Fast Landmark Subspace Clustering

TL;DR

This paper introduces a fast landmark subspace clustering method that uses randomized kernels to significantly reduce computational complexity while maintaining high accuracy, demonstrated through experiments.

Contribution

It proposes a new randomized kernel approach for spectral clustering and introduces the Fast Landmark Subspace (FLS) algorithm for efficient clustering.

Findings

FLS achieves faster clustering with marginal accuracy loss.

The randomized kernel method reduces complexity to O(KnD).

Experiments show superior performance on synthetic and real datasets.

Abstract

Kernel methods obtain superb performance in terms of accuracy for various machine learning tasks since they can effectively extract nonlinear relations. However, their time complexity can be rather large especially for clustering tasks. In this paper we define a general class of kernels that can be easily approximated by randomization. These kernels appear in various applications, in particular, traditional spectral clustering, landmark-based spectral clustering and landmark-based subspace clustering. We show that for $n$ data points from $K$ clusters with $D$ landmarks, the randomization procedure results in an algorithm of complexity $O(KnD)$. Furthermore, we bound the error between the original clustering scheme and its randomization. To illustrate the power of this framework, we propose a new fast landmark subspace (FLS) clustering algorithm. Experiments over synthetic and real datasets demonstrate the superior performance of FLS in accelerating subspace clustering with marginal sacrifice of accuracy.