Designing various component analysis at will

TL;DR

This paper introduces a versatile framework for component analysis that unifies various methods through a new mathematical expression, enabling flexible design of CA techniques including regularization, weighting, clustering, and semi-supervised extensions.

Contribution

It proposes the Generalized Pairwise Expression (GPE) framework, allowing systematic design of diverse CA methods by combining templates, simplifying the development process.

Findings

Unified framework covers standard and advanced CA methods

Enables easy creation of new CA algorithms via template combination

Demonstrates effectiveness through theoretical and experimental validation

Abstract

This paper provides a generic framework of component analysis (CA) methods introducing a new expression for scatter matrices and Gram matrices, called Generalized Pairwise Expression (GPE). This expression is quite compact but highly powerful: The framework includes not only (1) the standard CA methods but also (2) several regularization techniques, (3) weighted extensions, (4) some clustering methods, and (5) their semi-supervised extensions. This paper also presents quite a simple methodology for designing a desired CA method from the proposed framework: Adopting the known GPEs as templates, and generating a new method by combining these templates appropriately.