Robust Joint Graph Sparse Coding for Unsupervised Spectral Feature Selection

Abstract

In this paper, we propose a new unsupervised spectral feature selection model by embedding a graph regularizer into the framework of joint sparse regression for preserving the local structures of data. To do this, we first extract the bases of training data by previous dictionary learning methods and, then, map original data into the basis space to generate their new representations, by proposing a novel joint graph sparse coding (JGSC) model. In JGSC, we first formulate its objective function by simultaneously taking subspace learning and joint sparse regression into account, then, design a new optimization solution to solve the resulting objective function, and further prove the convergence of the proposed solution. Furthermore, we extend JGSC to a robust JGSC (RJGSC) via replacing the least square loss function with a robust loss function, for achieving the same goals and also avoiding the impact of outliers. Finally, experimental results on real data sets showed that both JGSC and RJGSC outperformed the state-of-the-art algorithms in terms of k -nearest neighbor classification performance.

Double regularized matrix factorization for image classification and clustering

“…In Tables 5 and 6, the number in parentheses is the number of the selected features that corresponds to the best clustering result. Since we use the same clustering experiment parameter setting with our previous work [21], the clustering results of some compared approaches are the same with [21]. Several interesting points can be observed from Tables 5 and 6.…”

“…The ten comparison approaches include LS [11], MCFS [8], SPEC [12], UDSFS [13], RUFS [16], RSR [18], SPNFSR [20], JGSC [21], NSSRD [23], and MFFS [27]. Meanwhile 4 , 10 5 } on all the databases.…”

“…To remedy it, a variety of extensions based on RSR have been put forward, i.e., Graph Regularized Nonnegative Self-Representation (GRNSR) [19] and Structure Preserving Nonnegative Feature Self-Representation (SPNFSR) [20]. Besides, Zhu et al combined manifold learning and sparse regression together and proposed Joint Graph Sparse Coding (JGSC) [21]. In JGSC, a dictionary is firstly learned from the training data; then, the feature weight matrix can be obtained automatically via the learned dictionary.…”

Simultaneous Bayesian Clustering and Feature Selection Through Student’s ${t}$ Mixtures Model

“…Existing feature selection algorithm can be categorized as supervised feature selection (on data with full class labels) [5]- [9], unsupervised feature selection (on data without class labels) [10]- [15], and semisupervised feature selection (on data with partial labels) [14], [16], [17]. Feature selection in unsupervised context is considered to be more difficult than the other two cases, since there is no target information available for training.…”

“…In [17], a global and local structure preservation framework that integrates global pairwise sample similarity and local geometric data structure is proposed for feature selection. In [15] and [28]- [31], spectral learning aiming to preserve the underlying manifold structure is applied for selecting proper features. In [32], embedding learning and sparse regression are jointly applied to perform feature selection.…”