Research On Self-Expressive-Based Subspace Clustering Model

In the era of big data,the emergence of massive data promotes the vigorous devel-opment of computer vision,machine learning and pattern recognition,but it also brings challenges in high-dimensional data processing.As one of the typical approach to handle the high-dimensional data,subspace clustering attracts more and more attentions.Sub-space clustering aims at discovering the low-dimensional structure of high-dimensional data.Generally speaking,the samples usually contain noise damage,and the data gener-ally have nonlinear and large-scale structures in the real-world.If the subspace clustering model cannot be established for the above-mentioned practical problems,it will not be conducive to the subsequent clustering tasks.This paper proposes several subspace clus-tering models to deal with the above-mentioned practical problems,and enhance the self-expressive ability of data,followed by their applications in computer vision.The main work includes the following four aspects:1.Self-Expressive-based Subspace Clustering（SESC）aims to learn a representation that can faithfully reflect the correlation between data points.However,most existing SESC methods directly use the original data as the dictionary,which miss the intrinsic structure（e.g.,low-rank and nonlinear）of the real-word data.To address this problem,we propose a novel Projection Low-Rank Subspace Clustering（PLRSC）method by inte-grating feature extraction and subspace clustering into a unified framework.In particular,PLRSC learns a projection transformation to extract the low-dimensional features and utilizes a low-rank regularizer to ensure the informative and important structures of the extracted features.Moreover,the extracted low-rank features effectively enhance the self-expressive property of the dictionary.Furthermore,we extend PLRSC to a nonlinear version（i.e.,NPLRSC）by integrating a nonlinear activator into the projection transfor-mation.NPLRSC cannot only effectively extract features but also guarantee the data structure of the extracted features.The corresponding optimization problem is solved by the Alternating Direction Method（ADM）,and we also prove that the algorithm con-verges to a stationary point.Experimental results on the real-world datasets validate the superior of our model over the existing subspace clustering methods.2.Block diagonal representation（BDR）is an effective subspace clustering method.The existing BDR methods usually obtain a self-expression coefficient matrix from the o-riginal features by a shallow linear model.However,the underlying structure of real-world data is often nonlinear,and thus those methods cannot faithfully reflect the intrinsic re-lationship among samples.To address this problem,we propose a novel Latent Block Diagonal Representation（LBDR）model to perform the subspace clustering on nonlin-ear structure,which jointly learns an auto-encoder and a block diagonal representation matrix.The auto-encoder,which consists of a nonlinear encoder and a linear decoder,plays an important role to learn features from the nonlinear samples.Meanwhile,the learned features are used as a new dictionary for a linear model with block-diagonal reg-ularization,which can ensure good performances for spectral clustering.Moreover,we theoretically prove that the learned features are located in the linear space,and thus en-suring the effectiveness of the linear model using self-expression.Extensive experiments on various real-world datasets verify the superiority of our LBDR over the state-of-the-art subspace clustering approaches.3.BDR has obtained great success in subspace clustering,yet high computational cost limits its wide-spread applications.To address this issue,we propose a novel ap-proach called Projective Block Diagonal Representation（PBDR）for subspace clustering.Firstly,an effective sampling strategy is utilized to select a small subset of the original large-scale data.Then,we learn a projection mapping to match the block diagonal repre-sentation matrix on the selected subset.After training,we employ the learned projection mapping to quickly generate the representation with an ideal block diagonal structure for the original large-scale data.Additionally,by capturing the global structure or local structure of the data to enhance block diagonal coding capability,we further extend the proposed PBDR model(i.e.,PBDR_l1and PBDR_*).We also theoretically and empirical-ly analyze the effectiveness of the proposed PBDR model by showing the block diagonal effect and feasibility guarantee.Especially,this is the first work to learn a projective-form-based BDR to handle the large-scale subspace clustering problem.Finally,experimental results on four publicly datasets show that our PBDR approach achieves faster and more accurate clustering results compared to the state-of-the-art block diagonal-based subspace clustering approaches.4.Most of the existing subspace clustering methods try to obtain a similarity matrix based on self-expressive.However,these methods directly adopt original samples as a set of basis to represent itself linearly,it is difficult to accurately describe the linear relation between samples in the real-world applications,which may lead to failure to find an ideal similarity matrix.To accurately represent the linear relation of samples,we present a subspace clustering model dubbed Linearity-Aware Subspace Clustering（LASC）,which can consciously to learn the similarity matrix by employing our proposed linearity-aware metric.Moreover,we provide detailed mathematical analysis to show that the metric can describe the linear correlation between samples.This is a completely new subspace clustering method that combines metric learning and subspace clustering into a consistent framework.In our model,we first utilize the self-expressive strategy to obtain an initial subspace structure and discovering a low dimensional representation of the original data.Subsequently,we use the defined metric to learn an ideal similarity matrix with linearity-aware on the obtained subspace.By such measures,the learned similarity matrix has such a property that the distance between samples in the same subspace is small,and the distance between samples in different subspaces is large.In addition,to enrich the similarity matrix with more consistent knowledge,we adopt a collaborative learning strategy for self-repressive subspace learning and linearity-aware subspace learning.Finally,extensive experimental results are conducted to reveal the effectiveness of the proposed approach.