Logistic Regression on Riemann Manifolds

Target audience: Advanced

Estimated reading time: 6'

Posts history

Newsletter: Geometric Learning in Python        

Traditional linear models in machine learning, such as logistic regression, struggle to grasp the complex characteristics of data in very high dimensions. 

Symmetric Positive Definite manifolds improve the output quality of logistic regression by enhancing feature representation in a lower-dimensional space.

Table of Contents

Introduction

Logistic regression on manifolds

        Logistic regression

        SPD manifolds

        Logarithmic map

        Affine invariant Riemannian metric

        Log Euclidean Riemannian metric

Implementation

        Setup

        Data generation

        Manifold creation

Validation

        Euclidean space

        Classification on SPD manifolds

References

Appendix

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What you will learn: How to implement and validate a binary logistic regression classifier on SPD manifolds using affine invariant and log Euclidean metrics.