guarantees innovation capability improvement and firm growth . The EurThe study also showed that the relationship between an imitation strategy and firm growth is moderated by country-specific factors as the relationship will be stronger for non-OECD countries compared to OECD countries (see Hypothesis 3). This result further supports the view by However, the results for the moderating effects of the country-specific factors seem contrary to the conclusions of some recent studies. For example, the research by We showed that the relationship between an imitation strategy and firm growth is moderated by variance in the firm performance over time (see Hypothesis 4). This relationship has been stronger over the shorter term rather than over the longer term. These results partly support the view by The sustainable growth of an enterprise is closely related to achieving long term strategic goals. The realization of short-term strategic goals can lay the foundation for achieving long-term strategic goals in providing sufficient firm resources and more advanced technology, etc. But in order to achieve long-term strategic goals, managers have to decide whether the enterprise can move toward a higher level of R&D development. As a result, managers need to pay greater attention to these two types of strategic goals at the same time. It is worth noting that, according to our research results, although an imitation strategy is important for improvements of both the long-term and the short-term, the degree of achieving these goals is different. Compared with long-term performance, the improvement over the short-term seems to be more dependent on an imitation strategy. This result demonstrates that the enterprises need to constantly adjust their imitation strategy over time. Although in the early stages of development, an imitation strategy can generate a competitive advantage for companies due to faster market entry and cheaper prices. However, with the continuous growth of enterprises and the gradual growth of markets toward maturity, the importance of independent innovation capabilities of enterprises is becoming increasingly vital with enterprises hardly being able to rely entirely on an imitation strategy . As discThe research results of this article demonstrate that an imitation strategy can promote firm growth more strongly in non-OECD member countries under low-tech industry conditions and when the firm is striving to achieve just short-term strategic goals. Meanwhile, the effects of an imitation strategy on firm growth are slightly weaker in OECD member countries in high-tech industries and when it is aiming at attaining long-term strategic goals.Taking these unique attributes into account, implementing an appropriate imitation strategy are essential for enterprises to generate sustained competitive advantages and to achieve sustainable long term development . In the In order to display our results with respect to moderating effects of industry conditions and country-specific factors, a chart showing the influence of an imitation strategy on firm growth has been drawn see . It can As the literature has shown that there are different strategies to adapt to various external conditions , it willCombining the meta-analysis results with the performance dimension (long versus short term), The findings of this paper are also of great significance to policymakers. Although the results of this study show that an imitation strategy is more effective in promoting firm growth under the low-tech industry conditions and when aiming at achieving short-term strategic goals in non-OECD countries, policymakers also need to pay attention to several factors that led to this result. It is hard to promote firm growth through R&D activities under low-tech industry conditions or in non-OECD countries due to the probable lack of R&D resources and the inadequacy of infrastructure construction. However, the ability of independent innovation may be an essential factor in ensuring the long-term development of an enterprise. Therefore, policymakers need to provide enterprises in the low-tech industry conditions or in non-OECD countries preferential policies for technology R&D to promote long-term firm growth.Although much attention has been paid in the academic literature to study the relationship between imitation strategy and firm growth over the past years, the studies in this area have been generated rather inconsistent results and more research is needed to deal with these shortcomings. To overcome the sampling errors and sample size limitations of single studies in this area, this paper adopted a meta-analysis method to find realistic and statistically proven evidence for the relationship between an imitation strategy and firm growth over the long term. In addition, this paper further examined the moderating effects of industry conditions, country-specific factors, and (short versus long-term) performance dimension. It further explored whether the inconsistent results of existing research studies were caused by moderating variables. In this context, the paper derived a conceptual framework from the literature to explain the relationship between an imitation strategy and firm growth. The research results show that, in non-OECD countries, under the low-tech industry conditions and when aiming at achieving short-term strategic goals, an imitation strategy is more effective in promoting firm growth. The research results of this paper can provide further insights for managers to choose an appropriate imitation strategy based on their choice between a pure or creative imitation strategy, thereby gaining a sustainable competitive advantage over the long term. Besides, the findings of this paper are also of great significance to policymakers. For enterprises in low-tech industries or non-OECD countries R&D, easy access to R&D incentives and support should be provided to enhance the innovation capabilities which could promote long-term firm growth.The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.HP designed and conceptualized the study. HP, CZ, and TS finished the literature search and data analysis. BS and CZ wrote and revised the manuscript. All authors read and approved the final manuscript.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Finding significant genes or proteins from gene chip data for disease diagnosis and drug development is an important task. However, the challenge comes from the curse of the data dimension. It is of great significance to use machine learning methods to find important features from the data and build an accurate classification model.The proposed method has proved superior to the published advanced hybrid feature selection method and traditional feature selection method on different public microarray data sets. In addition, the biomarkers selected using our method show a match to those provided by the cooperative hospital in a set of clinical cleft lip and palate data.In this paper, a feature selection algorithm ILRC based on clustering and improved L1 regularization is proposed. The features are firstly clustered, and the redundant features in the sub-clusters are deleted. Then all the remaining features are iteratively evaluated using ILR. The final result is given according to the cumulative weight reordering.The proposed method can effectively remove redundant features. The algorithm’s output has high stability and classification accuracy, which can potentially select potential biomarkers. Microarray data is a valuable tool for analyzing gene expression profiles . This kiExtensive research has shown that feature selection is crucial for building statistical models when mining large datasets of high dimension, especially for those generated from microarray and mass spectra analysis . It is aMeanwhile, results from the proteomic analysis are experiencing the same issue as high-dimensional gene expression data based on advanced mass spectroscopy. Many of identified proteins might be irrelevant to the disease and have high correlations among each other. Machine learning methods have shown a significant advantage in dealing with this genetic and clinical data in the past few years –15. ReceExisting researches have dedicated to improving