Leveraging Union of Subspace Structure to Improve Constrained Clustering

TL;DR

This paper introduces an active pairwise-constrained clustering method leveraging the union-of-subspaces model, significantly reducing human input and improving clustering accuracy in datasets with subspace structures.

Contribution

It proposes a novel query strategy based on subspace margins, applicable after any subspace clustering algorithm, to enhance clustering with minimal supervision.

Findings

Faster reduction in clustering error compared to state-of-the-art methods

Effective on datasets with subspace structure

Competitive performance on other datasets

Abstract

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this description, for example with face images or handwritten digits. While it is straightforward to request human input on these datasets, our goal is to reduce this input as much as possible. We present a pairwise-constrained clustering algorithm that actively selects queries based on the union-of-subspaces model. The central step of the algorithm is in querying points of minimum margin between estimated subspaces; analogous to classifier margin, these lie near the decision boundary. We prove that points lying near the intersection of subspaces are points with low margin. Our procedure can be used after any subspace clustering algorithm that outputs an affinity matrix. We demonstrate on several datasets that our algorithm drives the clustering error down considerably faster than the state-of-the-art active query algorithms on datasets with subspace structure and is competitive on other datasets.