On Methods Of Feature Representation And Graph Construction For Subspace Learning

Subspace learning is an important research subject in pattern recognition.Its essence is to map the data from the original high-dimensional space to a suitable low-dimensional subspace by means of a projection matrix.It is expected that in the projected subspace,the relationship between the input data,can be still kept and found.Feature representation shows the similarity between the data while graph construction is related to the feature embedding directly.They play the important roles in boosting the performance of subspace learning.This paper focuses on the study of feature representation and graph construction for subspace learning.The main research contents and the contributions are summarized as follows:First,as the Collaborative Graph-based Discriminant Analysis(CGDA)method ignores the separability for samples in different classes,a new supervised subspace learning method coined Complete Representation based Feature Extraction and Embedding(CRFEE)is proposed.Based on CGDA,CRFEE introduces a novel concept of anti-collaborative(Anti-CR)representation to characterize the coding ability of each sample by the samples from different classes.In this way,the label information can be fully exploited to capture the sample-by-sample dissimilarity.Thus,in the projected subspace,the collaborative relationship of the samples in the same class can be strengthened while the collaborative relationship of the samples from different classes can be largely inhibited.To further alleviate the issue of high computational complexity when constructing the Anti-CR representation coefficients in CRFEE,we present its accelerated version(CRFEE-A).By adopting the mean of the samples in each class,it replaces the sample-by-sample dissimilarity with class-by-class dissimilarity,which greatly reduces the computational complexity.At the same time,the intra-class/inter-class graph Laplacians,introduced in the feature extraction stage for obtaining the collaborative representation coefficients,help to preserve the local geometric structure among the samples and ensure the effectiveness of the feature representation.Second,as the Discriminant Hyper-Laplacian Projection(DHLP)method ignores the local inter-class discriminant information,a new method called Null-Space Discriminant Hyper-Laplacian Analysis(NDHLA)is proposed.Different from DHLP,for interclass graph construnction,we use the local penalty graph to map nearby samples from different classes to be farway in the low-dimensional subspace.In this way,the local information and marginal information between different classes are enhanced.At the same time,by using the null space technology,the discriminant information in null space can be further explored while the small-sample-size problem can be avoided.Third,we point out that most conventional methods of graph construction fail to maintain the relationship between each pair of samples,as well as the high-order relationship among multiple samples.To solve this issue,a new method named Multiple Graph and Collaborative Regression(MGCR)discriminant analysisis proposed.MGCR combines both the traditional graph and the hypergraph in the intrinsic-graph construction,so that the relationship between sample-pairs and the high-order relationship among multiple samples can be preserved.While for the penalty-graph construction,MGCR considers both the global penalty graph and the local penalty graph.In this way,the available discriminative information can be fully mined.At the same time,the collaborative regressive term is introduced so that the obtained subspace can approach the ideal subspace to the utmost.Finally,to alleviate the issue of the high-dimensionality of radar features,we apply the proposed algorithms to the task of specific emitter identification(SEI).It verfies that the recognition accuracy can be improved with the help of the proposed optimization methods presented above.As the feature redundancy is removed,the discriminant information can be effectively extracted to characterize the core features of the specific radar emitters.