the accuracy of prediction models with a smaller number of features. However, for the discovery of markers, the reliability and stability of the results must be emphasized. If part of the data is updated or modified, and the markers selected by the algorithm change significantly after the disturbance of the data set, ,which makes the original ones are no longer reliable for researchers . AlthougMeanwhile, there is little literature explaining and validating the clinical meaning of the selected genes or proteins in these literatures. Despite the high classification accuracy, a priori knowledge or manual verification is necessary for assessing the biological plausibility and the specificity of any biomarker clusters identified by the algorithm. Taken alpha-fetoprotein (AFP) as an example, it is a well-known biomarker for a variety of problems of pregnancy, such as open neural tube defects, abdominal wall defects and Down’s syndrome . HoweverIn this paper, a hybrid method combining improved L1 regularization and cluster-based (ILRC) biomarker selection is proposed to solve the above problems. The overall framework is shown in Fig. A hybrid feature selection method is designed for biomarker selection. This method focuses on the stability and validity of the results during the feature selection process while ensuring a high accuracy rate.A combination of clustering algorithm with filter method and embedded method for biomarker selection.Comparatively evaluation of the performance of various classifiers on microarray data.Introduce a data set that can be used for biomarker verification to prove the validity of the results.The contribution of this article is reflected in the following aspects: Traditional feature selection methods can be divided into filter, wrapper and embedded methods. In general, the filter method does not involve classification models. It only uses the intrinsic characteristics of the data to measure the important feature score . CompariWrapper methods usually add a classifier that involves evaluating the subset of features . It takeThe idea of embedded methods is similar to wrapper methods. They both involve classifiers. However, in the embedded method, the selection of feature subsets is directly embedded in the classifiers. In other words, the feature selection is carried out simultaneously with the training of the classifier. The common embedded method comprises supported vector machine recursive feature elimination (SVM-RFE), decision tree (DT) , random However, recent studies have shown that hybrid feature selection methods can simultaneously take the efficiency advantages of filter method and the accuracy advantages of warpper method to achieve superior performance . In addiFor the microarray data of DNA, Lu et al. combined mutual information maximization (MIM) and adaptive genetic algorithm (AGA) to propose a hybrid feature selection algorithm, MIMAGA-Selection . The metSalem et al. proposed a new method for finding biomarkers from gene microarray data that combines information gain (IG) and a standard genetic algorithm (SGA) for feature selection, called IG/SGA . The infAlshamlan et al. proposed a new feature selection algorithm, called the minimum redundancy maximum relevance (mRMR) method, and combined it with an Artificial Bee Colony algorithm (ABC) to filter biomarkers from gene microarray data . mRMR isJain et al. combine correlation-based feature selection (CFS) with an improved binary particle swarm optimization (iBPOS) to propose a two-stage hybrid feature selection method for biomarker selection of microarray data . Like otMoradi et al. proposed a hybrid feature selection method based on particle swarm optimization (PSO) algorithm . The maiShreem et al. proposed a two-stage feature selection hybrid method for solving the biomarker identification problem for microarray data . The metTwo hybrid feature selection methods based on the fast correlation based filter (FCBF) algorithm were studied by Djellali et al. . The firIn this section, we show the experimental results according to the processing flow of the feature engineering pipeline. In the data preprocessing process, the impact of different sampling methods on the unbalanced data set is compared. In the process of feature selection, we compared our proposed method with typical feature selection methods. In the model-building stage, we compared the effectiveness of different classification models. Finally, in the result evaluation, the proposed method was compared with the advanced feature selection method. In addition, we also evaluated the proposed method on the cleft lip and palate (CLP) dataset.Table Figure Usually, in microarray data analysis, the number of features that researchers pay attention to is between 5 and 30, which is also the focus of our attention. It can be seen that ILR has achieved better results in this area, and ILR is also part of the hybrid algorithm we proposed.Figure Figure Table In order to verify the performance of the proposed feature selection method in real data sets, we tracked the ranking of three known biomarkers in the algorithm in the CLP data set. These biomarkers have been labeled and verified to be effective.To ensure the stability of the results, we repeated 1042 experiments (consistent with the number of features) in different methods and respectively took the average weight ranking and average frequency corresponding to each feature as the final ranking. The feature weight comes from the classifier and is generated in the model building. The average frequency is the average number of occurrences of the feature in repeated experiments.p% node with the highest correlation with the seed node in the method. It can be seen that the three known biomarkers rank better than other methods in ILRC.Table From the results in Table The average classification accuracies of different feature selection methods with multiple datasets were compared in Figs. In Fig. In Table Table ILRC combines the clustering algorithm with the hybrid feature selection algorithm (T-Test and ILR), which can effectively filter redundant features, select biomarkers with diagnostic significance, and ensure high classification accuracy. However, the ILRC algorithm does not involve ensemble learning. Usually for feature selection tasks, especially the selection of biomarkers, the use of ensemble models and feature ranking fusion technology can improve the robustness of the results. We will focus on this direction in future research.Microarray data analyzes the genetic differences of tissues and cells. In clinical medicine, effective gene selection can greatly enhance the process of disease prediction and diagnosis. Genes useful for predicting cancer types may also provide support for the pathogenesis and pharmacology of cancer . The ILRIn our research, we found that the feature subsets generated by different models may have large deviations. Researchers need a stable subset of features. Supposing part of the data is updated or modified, the markers selected by the algorithm change significantly after the disturbance of the data set. These markers may be unreliable for researchers . The folThere are 17 different datasets used in this paper, including 17 publicly available genetic datasets and CLP protein dataset, as shown in Table Cleft lip and palate (CLP) are common congenital orofacial defects of a baby’s lip or mouth. It is originated from a failure joint of tissue and special cells during the formations of lip and mouth , which happens between the fourth and ninth weeks of pregnancy . Babies In general, this congenital malformation can be divided into two types: syndromic which is mainly caused by genetic mutations, and non-syndromic with more complicated inducing factors including a combination of genes and environment, such as smoking, diabetes, the usage of certain medicines before and during pregnancy –68. OverRoutine prenatal diagnosis method of CLP is conducted by anatomic ultrasonography between 18 and 20 weeks’ gestation . RepairiIn this paper, the CLP dataset is the only dataset in which biomarkers have been tagged and validated by clinical doctors. The dataset contains 60 maternal serum samples  that are collected between gestational weeks 22–30 for this study. 