Tensor Decomposition, Sparse Representations and Applications

on YouTube ↗58m

" summary

Recasts symmetric tensor decomposition as recovering a truncated power-series (sum of exponentials) and proves a concrete algorithm: build the truncated moment/Hankel matrix, do Gram–Schmidt orthogonalization to find its kernel, use the flat extension criterion to certify a zero‑dimensional ideal, assemble multiplication matrices and eigenvectors to read off points and weights. Works with low rank (often using ~2R samples in the univariate Prony case), extends to multiplicities (cactus/generalized rank), and performs robustly on examples (binary case in D log^2 D time, diffusion‑MRI with three components).

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" chapters (6)

1. 0:00Tensor decomposition intro
2. 12:55Prony's method and recurrences
3. 25:54Binary tensor decomposition
4. 37:33Flat extension and basis
5. 47:27Generalized tensor decomposition
6. 53:13Completion and matrix rank

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