Information-Enhanced Subspace Clustering

In many real-world applications such as image and video processing,we need to deal with a large amount of high-dimensional data.Such data can often be well approximated by a union of multiple low-dimensional subspaces,where each subspace corresponds to a class or a category.Subspace clustering refers to find the segmentation of high-dimensional data according to their underlying low dimensional subspaces.Recently,subspace clustering has attracted a lot of attentions and many methods have been developed.Among them,methods based on spectral clustering are the most popular,which divided the problem in two steps.In the first step,an affinity matrix is built from the data.Secondly,the data are segmented by applying spectral clustering to the affinity matrix.Once a good affinity matrix is learned from the data,spectral clustering can do well to find the segmentation of the data.However,subspace clustering is unsupervised,which does not take into account the available information of data.With the weighted effect of clustering result,block diagonal prior and convolutional feature extraction,our work can be summarized in the following aspects:(1).A low rank and structured sparse subspace clustering algorithm(LRS3C)is proposed based on the weighted effect of clustering results.Iii order to overcome the possible connectivity defect in structured sparse sub-space clustering(S3C),we introduce the low rank regularization term and propose the low rank and structured sparse subspace clustering method.Based on Low Rank Representation(LRR),the structured sparse infor-mation of data samples is integrated into the process of affinity learning.On the other hand,LRS3C construct a joint optimization framework for both spectral clustering and affinity learning,which can be optimized by Linearized Alternating Direction Method(LADM).Experiments on two benchmark datasets show the effectiveness of our proposal.(2).Inspired by the success of Convolutional Neural Networks(CNN)for ex-traction powerful features from visual data and the block diagonal prior for learning a good affinity matrix from self-expression coefficients,we propose a jointly trainable feature extraction and affinity learning frame-work with the block diagonal prior,termed as Convolutional Subspace Clustering Network with Block Diagonal prior(ConvSCN-BD).In addi-tion,we derive the connection between the block diagonal prior and the subspace structured norm,and reveal that using the block diagonal prior on the affinity matrix is essentially incorporating the feedback informa-tion from spectral clustering.Experiments on three benchmark datasets demonstrated the effectiveness of our proposal.(3).Despite the great success in the recent development of subspace cluster-ing,its applicability to real applications is very limited as result of lacking feature learning.To achieve simultaneous feature learning and subspace clustering,we propose an end-to-end trainable framework,called Self-Supervised Convolutional Subspace Clustering Network(S2ConvSCN),that combines a ConvNet module(for feature learning),a self-expression module(for subspace clustering)and a spectral clustering module(for self-supervision)into a joint optimization framework.Particularly,we introduce a dual self-supervision that exploits the output of spectral clus-tering to supervise the training of the feature learning module and the self-expression module.Our experiments on four benchmark datasets show the effectiveness of the dual self-supervision and demonstrate superior perfor-mance of our proposed approach.(4).In some applications,partial side-information to indicate"must-link" or"cannot-link" in clustering is available.This leads to the task of sub-space clustering with side-information,we present an enhanced approach for constrained subspace clustering with side-information,termed Con-strained Structured Sparse Subspace Clustering plus(CS3C+),in which the side-information is used not only in the stage of learning an affinity matrix but also in the stage of spectral clustering.We conduct experiments on three cancer gene expression datasets to validate the effectiveness of our proposals.