Solution Path Clustering with Adaptive Concave Penalty

TL;DR

This paper introduces a novel clustering method using an adaptive concave penalty that generates a sequence of solutions without pre-specifying the number of clusters, effectively handling noisy data and high-dimensional challenges.

Contribution

It develops a regularization path-based clustering approach with an adaptive minimax concave penalty, enhancing cluster detection and noise separation without needing to predefine cluster count.

Findings

Outperforms existing clustering methods on simulated data

Shows competitive results on gene expression datasets

Capable of identifying relevant clusters and separating noise

Abstract

Fast accumulation of large amounts of complex data has created a need for more sophisticated statistical methodologies to discover interesting patterns and better extract information from these data. The large scale of the data often results in challenging high-dimensional estimation problems where only a minority of the data shows specific grouping patterns. To address these emerging challenges, we develop a new clustering methodology that introduces the idea of a regularization path into unsupervised learning. A regularization path for a clustering problem is created by varying the degree of sparsity constraint that is imposed on the differences between objects via the minimax concave penalty with adaptive tuning parameters. Instead of providing a single solution represented by a cluster assignment for each object, the method produces a short sequence of solutions that determines not only the cluster assignment but also a corresponding number of clusters for each solution. The optimization of the penalized loss function is carried out through an MM algorithm with block coordinate descent. The advantages of this clustering algorithm compared to other existing methods are as follows: it does not require the input of the number of clusters; it is capable of simultaneously separating irrelevant or noisy observations that show no grouping pattern, which can greatly improve data interpretation; it is a general methodology that can be applied to many clustering problems. We test this method on various simulated datasets and on gene expression data, where it shows better or competitive performance compared against several clustering methods.