From Correlations to Manifolds: A Geometric Approach to Classifications

İnan Ünal; Özal Yıldırım

Abstract

This study addresses a machine learning application based on Riemannian geometry. The main objective is to demonstrate how classical learning algorithms, particularly Support Vector Machine (SVM), can be adapted for non-Euclidean data structures. The UCI Wine dataset is used as a real dataset. Instead of directly applying the algorithm to raw feature vectors, correlation matrices are obtained from these vectors through class-consistent windows, defining points on the SPD manifold. These matrices are then projected onto the tangent space around the Fréchet mean using the Riemannian logarithm map and provided as input to a Euclidean-form SVM classifier. Thus, the integration of manifold-based representation with classical methods is achieved, and its contribution to classification performance is examined.

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