Kernel Alignment Inspired Linear Discriminant Analysis

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.

Cite

Text

Zheng and Ding. "Kernel Alignment Inspired Linear Discriminant Analysis." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2014. doi:10.1007/978-3-662-44845-8_26

Markdown

[Zheng and Ding. "Kernel Alignment Inspired Linear Discriminant Analysis." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2014.](https://mlanthology.org/ecmlpkdd/2014/zheng2014ecmlpkdd-kernel/) doi:10.1007/978-3-662-44845-8_26

BibTeX

@inproceedings{zheng2014ecmlpkdd-kernel,
  title     = {{Kernel Alignment Inspired Linear Discriminant Analysis}},
  author    = {Zheng, Shuai and Ding, Chris H. Q.},
  booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
  year      = {2014},
  pages     = {401-416},
  doi       = {10.1007/978-3-662-44845-8_26},
  url       = {https://mlanthology.org/ecmlpkdd/2014/zheng2014ecmlpkdd-kernel/}
}