# Convex Covariate Clustering for Classification

## TL;DR

This paper introduces a convex covariate clustering method that incorporates class label information to improve interpretability and compression in classification tasks, with an efficient optimization algorithm and a new model selection criterion.

## Contribution

It presents a novel convex clustering approach that integrates class labels, along with a scalable ADMM solver and a marginal likelihood-based model selection criterion.

## Key findings

- Effective clustering on synthetic data
- Improved interpretability on real datasets
- Scalable to thousands of variables

## Abstract

Clustering, like covariate selection for classification, is an important step to compress and interpret the data. However, clustering of covariates is often performed independently of the classification step, which can lead to undesirable clustering results that harm interpretability and compression rate. Therefore, we propose a method that can cluster covariates while taking into account class label information of samples. We formulate the problem as a convex optimization problem which uses both, a-priori similarity information between covariates, and information from class-labeled samples. Like ordinary convex clustering [Chi and Lange, 2015], the proposed method offers a unique global minima making it insensitive to initialization. In order to solve the convex problem, we propose a specialized alternating direction method of multipliers (ADMM), which scales up to several thousands of variables. Furthermore, in order to circumvent computationally expensive cross-validation, we propose a model selection criterion based on approximating the marginal likelihood. Experiments on synthetic and real data confirm the usefulness of the proposed clustering method and the selection criterion.