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Explore a comprehensive mathematical framework extending Frechet means through this 48-minute conference talk from Harvard CMSA's Conference on Geometry and Statistics. Learn about generalized Frechet means as minimizers of cost functions, with the distinctive feature of allowing random minimizing domains that differ from population counterparts. Discover how this framework encompasses various Frechet mean extensions from existing literature while broadening applicability to diverse statistical scenarios, including sequential dimension reduction for non-Euclidean data. Examine the establishment of strong consistency theorems for these generalized means and investigate practical applications including consistency verification for principal geodesic analysis on hyperspheres, compositional principal component analysis on composition spaces, and k-medoids clustering for metric space data.
