Fast Approximate $K$-Means via Cluster Closures

TL;DR

This paper introduces a fast approximate $K$-Means algorithm that reduces computational costs by efficiently identifying active points near cluster boundaries, improving clustering speed and quality for large datasets.

Contribution

The paper presents a novel approximate $K$-Means method using cluster closures and neighborhood information to significantly speed up the assignment step.

Findings

Outperforms state-of-the-art approximate $K$-Means in efficiency.

Achieves comparable or better clustering quality.

Effective in image data clustering and retrieval applications.

Abstract

$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are computed and each data point is re-assigned to its nearest center. The cluster re-assignment step becomes prohibitively expensive when the number of data points and cluster centers are large. In this paper, we propose a novel approximate $k$-means algorithm to greatly reduce the computational complexity in the assignment step. Our approach is motivated by the observation that most active points changing their cluster assignments at each iteration are located on or near cluster boundaries. The idea is to efficiently identify those active points by pre-assembling the data into groups of neighboring points using multiple random spatial partition trees, and to use the neighborhood information to construct a closure for each cluster, in such a way only a small number of cluster candidates need to be considered when assigning a data point to its nearest cluster. Using complexity analysis, image data clustering, and applications to image retrieval, we show that our approach out-performs state-of-the-art approximate $k$-means algorithms in terms of clustering quality and efficiency.