MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 (English)

   Saturday, December 07, 2024   

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MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 By Lecture Notes together!

Lecture 1: Course Introduction of 18.065 by Professor Strang

Lecture 2: An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,...

Lecture 3: Lecture 1: The Column Space of A Contains All Vectors Ax

Lecture 4: Lecture 2: Multiplying and Factoring Matrices

Lecture 5: 3. Orthonormal Columns in Q Give Q'Q = I

Lecture 6: 4. Eigenvalues and Eigenvectors

Lecture 7: 5. Positive Definite and Semidefinite Matrices

Lecture 8: 6. Singular Value Decomposition (SVD)

Lecture 9: 7. Eckart-Young: The Closest Rank k Matrix to A

Lecture 10: Lecture 8: Norms of Vectors and Matrices

Lecture 11: 9. Four Ways to Solve Least Squares Problems

Lecture 12: Lecture 10: Survey of Difficulties with Ax = b

Lecture 13: Lecture 11: Minimizing ‖x‖ Subject to Ax = b

Lecture 14: 12. Computing Eigenvalues and Singular Values

Lecture 15: Lecture 13: Randomized Matrix Multiplication

Lecture 16: 14. Low Rank Changes in A and Its Inverse

Lecture 17: 15. Matrices A(t) Depending on t, Derivative = dA/dt

Lecture 18: 16. Derivatives of Inverse and Singular Values

Lecture 19: Lecture 17: Rapidly Decreasing Singular Values

Lecture 20: Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points

Lecture 21: 19. Saddle Points Continued, Maxmin Principle

Lecture 22: 20. Definitions and Inequalities

Lecture 23: Lecture 21: Minimizing a Function Step by Step

Lecture 24: 22. Gradient Descent: Downhill to a Minimum

Lecture 25: 23. Accelerating Gradient Descent (Use Momentum)

Lecture 26: 24. Linear Programming and Two-Person Games

Lecture 27: 25. Stochastic Gradient Descent

Lecture 28: 26. Structure of Neural Nets for Deep Learning

Lecture 29: 27. Backpropagation: Find Partial Derivatives

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

Lecture 31: 31. Eigenvectors of Circulant Matrices: Fourier Matrix

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

Lecture 33: 33. Neural Nets and the Learning Function

Lecture 34: 34. Distance Matrices, Procrustes Problem

Lecture 35: 35. Finding Clusters in Graphs

Lecture 36: Lecture 36: Alan Edelman and Julia Language