1042 proteins are identified by an iTraq based proteomics analysis. The serum samples were collected from pregnant women who underwent prenatal examination in a partner hospital. During the mass spectrum analysis experiment, every ten blood samples were mixed into one sample, so the actual sample size of the dataset is only six.P and N represent the number of positive and negative samples, TP and TN represent the number of positive and negative samples predicted correctly, FP and FN represent the number of positive and negative samples predicted incorrectly. The evaluation indicators used in this paper are calculated as Eq.  and Miss Discovery Rate (MDR) to evaluate the selected features and classification models. The estimation of the fdr and mdr are requirements for the analysis and documentation of mass spectrometry data according to the Paris guidelines of Molecular and Cellular Proteomics . These ed as Eq. .1\documeThe Improved L1 Regularization method, also known as stability selection, is based on a combination of sampling and feature selection . This meAn important feature of the L1 regularization method is the ability to generate sparse matrices of feature weight coefficients, i.e., the coefficients of some features become zero, so that feature selection can be achieved based on feature weights. Therefore L1 regularization is often used for feature selection of high dimensional data. However, to obtain the correct results, the L1 regularization method requires the data space to meet specific conditions. In addition, if there is a high correlation between features, the L1 regularization method is prone to distortion, making it difficult to achieve a high classification accuracy. The L1 regularization method is also very sensitive to the regular term coefficient alpha, so it is critical to choose the right parameters. When facing data with high dimensional and small sample, the number of features selected by L1 regularization method is less than timation .The improved L1 regularization algorithm’s core idea is first random sampling, and then use a feature selection model to evaluate the selection . When thE for the clustering partition Removing irrelevant features does not negatively affect the clustering accuracy and can reduce the required storage and computation time from a clustering perspective. Therefore, clustering algorithms are often used as one of the pre-processing methods to remove redundant features before feature selection . For theentclass1pt{minimaE value, the greater the similarity of the intra-cluster samples.Equation  depicts A hybrid feature selection method, improved L1 regularized clustering-based (ILRC) for biomarker discovery is proposed in this subsection. This method uses T-test and improved L1 regularization (ILR) method as a hybrid feature selection method, and combines the improved K-Means clustering algorithm into ILR . The expk) is determined using the elbow method [k sub-datasets (clusters), so each cluster’s features are similar. For each cluster, the p value of each feature (node) is calculated using the T-Test method. For each feature p value is calculated as Eq. (The overall flow of the algorithm is shown in the Fig. w method . The orid as Eq. .3\documep values, the node with the smallest p value is defined as the seed node, and the Pearson correlation coefficient between the remaining nodes and the seed node is calculated. The correlation coefficients are sorted in descending order and the top p% of nodes other than the seed nodes are removed. The purpose of this step is to remove the nodes in each cluster that have a high correlation with the seed node. The remaining features in each cluster are used to form a new dataset n, the experiment repeats n feature selections and statistically incorporates the weight of each feature and the number of occurrences of each feature as the final feature selection result. The process is shown in Algorithm 1.The nodes are then ranked according to their This method can effectively remove redundant features. In an experiment on the CLP data set, we removed the following proteins in one Cluster: P37837, P40197, A0AUP5, B2R701. By reviewing the relevant information on UniProt, we did not find any information indicating that these proteins are related to the clinical diagnosis of CLP, these proteins in this Cluster are removed for the clinical diagnosis redundancy.


Investors wish to obtain the best trade-off between the return and risk. In portfolio optimization, the mean-absolute deviation model has been used to achieve the target rate of return and minimize the risk. However, the maximization of entropy is not considered in the mean-absolute deviation model according to past studies. In fact, higher entropy values give higher portfolio diversifications, which can reduce portfolio risk. Therefore, this paper aims to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by incorporating the maximization of entropy. In addition, the proposed model incorporates the optimal value of each objective function using a goal-programming approach. The objective functions of the proposed model are to maximize the mean return, minimize the absolute deviation and maximize the entropy of the portfolio. The proposed model is illustrated using returns of stocks of the Dow Jones Industrial Average that are listed in the New York Stock Exchange. This study will be of significant impact to investors because the results show that the proposed model outperforms the mean-absolute deviation model and the naive diversification strategy by giving higher a performance ratio. Furthermore, the proposed model generates higher portfolio mean returns than the MAD model and the naive diversification strategy. Investors will be able to generate a well-diversified portfolio in order to minimize unsystematic risk with the proposed model. Complex economic relations and models due to unprecedented events in the ever-evolving financial markets make estimating stock market returns and volatility become complex nonlinear relations, in need of advancements in mathematical models to adapt to changes in the financial markets and mental resources of the investors. The COVID-19 pandemic has led investors to demand portfolios that are resilient towards the disease.Investors aim to minimize the risk as well as maximize the return in their portfolio investments. In past studies, portfolio management has been analyzed and solved with optimization models ,2,3. MarKonno and Yamazaki  have intEntropy is an important element in portfolio selection . ShannonN portfolio, without using a mathematical model  is equivalent to the linear programming model as shown below:According to Konno and Yamazaki , short sShannon  has intrn, when The main advantage of entropy is to generate a well-diversified portfolio. As shown in Equation (13), the entropy function is a concave function of the portfolio weights Another advantage of the principle of maximum entropy is the prevention of extreme weight on asset allocation due to a very small number of assets in portfolio selection. For the extreme case, according to Equation (13), the entropy function achieves the minimum value 0, when Additionally, the incorporation of entropy as an objective function in the optimization model can increase the diversification degree of the optimal portfolio. A multi-objective optimization model, namely mean-absolute deviation-entropy model is proposed in this section by incorporating the maximization of entropy. This is because the incorporation of entropy can diversify the allocation of various assets in portfolio selection. The proposed multi-objective optimization model consists of three objective functions that focus on the mean return, absolute deviation and entropy of the portfolio. The three objective functions of the proposed model are to maximize the mean return, minimize the absolute deviation and maximize the entropy of the portfolio. In addition, the proposed multi-objective optimization model incorporates the optimal value of each objective function and is solved using a goal-programming approach. This is because the goal-programming approach can solve multi-objective problems ,31,32. TR*, can be obtained by solving