Doubly Stochastic Mean-Shift Clustering

2026-02-17

AI Summary

This work addresses the sensitivity of the traditional Mean-Shift algorithm to the bandwidth hyperparameter, which often leads to over-segmentation and spurious clusters in sparse data regimes. To mitigate this limitation, the authors propose Dual Stochastic Mean-Shift (DSMS), a novel variant that, for the first time, models the bandwidth as a random variable. In each iteration, DSMS jointly samples both data points and kernel radii stochastically, thereby introducing an implicit regularization mechanism that enhances exploration of the underlying density landscape. Theoretical analysis confirms that the proposed method preserves convergence guarantees. Experimental results on synthetic Gaussian mixture datasets demonstrate that DSMS significantly outperforms both standard Mean-Shift and existing stochastic variants, effectively suppressing over-segmentation without sacrificing clustering performance.

Technology Category

• Machine Learning: Semi-Supervised Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Standard Mean-Shift algorithms are notoriously sensitive to the bandwidth hyperparameter, particularly in data-scarce regimes where fixed-scale density estimation leads to fragmentation and spurious modes. In this paper, we propose Doubly Stochastic Mean-Shift (DSMS), a novel extension that introduces randomness not only in the trajectory updates but also in the kernel bandwidth itself. By drawing both the data samples and the radius from a continuous uniform distribution at each iteration, DSMS effectively performs a better exploration of the density landscape. We show that this randomized bandwidth policy acts as an implicit regularization mechanism, and provide convergence theoretical results. Comparative experiments on synthetic Gaussian mixtures reveal that DSMS significantly outperforms standard and stochastic Mean-Shift baselines, exhibiting remarkable stability and preventing over-segmentation in sparse clustering scenarios without other performance degradation.

Problem

• Mean-Shift
• bandwidth sensitivity
• data scarcity
• over-segmentation
• spurious modes

Innovation

• Doubly Stochastic Mean-Shift
• randomized bandwidth
• implicit regularization
• density estimation
• clustering stability