Eckart–Young–Mirsky Theorem and Proof

Показать описание

Low Rank Matrix Approximation
Eckart–Young–Mirsky Theorem
Proof of the Theorem (for Euclidean norm)

Sanjoy Das

Рекомендации по теме

Комментарии

indeed, amazing work, do you know why are we using the constrain ||w||=1, from what i understood it's for simplyfing things, cause the scaling on a unit vector will be the same on all span(w) = a * w, a =real scalar, it's a aproach in physics where we calculate the electric field inside a gaussian sphere, or am i wrong ?

aymenferhat

hello, one quick question here: in 19:10, you mentioned that A'w = 0 can be ignored when minimize |Aw|. But i don't understand why here you ignore this condition because i think if we don't consider A'w = 0, the minimize objective in righthand side will be |Aw-A'w|.

yuezhao

why must w be expresses in terms of the first R+1 columns of V ? why not any other orthogonal basis of R+1 elements?

ibi

Eckart–Young–Mirsky Theorem and Proof

Eckart–Young–Mirsky Theorem and Proof

W6 Explanation - Proof of Eckart Young Mirsky Theorem

The Eckart-Young Theorem

W6 Proof of Eckart Young Mirsky Theorem

PCA and Its Beyond (PCA, SVD, Low-Rank Approximation, Eckart–Young–Mirsky Theorem)

7. Eckart-Young: The Closest Rank k Matrix to A

Multivariate Statistics: 3.5 SVD low rank approximation

Singular Value Decomposition

W5 Eckart Young Mirsky Theorem and Low Rank Approximation

2.3.6 The best rank k approximation

Advanced Linear Algebra - Lecture 41: Low Rank Approximation and Image Compression

Gerlind Plonka, Optimal Rank-1 Hankel Approximation of Matrices, 2020.11.03

Partial Orders 3: Examples, Mirsky's theorem, chain and antichain decomposition to understand P...

Análisis Matricial 25. Teorema de Eckart-Young

Dilworth Theorem for Competitive Programming | Mirsky's Theorem | Bipartite Matching | Flow

2.1.1 Launch: Low rank approximation

LinearData21cPCAapprox

SVD and rank deficient matrices

PCA by Determinant Optimization has no Spurious Local Optima

Piotr Indyk - Learning-Based Low-Rank Approximations - IPAM at UCLA

(Lecture 22) SVD: Low Rank Approximation

Bias-Variance Tradeoff in Low Rank Approximations

A nice proof in complex numbers using demoivres theorem

Mathematics of Machine Learning: Lecture 4, Afonso S. Bandeira (ETHZ, Spring 2021)