the following model.The optimal value for portfolio mean return, W*, can be determined by solving the following model.The optimal value for portfolio absolute deviation, Then, the optimal values n, because it is the maximum value of portfolio entropy. The objective function of the proposed model is to minimize deviations from the optimal values n using a goal-programming approach.The target value for portfolio entropy is set as lnShort sale is not allowed for the proposed model as shown in Equation (18). This is because the proposed model is developed based on the MAD model  and the The performance of the model is measured with performance ratio. The performance ratio is measured based on the mean-absolute deviation ratio  as shownN portfolio) are compared for the two periods which are January 2016–December 2019 (before the COVID-19 pandemic period) and January 2020–March 2021 (within the COVID-19 pandemic period). The January 2016–December 2019 period (before the COVID-19 pandemic period) is denoted by D1 period, while the January 2020–March 2021 period (within the COVID-19 pandemic period) is denoted by D2 period.The computational works of the MAD model and the proposed model are performed using LINGO software. The performance of the optimal portfolio for the MAD model, the proposed model and benchmark naive diversification strategy (1/N portfolio). Bootstrapping is repeated 5000 times for the tested D1 period and D2 period in this study with R software. Based on the simulation analyses, the performance of the optimal portfolios among the MAD model, the proposed model and the naive diversification strategy are compared using performance ratio.In this study, we test the stability of the proposed model using bootstrap simulation ,34. BootAs shown in As presented in For the D2 period, VZ is ranked the highest since it gives the largest weight to the portfolio composition using the MAD model. In contrast, JNJ is ranked the lowest as it gives the smallest weight to the portfolio composition using the MAD model for the D2 period.Based on According to The MAD model  and the Based on On the other hand, the proposed model generates the portfolio mean return at 0.4000% for the D1 period. In addition, the portfolio performance ratio of the proposed model is 0.3254.Besides that, the naive diversification strategy generates the portfolio mean return at 0.2425% for the D1 period. Moreover, the portfolio performance ratio of the naive diversification strategy is 0.2245.Based on On the other hand, the proposed model generates the portfolio mean return at 0.4400% for the D2 period. In addition, the portfolio performance ratio of the proposed model is 0.2041.Finally, the naive diversification strategy generates the portfolio mean return at 0.3185% for the D2 period. Moreover, the portfolio performance ratio of the naive diversification strategy is 0.1313.The proposed model outperforms the MAD model and the naive diversification strategy by giving a higher performance ratio for the D1 period  and the As shown in The simulation analysis shows that the proposed model outperforms the MAD model and the naive diversification strategy by giving a higher performance ratio for the D1 period. In addition, the proposed model generates a higher portfolio mean return than the MAD model and the naive diversification strategy for the D1 period. The simulation analysis is consistent with the results for actual portfolio mean return and performance ratio, which are presented in Based on Based on the simulation analysis, the proposed model outperforms the MAD model and the naive diversification strategy by giving a higher performance ratio for the D2 period. Furthermore, the proposed model generates a higher portfolio mean return than the MAD model and the naive diversification strategy for the D2 period. This shows that the simulation analysis is consistent with the results for actual portfolio mean return and performance ratio, which are presented in The simulation analyses show that proposed model generates a higher portfolio mean return and a higher performance ratio than the MAD model, as well as the naive diversification strategy, consistently for both periods of study, which are before the COVID-19 pandemic period  and withIn conclusion, a multi-objective optimization model, namely a mean-absolute deviation-entropy model is proposed in this paper by incorporating the entropy as well as the optimal value of each objective function using a goal-programming approach. The results indicate that the MAD model and the proposed model give different portfolio composition for both periods of study, which are before the COVID-19 pandemic period as well as within the COVID-19 pandemic period. In addition, the results show that the proposed model is able to generate well-diversified portfolios consistently, because the proposed model gives a higher portfolio entropy value than the MAD model for both periods of study. The incorporation of entropy in the proposed model will change the optimal portfolio composition in order to generate well-diversified portfolio.The proposed model outperforms the MAD model and the naive diversification strategy by giving higher performance ratios consistently for both periods of study. Besides that, the proposed model generates higher portfolio mean returns than the MAD model and the naive diversification strategy consistently, both before the COVID-19 pandemic period as well as within the COVID-19 pandemic period. Based on the simulation analyses, the proposed model generates higher portfolio mean returns and higher performance ratios than the MAD model, as well as the naive diversification strategy, consistently for both periods of study. This implies that the proposed model is robust and stable for portfolio investment.As presented in this paper, the proposed mean-absolute deviation-entropy model is superior to both the MAD model and the naive diversification strategy, as it gives higher performance ratios and higher portfolio mean returns. This study will contribute to the portfolio management of investors. This is because investors will be able to maximize the portfolio mean return, minimize the portfolio absolute deviation and maximize the portfolio entropy, therefore generating well-diversified portfolios and reducing the unsystematic risk of the portfolios using the proposed model. Portfolio optimization with the proposed model should be extended to the stock market of the other countries for future research. This proposed model can be applied using data from other markets, be it developed, emerging, or developing markets, with promising results, benefiting investors in various countries.


The minimum uncut chip thickness (MUCT), dividing the cutting zone into the shear region and the ploughing region, has a strong nonlinear effect on the cutting force of micro-milling. Determining the MUCT value is fundamental in order to predict the micro-milling force. In this study, based on the assumption that the normal shear force and the normal ploughing force are equivalent at the MUCT point, a novel analytical MUCT model considering the comprehensive effect of shear stress, friction angle, ploughing coefficient and cutting-edge radius is constructed to determine the MUCT. Nonlinear piecewise cutting force coefficient functions with the novel MUCT as the break point are constructed to represent the distribution of the shear/ploughing force under the effect of the minimum uncut chip thickness. By integrating the cutting force coefficient function, the nonlinear micro-milling force is predicted. Theoretical analysis shows that the nonlinear cutting force coefficient function embedded with the novel MUCT is absolutely integrable, making the micro-milling force model more stable and accurate than the conventional models. Moreover, by considering different factors in the MUCT model, the proposed micro-milling force model is more flexible than the traditional models. Micro-milling experiments under different cutting conditions have verified the efficiency and improvement of the proposed micro-milling force model. Micro milling is viewed as a promising technology for manufacturing micro devices because of its high machining accuracy and the ability to cut