Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reduction

• URL: http://arxiv.org/abs/2502.00168v3
• Date: Fri, 30 May 2025 16:27:22 GMT
• Title: Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reduction
• Authors: Daniel Herrera-Esposito, Johannes Burge,
• Abstract summary: Supervised dimensionality reduction aims to map labeled data to a low-dimensional feature space while maximizing class discriminability.<n>We present Supervised Quadratic Feature Analysis (SQFA), a linear dimensionality reduction method that maximizes Fisher-Rao distances between class distributions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Supervised dimensionality reduction aims to map labeled data to a low-dimensional feature space while maximizing class discriminability. Directly computing discriminability is often impractical, so an alternative approach is to learn features that maximize a distance or dissimilarity measure between classes. The Fisher-Rao distance is an important information geometry distance in statistical manifolds. It is induced by the Fisher information metric, a tool widely used for understanding neural representations. Despite its theoretical and pratical appeal, Fisher-Rao distances between classes have not been used as a maximization objective in supervised feature learning. Here, we present Supervised Quadratic Feature Analysis (SQFA), a linear dimensionality reduction method that maximizes Fisher-Rao distances between class distributions, by exploiting the information geometry of the symmetric positive definite manifold. SQFA maximizes distances using first- and second-order statistics, and its features allow for quadratic discriminability (i.e. QDA performance) matching or surpassing state-of-the-art methods on real-world datasets. We theoretically motivate Fisher-Rao distances as a proxy for quadratic discriminability, and compare its performance to other popular distances (e.g. Wasserstein distances). SQFA provides a flexible state-of-the-art method for dimensionality reduction. Its successful use of Fisher-Rao distances between classes motivates future research directions.

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