In this paper, we address the problem of Domain Adaptation (DA) using Optimal Transport (OT) on Riemannian manifolds. We model the difference between two domains by a diffeomorphism and use the polar factorization theorem to claim that OT is indeed optimal for DA in a well-defined sense, up to a volume preserving map. We then focus on the manifold of Symmetric and Positive-Definite (SPD) matrices, whose structure provided a useful context in recent applications. We demonstrate the polar factorization theorem on this manifold. Due to the uniqueness of the weighted Riemannian mean, and by exploiting existing regularized OT algorithms, we formulate a simple algorithm that maps the source domain to the target domain. We test our algorithm on two Brain-Computer Interface (BCI) data sets and observe state of the art performance.
Deep Optimal Transport for Domain Adaptation on SPD Manifolds
College of Computing and Data Science, Nanyang Technological University（计算与数据科学学院，南洋理工大学）；Université Paris-Saclay, Inria, CEA, Palaiseau, France（巴黎-萨克雷大学，法国国家信息与自动化技术研究所，法国原子能委员会，Palaiseau）
Learning Log-Determinant Divergences for Positive Definite Matrices
Mitsubishi Electric Research Labs (MERL)（三菱电机研究实验室）；Australian Centre for Robotic Vision, Australian National University（澳大利亚国立大学澳大利亚机器人视觉中心）；University of Minnesota（明尼苏达大学）；Research School of Engineering, The Australian National University（澳大利亚国立大学工程研究学院）；Monash University（莫纳什大学）；Data61-CSIRO（澳大利亚联邦科学与工业研究组织数据61）
SPDIM: Source-Free Unsupervised Conditional and Label Shift Adaptation in EEG
Nara Institute of Science and Technology (NAIST)（奈良科学技术大学）；Department of Dynamic Brain Imaging, ATR（动态脑成像部门，ATR）；Center for Advanced Intelligence Project, RIKEN（先进智能项目中心，RIKEN）
SPD domain-specific batch normalization to crack interpretable unsupervised domain adaptation in EEG
RIKEN Center for Advanced Intelligence Project (RIKEN AIP)（理化学研究所先进智能项目中心）；Advanced Telecommunications Research Institute International (ATR)（国际电气通信基础技术研究所）
Department of Applied Mathematics and Theoretical Physics, University of Cambridge（应用数学与理论物理系，剑桥大学）；Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU)（数学科学系，挪威科学技术大学（NTNU））；Department of Mathematics, Simon Fraser University（数学系，西蒙·弗雷泽大学）
Fusion of Physiological and Behavioural Signals on SPD Manifolds with Application to Stress and Pain Detection
CNRS（法国国家科学研究中心）；University of Lille（里尔大学）；Centrale Lille（里尔中央理工学院）；IMT Nord Europe（法国北部高等矿业电信学院）；Institut Mines-Télécom（法国矿业电信学院）；INSERM（法国国家健康与医学研究院）
Learning to Normalize on the SPD Manifold under Bures-Wasserstein Geometry
School of Artificial Intelligence and Computer Science, Jiangnan University（江南大学人工智能与计算机学院）；Department of Information Engineering and Computer Science, University of Trento（特伦托大学信息工程与计算机科学系）
Riemannian Networks over Full-Rank Correlation Matrices
Department of Information Engineering and Computer Science, University of Trento, Trento, Italy（特伦托大学信息工程与计算机科学系）；School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, China（江南大学人工智能与计算机科学学院）
Towards Robust EEG Decoding Based on Riemannian Self-Attention
School of Artificial Intelligence and Computer Science（人工智能与计算机科学学院）；Jiangnan University（江南大学）；Department of Information Engineering and Computer Science（信息工程与计算机科学系）；University of Trento（特伦托大学）；Centre for Vision, Speech and Signal Processing (CVSSP)（视觉、语音与信号处理中心）；University of Surrey（萨里大学）
A Unified SPD Token Transformer Framework for EEG Classification: Systematic Comparison of Geometric Embeddings
Independent Researcher（独立研究者）；Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan（国家阳明交通大学电子物理系）；Department of Mathematics, Boise State University, Boise, ID, USA（数学系，博伊州立大学）
Wrapped Gaussian on the manifold of Symmetric Positive Definite Matrices
LAMSADE, CNRS, PSL Univ. Paris-Dauphine, France（巴黎-萨克雷大学巴黎-达菲学院、国家科学研究中心、巴黎-达菲大学）；Inria center at the University of Bordeaux / LaBRI, France（波尔多大学/LaBRI与Inria中心）；TAU, LISN, University Paris-Saclay, France（巴黎-萨克雷大学、LISN、TAU）
Geodesic Optimization for Predictive Shift Adaptation on EEG data
Inria（法国国家信息与自动化研究所）；CEA（法国原子能和替代能源委员会）；Université Paris-Saclay（巴黎萨克雷大学）；TAU（特拉维夫大学）；LISN-CNRS（法国国家科学研究中心南巴黎大学实验室）；Roche Pharma Research and Early Development（罗氏制药研发与早期研发部）；Neuroscience and Rare Diseases（神经科学与罕见病部）；Roche Innovation Center Basel（罗氏巴塞尔创新中心）；F. Hoffmann–La Roche Ltd.（霍夫曼-拉罗什有限公司）
Joint Tensor-Train Parameterization for Efficient and Expressive Low-Rank Adaptation
Georgia Institute of Technology（佐治亚理工学院）；National Taiwan University（国立台湾大学）；University of Palermo（帕尔米奥大学）；NVIDIA Research（NVIDIA研究）；Hon-Hai Quantum Computing Research Center（鸿海量子计算研究中心）
Selective Aggregation for Low-Rank Adaptation in Federated Learning
The University of Hong Kong（香港大学）；Stanford University（斯坦福大学）；Shenyang Institute of Automation, Chinese Academy of Sciences（中国科学院沈阳自动化研究所）；Materials Innovation Institute for Life Sciences and Energy (MILES), HKU-SIRI（香港大学-SIRI生命科学与能源材料创新研究所）
Emory University（埃默里大学）；University of Chicago（芝加哥大学）；Georgia Institute of Technology（佐治亚理工学院）；University of International Business and Economics（对外经济贸易大学）
Department of Information Engineering and Computer Science, University of Trento（信息工程与计算机科学系，特伦托大学）；Computing and Mathematical Sciences, Caltech（计算与数学科学系，加州理工学院）；School of Artificial Intelligence and Computer Science, Jiangnan University（人工智能与计算机科学学院，江南大学）
DoRAN: Stabilizing Weight-Decomposed Low-Rank Adaptation via Noise Injection and Auxiliary Networks
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Science, VNU-HCM（胡志明市国家大学科学大学）；Vietnam National University, Ho Chi Minh City（胡志明市越南国家大学）；Trivita AI
