Supervised Quadratic Feature Analysis: An Information Geometry Approach to Dimensionality Reduction

Abstract

Supervised dimensionality reduction seeks to map class-conditional data to a low-dimensional feature space while maximizing class discriminability. Although differences in class-conditional second-order statistics can often aid discriminability, most supervised dimensionality reduction methods focus on first-order statistics. Here, we present Supervised Quadratic Feature Analysis (SQFA), a dimensionality reduction technique that finds a set of features that preserves second-order differences between classes. For this, we exploit a relation between class discriminability and the Information geometry of second-moment (or covariance) matrices as points on the symmetric positive definite (SPD) manifold. We discuss the reasoning behind the approach, and demonstrate its utility in a simple vision task.

Cite

Text

Herrera-Esposito and Burge. "Supervised Quadratic Feature Analysis: An Information Geometry Approach to Dimensionality Reduction." NeurIPS 2024 Workshops: NeurReps, 2024.

Markdown

[Herrera-Esposito and Burge. "Supervised Quadratic Feature Analysis: An Information Geometry Approach to Dimensionality Reduction." NeurIPS 2024 Workshops: NeurReps, 2024.](https://mlanthology.org/neuripsw/2024/herreraesposito2024neuripsw-supervised/)

BibTeX

@inproceedings{herreraesposito2024neuripsw-supervised,
  title     = {{Supervised Quadratic Feature Analysis: An Information Geometry Approach to Dimensionality Reduction}},
  author    = {Herrera-Esposito, Daniel and Burge, Johannes},
  booktitle = {NeurIPS 2024 Workshops: NeurReps},
  year      = {2024},
  url       = {https://mlanthology.org/neuripsw/2024/herreraesposito2024neuripsw-supervised/}
}