In this paper, we consider data acquired by multimodal sensors capturing complementary aspects and features of a measured phenomenon. We focus on a scenario in which the measurements share mutual sources of variability but might also be contaminated by other measurement-specific sources such as interferences or noise. Our approach combines manifold learning, which is a class of nonlinear data-driven dimension reduction methods, with the well-known Riemannian geometry of symmetric and positive-definite (SPD) matrices. Manifold learning typically includes the spectral analysis of a kernel built from the measurements. Here, we take a different approach, utilizing the Riemannian geometry of the kernels. In particular, we study the way the spectrum of the kernels changes along geodesic paths on the manifold of SPD matrices. We show that this change enables us, in a purely unsupervised manner, to derive a compact, yet informative, description of the relations between the measurements, in terms of their underlying components. Based on this result, we present new algorithms for extracting the common latent components and for identifying common and measurement-specific components.
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）
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）
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）
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）
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）
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）
Revisiting Multimodal KV Cache Compression: A Frequency-Domain-Guided Outlier-KV-Aware Approach
College of Future Information Technology, Fudan University（未来信息科技学院，复旦大学）；Shanghai Innovation Institute（上海创新研究院）；The Chinese University of Hong Kong（香港中文大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Zhangjiang Laboratory（张江实验室）
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）
