In multilinear algebra, the tensor rank decomposition, the exact decomposition of a tensor in terms of the minimum terms, is an open problem. Canonical polyadic decomposition (CPD) is a variant of the rank decomposition which computes the best fitting terms for a user specified . The CP decomposition has found some applications in linguistics and chemometrics. The CP rank was introduced by Frank Lauren Hitchcock in 1927 and later rediscovered several times, notably in psychometrics. The CP decomposition is referred to as CANDECOMP, PARAFAC, or CANDECOMP/PARAFAC (CP). Another popular generalization of the matrix SVD known as the higher-order singular value decomposition computes orthonormal mode matrices and has found applications in statistics, signal processing, computer vision, computer graphics, psychometrics. (Wikipedia).
Nick Vannieuwenhoven: "Sensitivity of tensor decompositions"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop III: Mathematical Foundations and Algorithms for Tensor Computations "Sensitivity of tensor decompositions" Nick Vannieuwenhoven - KU Leuven Abstract: Tensor decompositions such as the tensor rank de
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Singular Values of Tensors
From playlist Spring 2019 Symbolic-Numeric Computing
Average-Case Computational Complexity of Tensor Decomposition - Alex Wein
Computer Science/Discrete Mathematics Seminar I Topic: Average-Case Computational Complexity of Tensor Decomposition Speaker: Alex Wein Affiliation: University of California, Davis Date: October 24, 2022 Suppose we are given a random rank-r order-3 tensor---that is, an n-by-n-by-n array
From playlist Mathematics
Tensors Explained Intuitively: Covariant, Contravariant, Rank
Tensors of rank 1, 2, and 3 visualized with covariant and contravariant components. My Patreon page is at https://www.patreon.com/EugeneK
From playlist Physics
What is a Tensor? Lesson 30: Transformation of forms - formal study (Part I)
What is a Tensor? Lesson 30: Transformation of forms - formal study (Part I)
From playlist What is a Tensor?
Determine the Singular Value Decomposition of a Matrix
This video explains how to determine the singular value decomposition of a matrix. https://mathispower4u.com
From playlist Singular Values / Singular Value Decomposition of a Matrix
Determine the Singular Value Decomposition of a Matrix
This video explains how to determine the singular value decomposition of a matrix.
From playlist Singular Values / Singular Value Decomposition of a Matrix
What is a Tensor? Lesson 31: Tensor Densities (Part 2 of Tensor Transformations)
This video is about What is a Lesson 31: Tensor Densities (Part 2 of Tensor Transformations) We introduce the *classical* definition of a tensor density and connect that definition to our more robust approach associated with vector spaces and their associated bases. I will demonstrate som
From playlist What is a Tensor?
Polynomial-time tensor decompositions via sum-of-squares - Tengyu Ma
Computer Science/Discrete Mathematics Seminar I Topic: Polynomial-time tensor decompositions via sum-of-squares Speaker: Tengyu Ma Date: Monday, March 21 Tensor decompositions have been the key algorithmic components in provable learning of a wide range of hidden variable models such
From playlist Mathematics
Anna Seigal: "From Linear Algebra to Multi-Linear Algebra"
Watch part 2/2 here: https://youtu.be/f5MiPayz_e8 Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "From Linear Algebra to Multi-Linear Algebra" Anna Seigal - University of Oxford Abstract: Linear algebra is the foundation to methods for finding
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Ankur Moitra: "Tensor Decompositions and their Applications (Part 1/2)"
Watch part 2/2 here: https://youtu.be/npPaMknLJWQ Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensor Decompositions and their Applications (Part 1/2)" Ankur Moitra - Massachusetts Institute of Technology Abstract: Tensor decompositions play
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Aravindan Vijayaraghavan: "Smoothed Analysis for Tensor Decompositions and Unsupervised Learning"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop III: Mathematical Foundations and Algorithms for Tensor Computations "Smoothed Analysis for Tensor Decompositions and Unsupervised Learning" Aravindan Vijayaraghavan - Northwestern University Abstrac
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Ankur Moitra : Tensor Decompositions and their Applications
Recording during the thematic meeting: «Nexus of Information and Computation Theories » theJanuary 27, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Nexus Trimester - 2016 -Tutorial Week at CIRM
Computer Science/Discrete Mathematics Reading Seminar Topic: Tensor Rank Speaker: Avi Wigderson Affiliation: IAS, Herbert H. Maass Professor, School of Mathematics Date: June 22, 2021 Tensors occur throughout mathematics. Their rank, defined in analogy with matrix rank, is however much
From playlist Mathematics
Anna Seigal: "Tensors in Statistics and Data Analysis"
Watch part 1/2 here: https://youtu.be/9unKtBoO5Hw Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "Tensors in Statistics and Data Analysis" Anna Seigal - University of Oxford Abstract: I will give an overview of tensors as they arise in settings
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Jean Kossaifi: "Efficient Tensor Representation for Deep Learning with TensorLy and PyTorch"
Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021 Workshop IV: Efficient Tensor Representations for Learning and Computational Complexity "Efficient Tensor Representation for Deep Learning with TensorLy and PyTorch" Jean Kossaifi - Nvidia Corporation Abstrac
From playlist Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021
Tensor Decomposition Definitions of Neural Net Architectures
This paper describes complexity theory of neural networks, defined by tensor decompositions, with a review of simplification of the tensor decomposition for simpler neural network architectures. The concept of Z-completeness for a network N is defined in the existence of a tensor decomposi
From playlist Wolfram Technology Conference 2021
Definition of Rank and showing Rank(A) = Dim Col(A) In this video, I define the notion of rank of a matrix and I show that it is the same as the dimension of the column space of that matrix. This is another illustration of the beautiful interplay between linear transformations and matrice
From playlist Linear Equations