Machine learning algorithms | Matrix theory | Linear algebra | Factorization
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms or muscular activity, non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically. NMF finds applications in such fields as astronomy, computer vision, document clustering, missing data imputation, chemometrics, audio signal processing, recommender systems, and bioinformatics. (Wikipedia).
Positive Semi-Definite Matrix 3: Factorization of Invertible Matrices
Matrix Theory: Let A be an invertible nxn matrix with complex entries. Using the square root result from Part 1, we show that A factors uniquely as PX, where P is unitary and X is (Hermitian) positive definite.
From playlist Matrix Theory
Determine For Which Matrices and a Given Vector is an Eigenvector
This video explains how to determine if a given vector is a eigenvector for a matrix.
From playlist Eigenvalues and Eigenvectors
From playlist Sample Midterm
Ex: Simplifying the Opposites of Negatives Integers
This video provides several examples of simplifying opposites of negative integers. Search Complete Video Library at http://www.mathispower4u.wordpress.com
From playlist Introduction to Integers
Determine the Product of a Matrix and Vector using the Diagonalization of the Matrix
This video explains how to use the diagonalization of a 2 by 2 matrix to find the product of a matrix and a vector given matrix P and D.
From playlist The Diagonalization of Matrices
Factoring a binomial using distributive property
👉Learn how to factor quadratics using the difference of two squares method. When a quadratic contains two terms where each of the terms can be expressed as the square of a number and the sign between the two terms is the minus sign, then the quadratic can be factored easily using the diffe
From playlist Factor Quadratic Expressions | Difference of Two Squares
Evrim Acar - Constrained Multimodal Data Mining using Coupled Matrix and Tensor Factorizations
Recorded 11 January 2023. Evrim Acar of Simula Research Laboratory presents "Extracting Insights from Complex Data: Constrained Multimodal Data Mining using Coupled Matrix and Tensor Factorizations" at IPAM's Explainable AI for the Sciences: Towards Novel Insights Workshop. Abstract: In or
From playlist 2023 Explainable AI for the Sciences: Towards Novel Insights
Given One Zero or Factor Find the Remaining Zeros
👉 Learn how to find all the zeros of a polynomial given one irrational zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of
From playlist Find all the Remaining Zeros Given a Factor or Zero
Given One Zero or Factor Find the Remaining Zeros
👉 Learn how to find all the zeros of a polynomial given one irrational zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of
From playlist Find all the Remaining Zeros Given a Factor or Zero
Given One Zero or Factor Find the Remaining Zeros
👉 Learn how to find all the zeros of a polynomial given one irrational zero. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of
From playlist Find all the Remaining Zeros Given a Factor or Zero
Jamie Haddock - Hierarchical and neural nonnegative tensor factorizations - IPAM at UCLA
Recorded 02 December 2022. Jamie Haddock of Harvey Mudd College presents "Hierarchical and neural nonnegative tensor factorizations" at IPAM's Multi-Modal Imaging with Deep Learning and Modeling Workshop. Abstract: Nonnegative matrix factorization (NMF) has found many applications includin
From playlist 2022 Multi-Modal Imaging with Deep Learning and Modeling
Introduction to Laplacian Linear Systems for Undirected Graphs - John Peebles
Computer Science/Discrete Mathematics Seminar II Topic: Introduction to Laplacian Linear Systems for Undirected Graphs Speaker: John Peebles Affiliation: Member, School of Mathematics Date: February 23, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
James Lee: Semi Definite Extended Formulations and Sums of Squares (Part 2)
The lecture was held within the framework of the Hausdorff Trimester Program: Combinatorial Optimization
From playlist HIM Lectures 2015
Spectrahedral lifts of convex sets – Rekha Thomas – ICM2018
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Lieven Vandenberghe: "Bregman proximal methods for semidefinite optimization."
Intersections between Control, Learning and Optimization 2020 "Bregman proximal methods for semidefinite optimization." Lieven Vandenberghe - University of California, Los Angeles (UCLA) Abstract: We discuss first-order methods for semidefinite optimization, based on non-Euclidean projec
From playlist Intersections between Control, Learning and Optimization 2020
Jamie Haddock: "Scaling the Hierarchical Topic Modeling Mountain: Neural NMF and Iterative Proje..."
Deep Learning and Medical Applications 2020 "Scaling the Hierarchical Topic Modeling Mountain: Neural NMF and Iterative Projection Methods" Jamie Haddock - University of California, Los Angeles (UCLA), Mathematics Abstract: Datasets with hierarchical structure arise in a wide variety of
From playlist Deep Learning and Medical Applications 2020
Math 060 Linear Algebra 05 091714: Properties of Determinants
Interaction of determinants and elementary row operations: the "wrong cofactor lemma"; determinants and elementary matrices; invertibility and determinants; determinants of products
From playlist Course 4: Linear Algebra
Suvrit Sra: Lecture series on Aspects of Convex, Nonconvex, and Geometric Optimization (Lecture 3)
The lecture was held within the framework of the Hausdorff Trimester Program "Mathematics of Signal Processing". (28.1.2016)
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
Introduction to Homogeneous Systems of Equations: Trivial and Nontrivial Solutions
This video introduces homogeneous systems of equations. Then it explains how to determine nontrivial solutions.
From playlist Rank and Homogeneous Systems
multiplying negatives
From playlist Arithmetic and Pre-Algebra: Negative Numbers