Distributed Sparse Multicategory Discriminant Analysis

TL;DR

This paper introduces a convex approach for sparse multicategory discriminant analysis that is effective in distributed data settings, maintaining performance comparable to centralized methods after limited communication rounds.

Contribution

It develops a novel convex formulation for distributed sparse multicategory discriminant analysis with theoretical guarantees and practical efficiency.

Findings

Distributed method matches centralized performance after few rounds

Theoretical analysis confirms statistical properties

Numerical studies validate effectiveness

Abstract

This paper proposes a convex formulation for sparse multicategory linear discriminant analysis and then extend it to the distributed setting when data are stored across multiple sites. The key observation is that for the purpose of classification it suffices to recover the discriminant subspace which is invariant to orthogonal transformations. Theoretically, we establish statistical properties ensuring that the distributed sparse multicategory linear discriminant analysis performs as good as the centralized version after {a few rounds} of communications. Numerical studies lend strong support to our methodology and theory.