Fuzzy based affinity learning for spectral clustering

Abstract

Spectral clustering makes use of spectral-graph structure of an affinity matrix to partition data into disjoint meaningful groups. It requires robust and appropriate affinity graphs as input in order to form clusters with desired structures. Constructing such affinity graphs is a nontrivial task due to the ambiguity and uncertainty inherent in the raw data. Most existing spectral clustering methods typically adopt Gaussian kernel as the similarity measure, and employ all available features to construct affinity matrices with the Euclidean distance, which is often not an accurate representation of the underlying data structures, especially when the number of features is large. In this paper, we propose a novel unsupervised approach, named Axiomatic Fuzzy Set-based Spectral Clustering (AFSSC), to generate more robust affinity graphs via identifying and exploiting discriminative features for improving spectral clustering. Specifically, our model is capable of capturing and combining subtle similarity information distributed over discriminative feature subspaces to more accurately reveal the latent data distribution and thereby lead to improved data clustering. We demonstrate the efficacy of the proposed approach on different kinds of data. The results have shown the superiority of the proposed approach compared to other state-of-the-art methods.