Tensor Decomposition - A Mathematical Tool for Data Analysis

Overview

Explore tensor decomposition as a powerful mathematical tool for data analysis in this SIAM Invited Address from the 2018 Joint Mathematics Meetings. Delve into the fundamentals of tensors, vector outer products, and matrix decomposition for detecting low-rank structures. Learn about CP tensor factorization and its applications in neuroscience and hazardous gas detection. Discover advanced techniques like Rayleigh CP with linear link, generalized CP, and Boolean CP for analyzing diverse datasets including mouse experiments and binary chat data. Gain insights into solving least squares problems and implementing alternating least squares for CP fitting.

Syllabus

Intro
Tensor Decomposition: A Mathematical Tool for Data Analysis
Tensors Vector Outer Products
Matrix Decomposition: Detecting Low-Rank Structure
CP Tensor Factorization (3-way): Detecting low-rank 3-way structure
CP first invented in 1927
New Devices Enable Measuring Multiple Neurons Simultaneously
Neuron Data
Fitting CP: Alternating Least Squares
Solving the Least Squares Problem
Randomizing the Convergence Check
Application to Hazardous Gas Dataset
Factors from Gas Dataset
Rayleigh CP with Linear Link
Generalized CP
Mouse Data using Rayleigh (Nonnes)
Gas Data Using Rayleigh
Binary Chat Data using Boolean CP
CP Tensor Decomposition & Data Analysis