Twin Learning for Similarity and Clustering: A Unified Kernel Approach

TL;DR

This paper introduces a unified kernel-based model that simultaneously learns similarity matrices and cluster indicators, effectively handling nonlinear similarities and optimizing kernel selection for improved clustering performance.

Contribution

The paper presents a novel joint learning framework for similarity and clustering in kernel spaces, including multiple kernel learning, with theoretical analysis and extensive experiments.

Findings

Effective in capturing nonlinear similarities

Automatically selects optimal kernels for clustering

Outperforms existing methods in experiments

Abstract

Many similarity-based clustering methods work in two separate steps including similarity matrix computation and subsequent spectral clustering. However, similarity measurement is challenging because it is usually impacted by many factors, e.g., the choice of similarity metric, neighborhood size, scale of data, noise and outliers. Thus the learned similarity matrix is often not suitable, let alone optimal, for the subsequent clustering. In addition, nonlinear similarity often exists in many real world data which, however, has not been effectively considered by most existing methods. To tackle these two challenges, we propose a model to simultaneously learn cluster indicator matrix and similarity information in kernel spaces in a principled way. We show theoretical relationships to kernel k-means, k-means, and spectral clustering methods. Then, to address the practical issue of how to select the most suitable kernel for a particular clustering task, we further extend our model with a multiple kernel learning ability. With this joint model, we can automatically accomplish three subtasks of finding the best cluster indicator matrix, the most accurate similarity relations and the optimal combination of multiple kernels. By leveraging the interactions between these three subtasks in a joint framework, each subtask can be iteratively boosted by using the results of the others towards an overall optimal solution. Extensive experiments are performed to demonstrate the effectiveness of our method.