a variety of materials . The cutAt the beginning of the 21st century, Bao and Tansel  first inGenerally, the MUCT value could be obtained in three ways: Inferred from the measured cutting force and the surface profile, simulated by the finite element method and determined by an analytic MUCT model. Dib et al.  determinThe studies above reveal that the MUCT value depends on many different factors such as the friction angle, shear strength and flow stress. However, each study only considered some of these factors. For a better understanding of the MUCT, a more comprehensive MUCT model is required. Moreover, the constraint condition, that the stagnant angle corresponding to the MUCT should be greater than the friction angle, was not taken into account in the existing MUCT models. As will be demonstrated in In this study, based on the assumption that the normal shear force and the normal ploughing force are equivalent at the MUCT point, a novel analytic MUCT model is constructed to determine the minimum uncut chip thickness. Nonlinear piecewise cutting force coefficient functions with the novel MUCT as the break point are constructed to represent the distribution of the shear/ploughing force under the effect of minimum uncut chip thickness. Under the proposed assumption, the stagnant angle corresponding to the MUCT is constantly greater than the friction angle, and the cutting force coefficient function is absolutely integrable, making the force prediction model more stable than the traditional models. Moreover, under the proposed equilibrium normal force assumption, different factors such as the friction angle, shear stress and ploughing coefficient are comprehensively included in the MUCT model, making the proposed cutting force model more flexible than the conventional models.This paper evolves as follows. The comparability of the cutting-edge radius and the uncut chip thickness, viz. the cutting-edge radius size effect, leads to a minimum uncut phenomenon in micro-milling. As There are two classical principles to model the cutting force in the shear region: The minimum cutting energy principle  and the In the shear region with a negative rake angle (itive as  shows. TEquations (1) and (2) imply that the friction angle is a singularity of the stress distribution function. The stress tends to be infinite when the angle Although Son et al.  and MaleThe proposed assumption that the normal shear force and the normal ploughing force at the MUCT point are equivalent could be described by the following equation:The left of Equation (5) is the normal shear force CT point a, and thCT point b. NotatiTaking Denoting Decomposing Denoting For Equation (9), there are two solutions near the friction angle, written as:It could be proven that the solution According to Equations (11) and (12), it could be concluded that (1) the MUCT value is determined by the friction angle, the ratio of the ploughing coefficient he study .The MUCT divides the cutting zone into shear and ploughing regions. If the uncut chip thickness is smaller than the MUCT, the micro-milling force results from the ploughing effect. Otherwise, the cutting force corresponds to the shear force. In this section, nonlinear cutting force coefficient functions embedded with the novel MUCT are constructed to represent the distribution of the shear/ploughing force under the effect of MUCT. The input of the nonlinear cutting force coefficient function is the uncut chip thickness, and the output of the nonlinear cutting force coefficient function is the distribution of the shear/ploughing force. The MUCT is a breakpoint of the nonlinear cutting force coefficient function and switches the shear/ploughing process.The modeling flowchart is shown in The equivalent cutting form in a previous study  is adopteference .Nonlinear cutting force coefficient functions are constructed to represent the distribution of the shear/ploughing force on the cutting edge. For the convenience of mathematical representation, the uncut chip thickness s(1−hre) a. The idchanisms b. AccordNotation The distribution form of the cutting force in Equations (14) and (15) is valid for a ductile material. Due to the brittle–ductile transition phenomenon in cutting brittle material , the cutThe mechanical micro-milling force model embedded in the novel MUCT is mathematically represented as:Notation The forces in X and Y directions defined in Equations (18) and (19) are adopted to estimate the model parameters. The range of the parameters Micro slot milling experiments are conducted to estimate the model parameters and verify the proposed micro-milling force model. A total of nine experiments are conducted with different spindle speeds, axial cutting depths and feeds per tooth. The cutting conditions of the nine experiments are listed in The seven parameters listed in The calibrated MUCT value and the corresponding stagnant angle are listed in The micro-milling force is predicted via the proposed force model embedded with the novel MUCT model. The relative error listed in the fifth column of The MUCT models proposed by Son et al.  and Maleh. h, and the stability of the numerical calculation with the discrete UCT approach is poor. In this study, to find the optimal discrete UCT dh for the partial rake angle approach, the dh is set as a parameter to be estimated. According to the genetic optimization algorithm, the optimal dh for each experiment is estimated. Then, the partial rake angle approach with the optimal discrete UCT is adopted to predict the micro-milling force. The prediction error listed in the third column of In Malekian’s MUCT model, the stagnant angle equals to the friction angle. As discussed in Under the minimum cutting energy principle and the assumption that the shear angle is equal to the stagnation angle, Son et al.  derived The comparison above clearly shows that the proposed micro-milling force model embedded with the novel MUCT model is more flexible and more stable than the conventional models. The better flexibility and stability cause the cutting force prediction accuracy of the proposed model to be higher than the conventional models. As It should be noticed that all of the MUCT models mentioned above are derived under the minimum cutting energy principle. As discussed in Based on the minimum cutting energy principle and the proposed equilibrium normal force assumption, a novel MUCT model considering the comprehensive effect of the shear stress, friction angle, ploughing coefficient and cutting-edge radius is constructed to determine the minimum uncut chip thickness in micro-milling. A nonlinear cutting force coefficient function embedded with the novel MUCT is constructed to represent the distribution of shear/ploughing force under the effect of minimum uncut chip thickness. By integrating the proposed cutting force coefficient functions, the nonlinear micro-milling force is accurately predicted. The conclusions are as follows:Compared to the maximum shear stress principle, the minimum cutting energy principle is more reasonable to model the cutting force in the shear region on the round edge.Under the proposed equilibrium normal force assumption, the stagnant angle corresponding to the MUCT is constantly greater than the friction angle, resulting in an integrable stress distribution function and a stable cutting force model.Embedded with a more flexible and stable MUCT model, the proposed nonlinear micro-milling force model is more accurate than the conventional models. The prediction accuracy of the proposed model is improved by 5%–10% compared to the traditional models.The main contribution of this paper is proposing a novel analytical MUCT model with high flexibility and stability for predicting the micro-milling force. As more factors are considered, the proposed MUCT model is more flexible than the traditional models. Embedded with the novel MUCT, the distribution function of the shear/ploughing force is absolutely integrable and the micro-milling force model is numerically stable. In addition to the prediction of cutting force, the proposed MUCT model and the micro-milling force model could be further adopted to predict the tool deflection, vibration and energy consumption in the micro-milling process.


