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RMLR: Extending Multinomial Logistic Regression into General Geometries
Ziheng Chen, Yue Song, Rui Wang +2
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-value…
Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry
Ziheng Chen, Yue Song, Xiao-Jun Wu +2
Global Covariance Pooling (GCP) has been demonstrated to improve the performance of Deep Neural Networks (DNNs) by exploiting second-order statistics of high-level representations.…
Fast and Stable Riemannian Metrics on SPD Manifolds via Cholesky Product Geometry
Ziheng Chen, Yue Song, Xiao-Jun Wu +1
Recent advances in Symmetric Positive Definite (SPD) matrix learning show that Riemannian metrics are fundamental to effective SPD neural networks. Motivated by this, we revisit th…
A Lie Group Approach to Riemannian Batch Normalization
Ziheng Chen, Yue Song, Yunmei Liu +1
Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and…