Principal Components along Quiver Representations
Offered By: Institute for Pure & Applied Mathematics (IPAM) via YouTube
Course Description
Overview
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.
Syllabus
Introduction
Tensors
Blocks
Quiver representation
Optimization Problem
Space of Sections
General Quiver
Optimization
Principal Components
Taught by
Institute for Pure & Applied Mathematics (IPAM)
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