Kernel Spectral Clustering

TL;DR

This paper introduces a modified spectral clustering algorithm that automatically estimates the number of clusters and analyzes its convergence in a Hilbert space, with potential applications in learning transformation-invariant image representations.

Contribution

It proposes a new spectral clustering algorithm with automatic cluster number estimation and provides theoretical convergence analysis in a Hilbert space setting.

Findings

The algorithm converges under certain conditions.

It can estimate the number of clusters automatically.

Potential for learning transformation-invariant features.

Abstract

We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We modify the algorithm proposed by Ng, Jordan and Weiss in order to propose a new algorithm that automatically estimates the number of clusters and we characterize the convergence of this new algorithm in terms of convergence of Gram operators. We also give a hint of how this approach may lead to learn transformation-invariant representations in the context of image classification.