Convex Covariate Clustering for Classification
This work addresses a domain-specific issue in data compression and interpretability for classification tasks, representing an incremental improvement over existing clustering methods.
The paper tackles the problem of clustering covariates independently from classification, which can harm interpretability and compression, by proposing a convex optimization method that integrates class label information and a-priori similarity, with experiments on synthetic and real data confirming its usefulness.
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.