A dynamical spin injection based on the ferromagnetic resonance in a ferromagnetic/nonmagnetic bi-layered structure, is a powerful mean for generating and manipulating the spin current. Although the mechanism of the dynamical spin injection is mainly attributed to the spin pumping, the detailed mechanism and the quantitative understanding for related phenomena are still controversial. As an another important contribution to the dynamical spin injection, the heating effect due to the resonant precessional motion of the magnetization is pointed out recently. In order to quantify the contribution from the heating effect, we here investigate the dynamical spin injection in a CoFeB/Pt/CoFeB trilayer. Although the contribution from the spin pumping diminishes because of the symmetric spin injection from the upper and lower interfaces, a significant inverse spin Hall voltage has been clearly observed. We show that the observed voltage can be quantitatively understood by the thermal spin injection due to a heating effect during the ferromagnetic resonance. A proper combination between the spin pumping and the heat-flow control in the multi-layered system is a key for the efficient dynamical spin injection. It is well known that a spin current, a flow of spin angular momentum, plays a significant role in operations of the spintronic devices2. This is because the spin current can be utilized for manipulating the magnetization as well as for detecting the magnetization direction4. The spin current is, in general, created by applying an electric field across the FM/NM interface, resulting in injecting the spin-polarized electrons from the FM into the NM8. This is known as electrical spin injection, which is a widely utilized for generating the spin current because of its high selectivity and flexibility. In addition, since the Seebeck coefficient in the ferromagnet also shows the spin dependence, the spin current can be generated by using the temperature gradient across the FM/NM interface, instead of the electric field11. This is known as the thermal spin injection, where the generation efficiency often shows the significant enhancement in several ferromagnetic metals depending on its band structure14.Spintronic devices consisting of ferro-magnet (FM) /non-magnet (NM) hybrid structures have attracted much attention since the discovery of the spin-dependent transports17. This is because the FMR can be induced by microwave irradiation without electrical connection, leading to wireless spintronics19. So far, the mechanism of the dynamical spin injection is attributed to the spin pumping, where the excess spins in the FM due to the FMR spill out into the adjacent nonmagnetic heavy metal (HM)22. On the other hand, the resonant precessional motion of the magnetization is known to yield the heating effect through the magnon-phonon interaction26. This FMR heating effect produces the temperature gradient across the FM/NM interface, resulting in the thermal spin injection14. Since the temperature change due to the FMR heating exceeds 10 K, it could be the significant contribution on the dynamical spin injection24. However, since the dynamical spin injection is mainly evaluated by measuring the inverse spin Hall effect (ISHE), it is difficult to distinguish the dominant contribution in the dynamical spin injection. Moreover, the proper combination between the spin pumping and the thermal spin injection will enhance the dynamical spin injection efficiency significantly. Therefore, it is essential to understand how large the thermal spin injection contributes to the dynamical spin injection. We have developed an effective device structure for the quantitative evaluation of the dynamical spin injection27. In this method, the spin-rectified voltage caused by the charge current directly flowing in the ferromagnetic layer can be minimized by using a thick Cu electrode, leading to the quantitative analysis of the dynamical spin injection. Very recently, we showed that a CoFeB/Pt/CoFeB trilayered structure is effective for the investigation of a dynamical spin injection28. In the present paper, by extending our evaluation method, we investigate the contribution of the thermal spin injection in dynamical spin injection. Especially, by controlling the temperature gradient due to FMR heating effect, we clarify the importance of the thermal spin injection.Apart from the aforementioned statical spin injection, the dynamical spin injection based on a ferromagnetic resonance (FMR) is also an attractive mean for generating and manipulating the spin currentThe sample used for the present study consist of a CoFeB/Pt/CoFeB tri-layered structure with a Cu electrode, as schematically shown in Fig. 19. As schematically shown in Fig. 22, the magnitude of the spin injection due to the spin pumping from both sides are almost same. Therefore, the contribution of the spin pumping is expected to diminish in the present trilayer. On the other hand, from the viewpoint of the thermal spin injection, since the magnetic trilayer is sandwiched by the Cu electrode and the Si substrate, the temperature distribution becomes asymmetric14. In this case, the magnitude of the thermal spin injections from the upper and lower interfaces should be different. This leads to generate the detectable ISHE voltage. Thus, we are able to extract the contribution of the thermal spin injection due to the FMR heating effect effectively.The present CoFeB/Pt/CoFeB tri-layered structure is effective for acquiring the contribution of the thermal spin injection selectively because of the following reason. When the upper and lower CoFeB layers have the same magnetic property, the FMR can be excited simultaneously. In such a situation, the dynamical spin injections occur both from the upper CoFeB/Pt and lower Pt/CoFeB interfacesFirst, we evaluate the static magnetic property of the trilayed film by using a vibrating-sample magnetometer (VSM). As show in Fig. 29.We then evaluate the dynamic property of the present trilayer by measuring the dc voltage along the longitudinal direction under the RF current injection, as schematically shown in Fig. mentclass2pt{minimmentclass2pt{minim31.28, the negative ISHE signal in the present coordinate corresponds to the dynamical spin injection from the upper interface. This indicates that the dynamical spin injection from the upper interface is larger than that from the lower interface. The small amplitude of the symmetric component is due to the cancellation of the dynamical spin injection from both side. We also observed the anti-symmetric field dependence within the same order of the magnitude. As mentioned in the introduction28, the origin of the anti-symmetric component is mainly caused by the galvanomagnetic effect due to the direct current flow in the FM, but its quantitative understanding is still controversial issue. Moreover, the similar undesired effects is known to contribute to the symmetric component. However, its magnitude is comparable or smaller than the anti-symmetric component. We emphasize that the clear negative change is observed in the symmetric signal even by subtracting the undesired component. This is a reasonable scenario because the generated heat mainly diffuses from the top to the bottom layers (We now discuss the shape of the voltage spectra. Figure entclass1pt{minimaWe have also performed a similar measurement at 77K by immersing the sample in liquid Nitrogen. In this situation, the temperature of the specimen surface is fixed at the liquid Nitrogen temperature. leading to the acceleration of the upward heat-flow. Therefore, we expect the enhancement of the symmetric voltage with the same sign as that at RT. As can be seen in Fig. entclass1pt{minima24. In the present structure, at room temperature, the Cu heat sink in between the trilayer and the Si substrate increases the downward heat flow, leading to the enhancement of the negative ISHE signal. On the other hand, at 77K, the upward heat flow decreases, leading to the reduction of the ISHE signal. Figure To obtain more definite evidence of the significant contribution of the thermal spin injection, we have prepared a similar trilayer on a Cu strip line, as schematically shown in Fig. 33. Since it is still an important milestone to identify the contribution of each component separately, the dynamical spin injection under the temperature control may solve the key for the quantitative analysis of each contribution Thus, the combination between the spin pumping and the thermal spin injection is a key for the efficient dynamical spin injection.It also should be noted that there are two possible contributions for the thermal spin injection. One is the spin-dependent Seebeck effect driven by the spin-polarized current and the other one is the spin Seebeck effect driven by the magnon spin current. In the metallic structure, the spin-dependent Seebeck effect was naively considered as the major mechanism. However, recent studies indicates the importance of the magnon Seebeck effect in the metallic systemWe have examined the dynamical spin injection in the CoFeB/Pt/CoFeB trilayer by the electrical detection method using a thick Cu electrode. The efficiency of the dynamical spin injection was significantly reduced because of the symmetric spin pumping from the upper and lower interfaces. However, the finite symmetric component due to the ISHE was found to be induced in the voltage spectra. By changing the temperature gradient in the trilayer, we confirmed that the origin of the ISHE voltage is the thermal spin injection. Our results indicate that the heat control is significant in order to perform the efficient dynamical spin injection.


