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