Sketched Clustering via Hybrid Approximate Message Passing

TL;DR

This paper introduces a new sketched clustering algorithm using approximate message passing, which improves efficiency over existing methods like CL-OMPR and k-means++ for large datasets by reducing computational and sample complexity.

Contribution

The paper proposes a novel sketched clustering method based on approximate message passing, enhancing efficiency over prior sketching algorithms and traditional clustering methods.

Findings

More efficient than CL-OMPR in computational and sample complexity

Outperforms k-means++ for large datasets

Effective in reducing storage and extraction complexity

Abstract

In sketched clustering, a dataset of $T$ samples is first sketched down to a vector of modest size, from which the centroids are subsequently extracted. Advantages include i) reduced storage complexity and ii) centroid extraction complexity independent of $T$. For the sketching methodology recently proposed by Keriven, et al., which can be interpreted as a random sampling of the empirical characteristic function, we propose a sketched clustering algorithm based on approximate message passing. Numerical experiments suggest that our approach is more efficient than the state-of-the-art sketched clustering algorithm "CL-OMPR" (in both computational and sample complexity) and more efficient than k-means++ when $T$ is large.