Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

Video Lectures

Note: Videos of Lectures 28 and 29 are not available because those were in-class lab sessions that were not recorded.

Lecture 1: The Column Space of A Contains All Vectors Ax

Lecture 2: Multiplying and Factoring Matrices

Lecture 3: Orthonormal Columns in Q Give Q’Q = I

Lecture 4: Eigenvalues and Eigenvectors

Lecture 5: Positive Definite and Semidefinite Matrices

Lecture 6: Singular Value Decomposition (SVD)

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

Lecture 8: Norms of Vectors and Matrices

Lecture 9: Four Ways to Solve Least Squares Problems

Lecture 10: Survey of Difficulties with Ax = b

Lecture 11: Minimizing ‖x‖ Subject to Ax = b

Lecture 12: Computing Eigenvalues and Singular Values

Lecture 13: Randomized Matrix Multiplication

Lecture 14: Low Rank Changes in A and Its Inverse

Lecture 15: Matrices A(t) Depending on t, Derivative = dA/dt

Lecture 16: Derivatives of Inverse and Singular Values

Lecture 17: Rapidly Decreasing Singular Values

Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points

Lecture 19: Saddle Points Continued, Maxmin Principle

Lecture 20: Definitions and Inequalities

Lecture 21: Minimizing a Function Step by Step

Lecture 22: Gradient Descent: Downhill to a Minimum

Lecture 23: Accelerating Gradient Descent (Use Momentum)

Lecture 24: Linear Programming and Two-Person Games

Lecture 25: Stochastic Gradient Descent

Lecture 26: Structure of Neural Nets for Deep Learning

Lecture 27: Backpropagation: Find Partial Derivatives

Lecture 30: Completing a Rank-One Matrix, Circulants!

Lecture 31: Eigenvectors of Circulant Matrices: Fourier Matrix

Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule

Lecture 33: Neural Nets and the Learning Function

Lecture 34: Distance Matrices, Procrustes Problem

Lecture 35: Finding Clusters in Graphs

Lecture 36: Alan Edelman and Julia Language