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COMP_SCI 496: Mathematical and Computational Foundations of Tensors and Applications


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Prerequisites

Familiarity with linear algebra is expected. In addition, students should have taken a proof-based course such as CS 212 or Math 300.

Description

Tensors, or multiindexed arrays, generalize matrices (two dimensional) to three dimensions and beyond. Due to the great ability of tensors to model higher-order data and nonlinear functions, tensor techniques have seen great success in a variety of applications including machine learning, computer vision, and signal processing. In addition, tensors have a rich underlying mathematical structure.

  • This course fulfills the Technical Elective area.

REFERENCE TEXTBOOKS: N/A
REQUIRED TEXTBOOK: N/A

COURSE COORDINATORS: Eric Evert

COURSE INSTRUCTOR: Eric Evert

COURSE GOALS:
This course will discuss mathematical, computational and applied aspects of tensor decomposition. Topics will include tensor rank, border rank, the multilinear singular value and canonical polyadic decompositions, uniqueness of tensor decompositions, computation of tensor decompositions and low rank approximations, matrix multiplication tensors and fast matrix multiplication, tensors as multilinear forms, and applications of tensors in image classification.