# Kernel Alignment Inspired Linear Discriminant Analysis

arXiv: https://arxiv.org/abs/1610.04576 · HTML: https://mlsanity.com/paper/1610.04576/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2016.

## Built on by (most cited first, 1 of 1)

- [On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants](https://mlsanity.com/paper/2605.03283/) (2026)

## Abstract (arXiv)

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.