Subspace clustering via good neighbors

Finding the informative clusters of a high-dimensional dataset is at the core of numerous applications in computer vision, where spectral based subspace clustering algorithm is arguably the most widely-studied methods due to its empirical performance and provable guarantees under various assumptions. It is well-known that sparsity and connectivity of the affinity graph play important rules for effective subspace clustering. However, it is difficult to simultaneously optimize both factors due to their conflicting nature, and most existing methods are designed to deal with only one factor. In this paper, we propose an algorithm to optimize both sparsity and connectivity by finding good neighbors which induce key connections among samples within a subspace. First, an initial coefficient matrix is generated from the input dataset. For each sample, we find its good neighbors which not only have large coefficients but are strongly connected to each other. We reassign the coefficients of good neighbors and eliminate other entries to generate a new coefficient matrix, which can be used by spectral clustering methods. Experiments on five benchmark datasets show that the proposed algorithm performs favorably against the state-of-the-art methods in terms of accuracy with a negligible increase in speed

Simultaneous subspace clustering and cluster number estimating based on triplet relationship

In this paper we propose a unified framework to discover the number of clusters and group the data points into different clusters using subspace clustering simultaneously. Real data distributed in a high-dimensional space can be disentangled into a union of low-dimensional subspaces, which can benefit various applications. To explore such intrinsic structure, stateof- the-art subspace clustering approaches often optimize a selfrepresentation problem among all samples, to construct a pairwise affinity graph for spectral clustering. However, a graph with pairwise similarities lacks robustness for segmentation, especially for samples which lie on the intersection of two subspaces. To address this problem, we design a hyper-correlation based data structure termed as the triplet relationship, which reveals high relevance and local compactness among three samples. The triplet relationship can be derived from the self-representation matrix, and be utilized to iteratively assign the data points to clusters. Based on the triplet relationship, we propose a unified optimizing scheme to automatically calculate clustering assignments. Specifically, we optimize a model selection reward and a fusion reward by simultaneously maximizing the similarity of triplets from different clusters while minimizing the correlation of triplets from same cluster. The proposed algorithm also automatically reveals the number of clusters and fuses groups to avoid over-segmentation. Extensive experimental results on both synthetic and real-world datasets validate the effectiveness and robustness of the proposed method

Automatic Model Selection in Subspace Clustering via Triplet Relationships

This paper addresses both the model selection (i.e., estimating the number of clusters K) and subspace clustering problems in a unified model. The real data always distribute on a union of low-dimensional sub-manifolds which are embedded in a high-dimensional ambient space. In this regard, the state-of-the-art subspace clustering approaches firstly learn the affinity among samples, followed by a spectral clustering to generate the segmentation. However, arguably, the intrinsic geometrical structures among samples are rarely considered in the optimization process. In this paper, we propose to simultaneously estimate K and segment the samples according to the local similarity relationships derived from the affinity matrix. Given the correlations among samples, we define a novel data structure termed the Triplet, each of which reflects a high relevance and locality among three samples which are aimed to be segmented into the same subspace. While the traditional pairwise distance can be close between inter-cluster samples lying on the intersection of two subspaces, the wrong assignments can be avoided by the hyper-correlation derived from the proposed triplets due to the complementarity of multiple constraints. Sequentially, we propose to greedily optimize a new model selection reward to estimate K according to the correlations between inter-cluster triplets. We simultaneously optimize a fusion reward based on the similarities between triplets and clusters to generate the final segmentation. Extensive experiments on the benchmark datasets demonstrate the effectiveness and robustness of the proposed approach