📝 Selected Publications

Gyrogroup Batch Normalization
Ziheng Chen, Yue Song, Xiaojun Wu, Nicu Sebe. [Code]

• Proposes pseudo-reductive gyrogroups, a relaxed structure of gyrogroups, with complete theoretical analyses.
• Establishes the conditions for theoretical control over sample statistics in Riemannian batch normalization over gyrogroups, i.e., pseudo-reduction and gyroisometric gyrations.
• Introduces a GyroBN framework for Riemannian Batch Normalization over gyrogroups, applicable to various geometries.
• Manifests GyroBN on the Grassmannian and hyperbolic spaces.

Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry
Ziheng Chen, Yue Song, Xiaojun Wu, Gaowen Liu, Nicu Sebe. [Code]

• Explains the working mechanism of matrix functions in Global Covariance Pooling from the perspectives of tangent and Riemannian classifiers, and finally claims that the rationality of matrix functions should be attributed to the Riemannian classifiers they implicitly respect.
• Validates the theoretical argument on the ImageNet and three FGVC datasets through comprehensive experiments.

RMLR: Extending Multinomial Logistic Regression into General Geometries
Ziheng Chen, Yue Song, Rui Wang, Xiaojun Wu, Nicu Sebe. [Code]

• Extends our flat SPD MLR (CVPR24) into Riemannian MLR over general geometries.
• Proposes five families of SPD MLRs based on different geometries of the SPD manifold.
• Proposes a novel Lie MLR for deep neural networks on rotation matrices.

A Lie Group Approach to Riemannian Batch Normalization
Ziheng Chen, Yue Song, Yunmei Liu, Nicu Sebe. [Code]

• Propose a Riemannian batch normalization (LieBN) framework over general Lie groups, with controllable first- and second-order statistical moments.
• Manifests specific LieBN layers on SPD manifolds under three deformed Lie groups as well as the Lie group of rotation matrices.

Riemannian Multinomial Logistics Regression for SPD Neural Networks
Ziheng Chen, Yue Song, Gaowen Liu, Ramana Rao Kompella, Xiaojun Wu, Nicu Sebe. [Code]

• Extends the Euclidean Multinomial Logistic Regression (MLR) to the SPD manifold under flat Riemannian metrics.
• Manifests the framework on the Log-Euclidean (LE) and Log-Cholesky (LC) metrics.
• Provides the first intrinsic explanation for the widely used LogEig classifier.

Product Geometries on Cholesky Manifolds with Applications to SPD Manifolds
Ziheng Chen, Yue Song, Xiao-Jun Wu, Nicu Sebe. [Code]

• Identifies the underlying product structure in the existing Cholesky metric.
• Introduces two novel Riemannian metrics on the Cholesky manifold, along with a comprehensive analysis of their geometric properties.
• Proposes two numerically stable Riemannian metrics on the SPD manifold, with a detailed analysis of their geometric properties.

Adaptive Log-Euclidean Metrics for SPD Matrix Learning
Ziheng Chen, Yue Song, Tianyang Xu, Zhiwu Huang, Xiao-Jun Wu, and Nicu Sebe. [Code]

• Proposes a general framework for pullback metrics over the SPD manifold from the Euclidean space.
• Extends the existing Log-Euclidean Metric (LEM) into ALEM.