Transformed Subspace Clustering

TL;DR

This paper introduces transformed subspace clustering (TSC), a novel approach that learns representations to make data separable into subspaces, improving clustering performance on image and document datasets.

Contribution

It proposes a new class of methods called transformed subspace clustering that jointly learns transformations and clustering, including kernelized extensions for non-linear data.

Findings

TSC outperforms state-of-the-art clustering methods on benchmark datasets.

Joint learning of transformation and clustering improves separability.

Kernelized TSC handles non-linear data effectively.

Abstract

Subspace clustering assumes that the data is sepa-rable into separate subspaces. Such a simple as-sumption, does not always hold. We assume that, even if the raw data is not separable into subspac-es, one can learn a representation (transform coef-ficients) such that the learnt representation is sep-arable into subspaces. To achieve the intended goal, we embed subspace clustering techniques (locally linear manifold clustering, sparse sub-space clustering and low rank representation) into transform learning. The entire formulation is jointly learnt; giving rise to a new class of meth-ods called transformed subspace clustering (TSC). In order to account for non-linearity, ker-nelized extensions of TSC are also proposed. To test the performance of the proposed techniques, benchmarking is performed on image clustering and document clustering datasets. Comparison with state-of-the-art clustering techniques shows that our formulation improves upon them.