Covariance data as represented by symmetric positive definite (SPD) matrices are ubiquitous throughout technical study as efficient descriptors of interdependent systems. Euclidean analysis of SPD matrices, while computationally fast, can lead to skewed and even unphysical interpretations of data. Riemannian methods preserve the geometric structure of SPD data at the cost of expensive eigenvalue computations. In this paper, we propose a geometric method for unsupervised clustering of SPD data based on the Thompson metric. This technique relies upon a novel "inductive midrange" centroid computation for SPD data, whose properties are examined and numerically confirmed. We demonstrate the incorporation of the Thompson metric and inductive midrange into X-means and K-means++ clustering algorithms.
Multi-modal Graph Fusion for Inductive Disease Classification in Incomplete Datasets
Technical University of Munich (TUM)（慕尼黑工业大学）；German Center for Vertigo and Balance Disorders (DSGZ), Ludwig-Maximilians-Universität (LMU)（路德维希-马克西米利安大学（LMU）德国眩晕与平衡障碍中心（DSGZ））；Johns Hopkins University（约翰斯·霍普金斯大学）
STREAM: A Universal State-Space Model for Sparse Geometric Data
Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI)（可扩展数据分析与人工智能中心（ScaDS.AI））；Centre for Tactile Internet (CeTI) with Human-in-the-Loop（人机协作触觉互联网中心（CeTI））；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）；Bielefeld University（比勒费尔德大学）；TUD Dresden University of Technology（德累斯顿工业大学）；BITS Pilani（皮拉尼 Bits 大学）
