[Paper Review] Enhanced Mode Clustering

Yen‐Chi Chen, Christopher R. Genovese+1 more|arXiv (Cornell University)|Jun 6, 2014

Bayesian Methods and Mixture Models44 references3 citations

TL;DR

This paper enhances mode clustering by introducing soft cluster assignments, a connectivity measure between clusters, and visualization techniques for density-based clusters. It improves interpretability and robustness by leveraging the basins of attraction of a density estimator’s modes, offering a more nuanced understanding of cluster structure without requiring predefined cluster counts.

ABSTRACT

Mode clustering is a nonparametric method for clustering that defines clusters as the basins of attraction of a density estimator’s modes. We provide several enhancements to mode clustering: (i) a “soft ” cluster assignment, (ii) a measure of connectivity between clusters, and (iii) an approach to visualizing the clusters.

Motivation & Objective

• To address limitations in traditional mode clustering by enabling soft cluster assignments instead of hard partitions.
• To develop a quantitative measure of connectivity between clusters to assess their structural relationships.
• To provide effective visualization methods for interpreting complex cluster configurations in high-dimensional data.
• To enhance the interpretability and robustness of mode clustering in practical applications.

Proposed method

• Proposes a soft cluster assignment using the posterior probability of data points belonging to each mode’s basin of attraction.
• Introduces a connectivity measure based on the minimum density along paths connecting clusters, quantifying cluster separation.
• Employs kernel density estimation (KDE) as the underlying density estimator to identify modes and their basins.
• Visualizes clusters using density contour plots and cluster assignment heatmaps to illustrate basin boundaries and assignment confidence.
• Uses gradient ascent paths from data points to locate their mode of attraction, forming the basis for cluster assignment.
• Applies the method to both synthetic and real-world datasets to validate robustness and interpretability.

Experimental results

Research questions

• RQ1 How can mode clustering be enhanced to provide probabilistic, rather than hard, cluster assignments?
• RQ2 What metrics can effectively quantify the connectivity or separation between clusters in a nonparametric framework?
• RQ3 How can cluster structures be meaningfully visualized to support interpretation and analysis?
• RQ4 To what extent do the proposed enhancements improve the robustness and interpretability of mode clustering in practice?

Key findings

• Soft cluster assignments provide a more nuanced representation of data points near cluster boundaries, reflecting uncertainty in cluster membership.
• The connectivity measure successfully identifies weakly connected clusters that may represent substructures or noise.
• Visualization techniques effectively reveal complex cluster geometries and assignment confidence across data regions.
• The enhanced method maintains the nonparametric nature of mode clustering while improving interpretability and robustness.
• The approach is effective on both low- and high-dimensional data, demonstrating scalability and practical utility.