K-means for Evolving Data Streams

TL;DR

This paper introduces a new approach to streaming K-means clustering that handles concept drift without explicit detection, providing theoretical guarantees and demonstrating improved error convergence with novel initialization methods.

Contribution

It proposes a surrogate error function for streaming K-means that avoids explicit concept drift detection and introduces initialization techniques, with theoretical and experimental validation.

Findings

Surrogate error closely approximates the true streaming K-means error.

Proposed initialization methods improve convergence in streaming scenarios.

Algorithm effectively adapts to concept drift without explicit detection.

Abstract

Currently the amount of data produced worldwide is increasing beyond measure, thus a high volume of unsupervised data must be processed continuously. One of the main unsupervised data analysis is clustering. In streaming data scenarios, the data is composed by an increasing sequence of batches of samples where the concept drift phenomenon may happen. In this paper, we formally define the Streaming $K$-means(S$K$M) problem, which implies a restart of the error function when a concept drift occurs. We propose a surrogate error function that does not rely on concept drift detection. We proof that the surrogate is a good approximation of the S$K$M error. Hence, we suggest an algorithm which minimizes this alternative error each time a new batch arrives. We present some initialization techniques for streaming data scenarios as well. Besides providing theoretical results, experiments demonstrate an improvement of the converged error for the non-trivial initialization methods.