Intrinsic Riemannian Classifiers on the Deformed SPD Manifolds: A Unified Framework

Ziheng Chen, Yue Song, Yunmei Liu, Xiaojun Wu, Emanuele Strano, Nicu Sebe

Primary Area: learning on graphs and other geometries & topologies

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Keywords: Riemannian geometry, Riemannian classifier, SPD Neural Networks, Matrix manifolds

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

TL;DR: We propose a general framework for building intrinsic classifiers on Riemannian manifolds, and showcase our framework on different geometries of SPD manifolds

Abstract: Geometric deep learning, which extends deep learning techniques to non-Euclidean spaces, has gained significant attention in machine learning. To better classify non-Euclidean features in geometric deep learning, researchers started exploring intrinsic classifiers based on Riemannian geometry. However, existing approaches suffer from limited applicability due to their strong reliance on specific geometric properties. In this paper, we propose a general framework to design intrinsic Riemannian classifiers. Our framework exhibits broad applicability while requiring only minimal geometric properties, enabling its use with a wide range of Riemannian metrics on various Riemannian manifolds. Specifically, we focus on symmetric positive definite (SPD) manifolds and systematically study five families of deformed parameterized Riemannian metrics, developing diverse SPD classifiers respecting these metrics. The versatility and effectiveness of the proposed framework are showcased in three applications, including radar recognition, human action recognition, and electroencephalography (EEG) classification.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 4035