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

Calendar

LEC #	TOPICS
1	The Column Space of \(A\) Contains All Vectors \(A\boldsymbol{x}\)
2	Multiplying and Factoring Matrices
3	Orthonormal Columns in \(Q\) Give \(Q’Q= I\)
4	Eigenvalues and Eigenvectors
5	Positive Definite and Semidefinite Matrices
6	Singular Value Decomposition (SVD)
7	Eckart-Young: The Closest Rank \(k\) Matrix to \(A\)
8	Norms of Vectors and Matrices
9	Four Ways to Solve Least Squares Problems
10	Survey of Difficulties with \(A\boldsymbol{x} = \boldsymbol{b}\)
11	Minimizing \(‖\boldsymbol{x}‖\) Subject to \(A\boldsymbol{x} = \boldsymbol{b}\)
12	Computing Eigenvalues and Singular Values
13	Randomized Matrix Multiplication
14	Low Rank Changes in \(A\) and Its Inverse
15	Matrices \(A(t)\) Depending on \(t\), Derivative = \(dA/dt\)
16	Derivatives of Inverse and Singular Values
17	Rapidly Decreasing Singular Values
18	Counting Parameters in SVD, LU, QR, Saddle Points
19	Saddle Points Continued, Maxmin Principle
20	Definitions and Inequalities
21	Minimizing a Function Step by Step
22	Gradient Descent: Downhill to a Minimum
23	Accelerating Gradient Descent (Use Momentum)
24	Linear Programming and Two-Person Games
25	Stochastic Gradient Descent
26	Structure of Neural Nets for Deep Learning
27	Backpropagation: Find Partial Derivatives
28	Computing in Class [No video available]
29	Computing in Class (cont.) [No video available]
30	Completing a Rank-One Matrix, Circulants!
31	Eigenvectors of Circulant Matrices: Fourier Matrix
32	ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule
33	Neural Nets and the Learning Function
34	Distance Matrices, Procrustes Problem
35	Finding Clusters in Graphs
36	Alan Edelman and Julia Language