“天地有正气，杂然赋流形 – 文天祥”
I am a Ph.D. student affiliated with Multimedia and Human Understanding Group (MHUG) at University of Trento, Italy, advised by Prof. Nicu Sebe. My research lies in the intersection of machine learning and differential geometry. Specifically, my current focuses are geometric deep learning and theories of matrix manifolds.
Before my Ph.D. studies, I received a B.A. degree in logistics management from Shandong University, Jinan, China, and an M.S. degree in computer science and technology from Jiangnan University, Wuxi, China, under the supervision of Prof. Xiao-Jun Wu.
Currently, I co-supervise several students with Rui Wang.
🌟 News
- 2024.09: One paper on Riemannian classifiers over general geometries was accepted to NeurIPS 2024 (final rating: 877).
- 2024.08: One paper on adaptive Riemannian metrics for SPD matrix learning was accepted by TIP.
- 2024.04: One paper on Grassmannian self-attention was accepted to IJCAI 2024. Congrats Rui and Chen!
- 2024.03: Our CVPR 2024 paper on Riemannian classifiers was selected as poster to VALSE 2024.
- 2024.03: One paper on SPD deep metric learning was early accessed in TNNLS.
- 2024.02: One paper on Riemannian classifiers on SPD manifolds was accepted to CVPR 2024.
- 2024.01: One paper on Riemannian batch normalization on general Lie groups was accepted to ICLR 2024.
📝 Selected Publications
(† denotes the corresponding author)
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.
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 of 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.
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.
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.
A Grassmannian Manifold Self-Attention Network for Signal Classification
Rui Wang, Chen Hu, Ziheng Chen†, Xiao-Jun Wu†, Xiaoning Song. Code
- Designs the self-attention over the Grassmannian for EEG decoding.
Preprints
- Arxiv 2024 Understanding Matrix Function Normalizations in Covariance Pooling through the Lens of Riemannian Geometry, Ziheng Chen, Yue Song, Xiao-Jun Wu, Gaowen Liu, Nicu Sebe.
- Arxiv 2024 Product Geometries on Cholesky Manifolds with Applications to SPD Manifolds, Ziheng Chen, Yue Song, Xiao-Jun Wu, Nicu Sebe. [Code]
Conferences
- NeurIPS 2024 RMLR: Extending Multinomial Logistic Regression into General Geometries, Ziheng Chen, Yue Song, Rui Wang, Xiaojun Wu, Nicu Sebe. [Code] [Slides] [Poster]
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IJCAI 2024 A Grassmannian Manifold Self-Attention Network for Signal Classification, Rui Wang, Chen Hu, Ziheng Chen†, Xiao-Jun Wu†, Xiaoning Song. [Code]
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CVPR 2024 Riemannian Multinomial Logistics Regression for SPD Neural Networks, Ziheng Chen, Yue Song, Gaowen Liu, Ramana Rao Kompella, Xiaojun Wu, Nicu Sebe. [Code] [Slides] [Poster] [Video]
- ICLR 2024 A Lie Group Approach to Riemannian Batch Normalization, Ziheng Chen, Yue Song, Yunmei Liu, Nicu Sebe. [Code] [Slides] [Poster] [Video]
- AAAI 2023 Riemannian Local Mechanism for SPD Neural Networks, Ziheng Chen, Tianyang Xu, Xiao-Jun Wu, Rui Wang, Zhiwu Huang, Josef Kittler. [Code] [Slides] [Poster]
Journals
- TIP 2024 Adaptive Log-Euclidean Metrics for SPD Matrix Learning, Ziheng Chen, Yue Song, Tianyang Xu, Zhiwu Huang, Xiao-Jun Wu, and Nicu Sebe. [Code]
- TNNLS 2024 SPD Manifold Deep Metric Learning for Image Set Classification, Rui Wang, Xiao-Jun Wu, Ziheng Chen, Cong Hu, Josef Kittler. [Code]
- TBD 2021 Hybrid Riemannian Graph-Embedding Metric Learning for Image Set Classification, Ziheng Chen, Tianyang Xu, Xiao-Jun Wu, Rui Wang, Josef Kittler. [Code]
🎖 Honors and Awards
- 2023.12, Excellent Master’s Thesis of Jiangsu Association of Artificial Intelligence (江苏省人工智能学会优秀硕士论文)
💬 Talks and Short Courses
- 2024.03, Naïve Riemannian Geometry: A One Hour Tour. Jiangnan University internal talk (online).
📖 Courses
To obtain basic foundations for my research, I have self-studied several math courses, most of which were done during my master studies:
- Mathematical Analysis I, II, III, Real Analysis, Complex Analysis, Functional Analysis;
- Advanced Algebra I, II, Abstract Algebra I;
- Topology, Differential Geometry, Differential Manifolds, Riemannian Geometry;
- Differential Equations, Convex Optimization, Numerical Optimization…
💻 Personal Channels
- Differential Equations (1k+ viewers)
- Topology (1k+ viewers)
- Differential Geometry (9k+ viewers)
- Riemannian Geometry (2k+ viewers)