Integrative Generalized Convex Clustering Optimization and Feature Selection for Mixed Multi-View Data

TL;DR

This paper introduces iGecco+, a convex optimization framework for integrative clustering and feature selection in high-dimensional multi-view data, demonstrating superior performance on real-world datasets.

Contribution

It develops a novel convex formalization for multi-view clustering with feature selection, employing adaptive penalties and an efficient multi-block ADMM algorithm.

Findings

iGecco+ outperforms existing methods in empirical tests

Effective feature selection improves clustering accuracy

Applicable to high-dimensional text and genomics data

Abstract

In mixed multi-view data, multiple sets of diverse features are measured on the same set of samples. By integrating all available data sources, we seek to discover common group structure among the samples that may be hidden in individualistic cluster analyses of a single data-view. While several techniques for such integrative clustering have been explored, we propose and develop a convex formalization that will inherit the strong statistical, mathematical and empirical properties of increasingly popular convex clustering methods. Specifically, our Integrative Generalized Convex Clustering Optimization (iGecco) method employs different convex distances, losses, or divergences for each of the different data views with a joint convex fusion penalty that leads to common groups. Additionally, integrating mixed multi-view data is often challenging when each data source is high-dimensional. To perform feature selection in such scenarios, we develop an adaptive shifted group-lasso penalty that selects features by shrinking them towards their loss-specific centers. Our so-called iGecco+ approach selects features from each data-view that are best for determining the groups, often leading to improved integrative clustering. To fit our model, we develop a new type of generalized multi-block ADMM algorithm using sub-problem approximations that more efficiently fits our model for big data sets. Through a series of numerical experiments and real data examples on text mining and genomics, we show that iGecco+ achieves superior empirical performance for high-dimensional mixed multi-view data.