Affinity Learning Via Self-Supervised Diffusion for Spectral Clustering

Abstract

Spectral clustering makes use of the spectrum of an input affinity matrix to segment data into disjoint clusters. The performance of spectral clustering depends heavily on the quality of the affinity matrix. Commonly used affinity matrices are constructed by either the Gaussian kernel or the self-expressive model with sparse or low-rank constraints. A technique called diffusion which acts as a post-process has recently shown to improve the quality of the affinity matrix significantly, by taking advantage of the contextual information. In this paper, we propose a variant of the diffusion process, named Self-Supervised Diffusion, which incorporates clustering result as feedback to provide supervisory signals for the diffusion process. The proposed method contains two stages, namely affinity learning with diffusion and spectral clustering. It works in an iterative fashion, where in each iteration the clustering result is utilized to calculate a pseudolabel similarity so that it can aid the affinity learning stage in the next iteration. Extensive experiments on both synthetic and real-world data have demonstrated that the proposed method can learn accurate and robust affinity, and thus achieves superior clustering performance.

Edge-based Local Push for Personalized PageRank

“…Let take the affinity graphs as an example. Affinity graphs are frequently used in a variety of practical tasks [43,50,58,59,61,63,67,68]. The nodes in affinity graphs (denoted as data points 𝑥 𝑖 ∈ R 𝑚 ) represent entities in the given data source.…”

“…Thus, small differences among pairwise distances can lead to significantly-skewed edge weights distribution. On the other hand, computing PPR values on affinity graphs is a commonly adopted technique for label propagation [67], spectral clustering [63], image segmentation [61] and relationship profiling [59]. Consequently, to apply LocalPush for PPR computation on such heavily unbalanced weighted graphs can invoke expensive but unnecessary time cost.…”

Multi-Scale Deep Subspace Clustering With Discriminative Learning

“…They comprise two steps, 1) learning the self-expressiveness coefficient matrix to construct an affinity matrix, and 2) applying spectral clus-tering algorithm on the affinity matrix to segment data. Some techniques are used to improve the quality of affinity matrix, i.e., diffusion process [11], [12]. In the self-expressiveness based subspace clustering methods, different types of regularizer are used for the self-expressiveness coefficient matrix to increase robustness to noise, and outliers.…”