Kernel Alignment Inspired Linear Discriminant Analysis

TL;DR

This paper introduces kaLDA, a new linear discriminant analysis method inspired by kernel alignment, which maximizes kernel similarity to improve classification, and demonstrates strong performance on multiple datasets.

Contribution

Proposes a novel kernel alignment-based LDA formulation that extends to multi-label data and uses a Stiefel-manifold gradient descent for optimization.

Findings

kaLDA performs well on multiple datasets.

The objective relates closely to classical LDA.

Effective for both single-label and multi-label problems.

Abstract

Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two kernels, data kernel and class indicator kernel. The problem is to find a subspace to maximize the alignment between subspace-transformed data kernel and class indicator kernel. Surprisingly, the kernel alignment induced kaLDA objective function is very similar to classical LDA and can be expressed using between-class and total scatter matrices. This can be extended to multi-label data. We use a Stiefel-manifold gradient descent algorithm to solve this problem. We perform experiments on 8 single-label and 6 multi-label data sets. Results show that kaLDA has very good performance on many single-label and multi-label problems.