Convex Clustering: An Attractive Alternative to Hierarchical Clustering

TL;DR

This paper introduces convex clustering, a method that combines the visual appeal of hierarchical clustering with improved robustness to noise, using a novel algorithm based on the proximal distance principle, and demonstrates its effectiveness on biological data.

Contribution

It develops a new convex clustering algorithm leveraging the proximal distance principle, offering improved accuracy and interpretability over traditional hierarchical clustering methods.

Findings

Convex clustering preserves hierarchical visualizations.

The method handles high-dimensional biological data effectively.

Software implementation supports GPU acceleration for speed.

Abstract

The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The current paper exploits the proximal distance principle to construct a novel algorithm for solving the convex clustering problem. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. Our convex clustering software separates parameters, accommodates missing data, and supports prior information on relationships. The software is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems.