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Explore principal components along quiver representations in this 34-minute lecture from the Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 workshop. Delve into the concept of quivers as sets of vertices and directed edges, and learn how their representations assign vector spaces to vertices and linear maps to edges. Discover how this framework generalizes tensors of multi-indexed data. Investigate the process of finding principal components compatible with the linear maps of quiver representations. Examine the computation of the vector space of sections and understand how principal components are derived through optimization over this space. Gain insights from the joint work of Anna Seigal, Vidit Nanda, and Heather Harrington, presented at the Institute for Pure and Applied Mathematics, UCLA.