In an autonomous driving assistance system (ADAS), top views effectively represent objects around the vehicle on a 2D plane. Top-view images are therefore widely used to detect lines in ADAS applications such as lane-keeping assistance and parking assistance. Because line detection is a crucial step for these applications, the false positive detection of lines can lead to failure of the system. Specular reflections from a glossy surface are often the cause of false positives, and since certain specular patterns resemble actual lines in the top-view image, their presence induces false positive lines. Incorrect positions of the lines or parking stalls can thus be obtained. To alleviate this problem, we propose two methods to estimate specular pixels in the top-view image. The methods use a geometric property of the specular region: the shape of the specular region is stretched long in the direction of the camera as the distance between the camera and the light source becomes distant, resulting in a straight line. This property can be used to distinguish the specular region in images. One estimates the pixel-wise probability of the specularity using gradient vectors obtained from an edge detector and the other estimates specularity using the line equation of each line segment obtained by line detection. To evaluate the performance of the proposed method, we added our methods as a pre-processing step to existing parking stall detection methods and investigated changes in their performance. The proposed methods improved line detection performance by accurately estimating specular components in the top-view images. Perspective geometry of a camera causes planar surfaces such as a parking-lot floor to distort into peculiar shapes. Inverse perspective mapping  is a metAlthough researchers have previously tried to remove specular regions from images ,26,27,28In general, light sources such as traffic lights, street lights, car headlights, and indoor lighting in parking buildings tend to have oval-shaped specular regions on the floor when they are reflected by an inhomogeneous surface . The disThe geometric property of specularity is used to identify specular pixels. We tried to use the orientational characteristic of the specularity in the image to overcome the limitations of color-based approaches in the line detection.Two methods which can be applied to the line detection using the top-view image are presented. Our two methods estimate the specularity using the intermediate outputs of line filter-based and edge-based line detection approaches.The proposed methods were tested using real-world applications and environments. We applied our methods to existing parking stall detection methods, to demonstrate that our methods can remove artifacts caused by the specularity in various environments.Two pre-processing methods are proposed to identify false lines due to the reflected light from the light source on the glossy floor by using a geometric property that the specular region appears as a straight line toward the camera in the top-view image. The first generates a probability map that is part of the specularity. Specifically, considering the camera location in the top-view image, the possible direction of specularity can be identified, and at this time, the probability that the pixel is a specular is calculated using gradient vector indicating the direction of intensity changes around the pixel. The second directly applies the geometric property of the specularity to line segments, producing a binary output. False line segments generated by specularity are filtered by investigating a direction of each line segment. Although this method needs processed data as an input, it incurs a low computational burden, and the results of the detection are intuitive. We applied our methods to existing parking stall detection methods as a pre-processing step. Manually collected outdoor and indoor sequences were used to investigate the changes in quantitative performance of the line detection of these methods. There are two versions of each parking stall detection method: one is the original version and the other is an enhanced version, including our methods for suppressing specularity. Our two methods improved the line detection performance in real-world applications. To the best of our knowledge, ours is the first attempt to tackle this issue in ADAS applications. The contributions of this paper are as follows:The rest of the paper is organized as follows. Related studies into removing specular regions from images are summarized in The existing literature addressing the problem of false detection caused by specularity can be categorized into two approaches: threshold-based ,26,27,28These approaches use the intensity or color property of specular regions in images. They are assumed to be outliers with color values distinct from those of other objects in the image.Saint-Pierre et al.  presenteTchoulack et al.  tried toChang et al.  removed Karapetyan and Sarukhanyan  proposedMorgand and Tamaazousti  used theGuo et al.  presenteSilva et al.  performeLi et al.  used twoThese approaches have been reported more recently than the threshold-based approaches. Various types of a network have been designed for different applications. Backbones of the network have been shown to generate more powerful features to distinguish objects than traditional hand-crafted features.Rodriguez-Sanchez et al.  used twoFunke et al.  proposedThe deep learning-based methods are state-of-the-art approaches that are widely used for computer vision applications such as object detection, classification, and semantic segmentation. They could be applied to classify specular regions based on trained features of convolutional neural networks. However, aside from the computational issue, the deep learning-based methods have a critical drawback that they can produce unexpected results for the input with different characteristics from the training dataset ,38. The Our proposed methods use a geometric clue; the specular regions are stretched toward the camera. Although this geometric clue can be observed in any scene captured by a camera, we set our target domain as top-view images. We chose this domain because the location of the camera in the top-view image can be obtained in generating the top-view image, and the specular regions are overstated in top-view images and can significantly hinder the line detection. In this section, the geometric property of specularity is explained, and the way in which we implement this concept to estimate specularity is discussed in detail.From a macroscopic point of view, there are two terms used to describe reflection: specular or diffuse. Specular reflection means that the light rays reflect at the same angle as the angle of incidence, whereas diffuse reflection means that the light rays scatter equally in every direction. In real-world situations, both types are ideal and rarely happen in isolation. Reflections from most existing materials have mixed characteristics, being neither completely specular nor completely diffuse. Phong  empiricaSince specularity caused by this reflection produces a striking effect in the image, many researchers have tried to detect and remove this effect, as mentioned in d is the major axis of an ellipse from the projection of the virtual sphere,L is the horizontal distance between the virtual sphere and the camera,r is the radius of the virtual sphere,a is angle between two lines; one is a tangent line to the virtual sphere from the camera and the other is a line passing through the center of the virtual sphere from the camera.d increases as L increases, the specular region stretches toward the camera direction in the image, while retaining its width. A length of d in the image changes according to a projection angle between the image plane and camera plane. This length is proportional to cosine Since  objects , the speBecause the intensity values and profiles of the lines and specular regions are very similar, the latter can induce false line detection results. The specularity inducing the false line detection has a linear shape due to a long distance between the camera and light source. According to the geometric property discussed in Due to the quantization error caused by the process of generating top-view images and the non-spherical shape of the light source, it is difficult to determine specular pixels discretely. Therefore, a probability map indicating pixel-wise probability that a pixel is specular is generated to fill this gap. The information from the probability map is then used to suppress specular pixels. There can be many possible applications using this map to suppress specular pixels. As an example, we describe how to apply this probability map to other applications in G is the grayscale top-view image, To obtain a local gradient around a pixel, vertical and horizontal gradient maps are first extracted by applying a 3 × 3 Sobel filter to a grayscale top-view image. This process can be expressed using the following equations:Specularity appears as radial lines centered on the