Continuum directions for supervised dimension reduction

TL;DR

This paper introduces continuum directions, a novel supervised dimension reduction technique that smoothly transitions between unsupervised and fully supervised methods, with strong theoretical backing and practical advantages.

Contribution

It proposes a new continuum regression-based basis for supervised dimension reduction, bridging principal component, mean difference, and linear discriminant directions.

Findings

Continuum directions effectively interpolate between different dimension reduction methods.

The method performs well in high-dimensional settings with binary supervision.

It offers faster computation and comparable or better performance than existing methods.

Abstract

Dimension reduction of multivariate data supervised by auxiliary information is considered. A series of basis for dimension reduction is obtained as minimizers of a novel criterion. The proposed method is akin to continuum regression, and the resulting basis is called continuum directions. With a presence of binary supervision data, these directions continuously bridge the principal component, mean difference and linear discriminant directions, thus ranging from unsupervised to fully supervised dimension reduction. High-dimensional asymptotic studies of continuum directions for binary supervision reveal several interesting facts. The conditions under which the sample continuum directions are inconsistent, but their classification performance is good, are specified. While the proposed method can be directly used for binary and multi-category classification, its generalizations to incorporate any form of auxiliary data are also presented. The proposed method enjoys fast computation, and the performance is better or on par with more computer-intensive alternatives.