Fuzzy Discriminant Clustering with Fuzzy Pairwise Constraints

TL;DR

This paper introduces a fuzzy discriminant clustering model that incorporates fuzzy pairwise constraints, enabling more nuanced semi-supervised clustering by capturing complex sample relationships and extending to various metric spaces.

Contribution

It proposes a novel fuzzy discriminant clustering model using fuzzy pairwise constraints and develops algorithms guaranteeing convergence and global solutions.

Findings

Outperforms state-of-the-art clustering models on benchmark datasets.

Effectively captures complex relationships between samples.

Extends to multiple metric spaces including RKHS.

Abstract

In semi-supervised fuzzy clustering, this paper extends the traditional pairwise constraint (i.e., must-link or cannot-link) to fuzzy pairwise constraint. The fuzzy pairwise constraint allows a supervisor to provide the grade of similarity or dissimilarity between the implicit fuzzy vectors of a pair of samples. This constraint can present more complicated relationship between the pair of samples and avoid eliminating the fuzzy characteristics. We propose a fuzzy discriminant clustering model (FDC) to fuse the fuzzy pairwise constraints. The nonconvex optimization problem in our FDC is solved by a modified expectation-maximization algorithm, involving to solve several indefinite quadratic programming problems (IQPPs). Further, a diagonal block coordinate decent (DBCD) algorithm is proposed for these IQPPs, whose stationary points are guaranteed, and the global solutions can be obtained under certain conditions. To suit for different applications, the FDC is extended into various metric spaces, e.g., the Reproducing Kernel Hilbert Space. Experimental results on several benchmark datasets and facial expression database demonstrate the outperformance of our FDC compared with some state-of-the-art clustering models.