camera position in the top-view image. This geometric property gives us a clue with which to distinguish between specular and non-specular pixels. The gradient vector of the possible specularity at a certain pixel can be calculated using the camera location. However, as shown in w indicates half of the predefined window size, A probability map l filter  was adopWe generated probability maps using synthetic and real images for qualitative evaluation. The set operation ‘or’ was used to combine the positive and negative probability maps. The combined probability maps are depicted in We qualitatively compared the proposed probability map with the results of other existing specularity detection methods . The metS indicates specularity, i is the index of line segments, ith line segment, M is a pre-defined margin.In the previous section, we described the process of generating the probability map to estimate specular pixels. To apply this map to other applications, gradient information is required to calculate the probability of specularity of each pixel. Since the line filter-based methods do not use edge detector to extract line responses, the pixel-wise specularity estimation cannot be directly applied to these methods. To address this issue, we developed a line-segment-level specularity estimation using line segments, which is the intermediate output of the line filter-based methods. For this estimation, the line equation of each line segment is used to determine specularity. If a line passes through the center location of the camera, the corresponding line segment is regarded as specular. To consider the quantization error described in the previous section, we give an extra margin to a tolerance range used for this estimation. Specularity can be determined as follows:To evaluate the performance of the proposed methods, we applied them to existing parking stall detection methods ,15 as a The two proposed methods focus on detecting elements caused by specularity in the intermediate output generated during the line detection process. The pixel-wise probability map provides probabilistic information for the edge of a specular region, and the line-segment-level estimation identifies specular line segments among detected line segments generated by the line detection. Since the goal of these two methods is not to estimate all specular regions, the performance of existing parking stall detection methods was measured by comparing junction detection results when the proposed specularity suppression methods were applied at the pre-processing stage, and when it was not. Let us define the junction as an intersection between a horizontal and vertical parking lines. Assume that we have detected a junction by using a parking stall detection method. Junctions located within a 10-pixel radius from the ground truth are considered to be positive, and all others are negative. Because the quality of top-view images degrades as the distance increases from the camera, we only consider junctions close to the camera in the performance evaluation. Junctions whose distance from the camera is less than 200 pixels in the y-axis are our main target . The welWe reproduced two existing parking stall detection methods: Lee’s method  and SuhrLee’s method adopts the line-filter-based approach to detect parking lines in the top-view image. It generates a line response map from the grayscale image using a top-hat filter. Since this filter is symmetrical and designed to extract center points of a parking line with a certain thickness, gradient information is not obtained during this process. It is, therefore, redundant to apply an additional edge filter to generate the specularity probability map. In this case, the line-segment-level estimation can be used to filter out specularity. We added this process between the clustering and line segment combining processes, as depicted in Suhr’s method is an edge-based parking line detection method using positive and negative gradients. Since this method obtains gradient information to extract the line response, the probability map can be generated from this intermediate output. Specularity suppression using the probability map is applied to the process of guide line detection. Grayscale images and Sobel filters are used for the extraction of positive and negative gradients. RANSAC is then applied to each the positive and negative gradient map to detect guide lines, with the specularity suppression process placed between the gradient extraction and RANSAC processes, as depicted in The enhanced version has precision values improved by up to 29.8% in most sequences. This result indicates that our method successfully detects specularity and reduces false positives. Since the indoor sequences contain specularity, the enhanced version shows better performance in these images. However, the proposed approach also shows higher precision when applied to the outdoor sequences. If the specularity filtering worked as intended, there should be no difference in precision and recall for the outdoor sequences, which do not contain specularity. A discrepancy arises because of the distortion caused by objects standing perpendicular to the ground in the top-view image. Although in theory the background is different, the edges of these objects are also oriented towards the camera location, in the same manner as specularity [There was no improvement for recall, because Lee’s method finds all line segments in the top-view image. Lee’s method combines the line segments by considering geometric constraints. Then, the structural information containing a distance between adjacent junctions and each direction of line segments from a connected junction is used to detect parking stalls. In this algorithm, specularity filtering cannot help in finding missing true positives in line detection. However, it may be important for parking stall detection. Comparing the fifth column in To test the effectiveness of the proposed pixel-wise specularity estimation, we applied it to Suhr’s method  for guidHowever, the recall of the enhanced version is almost same as that of the baseline in some indoor sequences. This phenomenon occurs because Suhr’s method locates parking stalls by sequentially detecting two types of lines: guide lines and segment lines. Suhr’s method first detects a guide line and then finds segment lines based on the detected guide line information. To detect the guide line, his method uses RANSAC and considers a line with the maximum inlier ratio to be a guide line. This scheme shows different performance according to the pattern of specularity. If specular pixels are widely scattered and form many short lines, the line response of the actual parking line is dominant over specularity. In this case, the baseline correctly detects the guide line, and recall is the same in both versions, as shown in first and second column of ROC curves were calculated by changing the threshold for adjusting the sensitivity of segment line detection. We measured the running time for generating the probability map and for line-segment-level estimation. All source code is written in C/C++ and runs on a Ryzen7 2700X CPU with 64 GB memory. Generating the probability map takes about 13 ms for processing the 400 × 300 top-view image. This process can take less time if we take advantage of a multi-core environment. In the case of line-segment-level estimation, it requires too little computation to measure processing times. Since our methods run far beyond the real time, these methods can easily be adopted as a pre-processing step for various ADAS applications that use top-view images.We proposed specularity estimation methods that can be used as a pre-processing step in line detection applications using top-view images. The geometric property of specularity was used to overcome the limitation of the color-based approach, with which white lines and specular regions cannot be distinguished. The pixel-wise specularity estimation can be applied to edge-based approaches, and the line-segment-level specularity estimation can be applied to line-filter-based approaches. For quantitative evaluation, we used 12 manually collected sequences and two existing parking stall detection methods. The quantitative results showed that our methods successfully estimate specularity and improve the line detection performance in the environment with specularity, while maintaining performance in the environment without specularity. Despite the two existing methods adopt different approach to detect parking stalls, the proposed methods can detect the specularity using the intermediate output of each these approaches. All of the processes to generate the probability map are completed within 13 ms for 400 × 300 image, and the line-segment-level estimation has a much lower computational cost. Our specularity estimation methods can therefore be widely applied to existing line detection methods. In future studies, we intend to set a hyperparameter such as standard deviation, to generate the probability map adaptively, using a mathematical approach, to make our methods more generic.