Compound Rank-k Projections for Bilinear Analysis

TL;DR

This paper introduces a novel Compound Rank-k Projection (CRP) algorithm for bilinear analysis that directly handles matrix data, preserves correlations, reduces complexity, and enhances discriminant ability through multiple projection models.

Contribution

The paper proposes a flexible CRP algorithm that directly processes matrices, increasing search space and discriminant power compared to existing methods.

Findings

CRP preserves matrix correlations and reduces computation complexity.

CRP's objective function increases monotonically, ensuring stable optimization.

Using multiple rank-k projections enhances discriminant analysis performance.

Abstract

In many real-world applications, data are represented by matrices or high-order tensors. Despite the promising performance, the existing two-dimensional discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection, making the model less flexible. In this paper, we propose a novel Compound Rank-k Projection (CRP) algorithm for bilinear analysis. CRP deals with matrices directly without transforming them into vectors, and it therefore preserves the correlations within the matrix and decreases the computation complexity. Different from the existing two dimensional discriminant analysis algorithms, objective function values of CRP increase monotonically.In addition, CRP utilizes multiple rank-k projection models to enable a larger search space in which the optimal solution can be found. In this way, the discriminant ability is enhanced.