Sketched Subspace Clustering

TL;DR

This paper introduces Sketch-SC, a randomized subspace clustering method that uses random projections to efficiently handle large-scale, high-dimensional data while maintaining high clustering accuracy.

Contribution

The paper presents a novel randomized scheme for subspace clustering that significantly reduces computational complexity using data compression via random projections.

Findings

Sketch-SC achieves faster clustering on large high-dimensional datasets.

It maintains competitive accuracy compared to existing scalable SC methods.

Performance is validated through extensive experiments on real data.

Abstract

The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data. Subspace clustering (SC) is a relatively recent method that is able to successfully classify nonlinearly separable data in a multitude of settings. In spite of their high clustering accuracy, SC methods incur prohibitively high computational complexity when processing large volumes of high-dimensional data. Inspired by random sketching approaches for dimensionality reduction, the present paper introduces a randomized scheme for SC, termed Sketch-SC, tailored for large volumes of high-dimensional data. Sketch-SC accelerates the computationally heavy parts of state-of-the-art SC approaches by compressing the data matrix across both dimensions using random projections, thus enabling fast and accurate large-scale SC. Performance analysis as well as extensive numerical tests on real data corroborate the potential of Sketch-SC and its competitive performance relative to state-of-the-art scalable SC approaches.