Sparse Sample Self-representation For Subspace Clustering

In real applications, subspace clustering may find the low-dimensional representation of a high-dimensional data set by using only a small subset of the data set to describe the entire data set. This could greatly improve the efficiency of the processing of high-dimensional data. To date, there exist different types of subspace clustering methods, which have been designed for different applications. In these previous methods of subspace clustering, spectral subspace clustering is a classic method for dealing with high-dimensional data, as it usually takes the local or global information of the data into account to first construct an affinity matrix and then perform k-means clustering. Thus, in spectral subspace clustering, the similarity matrix is expected to describe the data distribution in detail for accurately reflecting the complex structure of the data, which takes the advantages of dealing with the high-dimensional data drawn from multiple subspaces. Thus, this paper proposes a sparse sample self-representation model to construct the affinity matrix, with the following steps and contributions:1. The proposed method takes the correlations among the samples (i.e., the sample self-representation property) into account to seek a subset of samples, which can be used for measuring the similarity of samples so that better reflecting the correlations among the samples.2. This paper employs a new sparse self-representation model to analyze the correlations among the samples. Specifically, the l1-norm regularization makes the self-representation matrix sparse, while the l2,1-norm regularization results in the row sparsity to reduce the influence of the noise or outliers so that leading to robustness.3. This paper also proposes a new optimization method to solve the resulting objective function. Moreover, the proposed optimization enables the algorithm to converge fast to its global solution by reducing the time complexity of the optimization algorithm and including the effectiveness of spectral subspace clustering.