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MIT 18.065 数据分析、信号处理和机器学习中的矩阵方法

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2019-05-19 19:27:49

https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang https://ocw.mit.edu/18-065S18

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Course Introduction of 18.065 by Professor Strang

07:04

1. The Column Space of A Contains All Vectors Ax

52:15

2. Multiplying and Factoring Matrices

48:26

3. Orthonormal Columns in Q Give Q Q = I

49:24

4. Eigenvalues and Eigenvectors

48:56

5. Positive Definite and Semidefinite Matrices

45:28

6. Singular Value Decomposition SVD

53:34

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

47:16

8. Norms of Vectors and Matrices

49:21

9. Four Ways to Solve Least Squares Problems

49:51

10. Survey of Difficulties with Ax = b

49:36

11. Minimizing x Subject to Ax = b

50:22

12. Computing Eigenvalues and Singular Values

49:28

13. Randomized Matrix Multiplication

52:24

14. Low Rank Changes in A and Its Inverse

50:35

15. Matrices A t Depending on t Derivative = dA dt

50:52

16. Derivatives of Inverse and Singular Values

43:09

17. Rapidly Decreasing Singular Values

50:34

18. Counting Parameters in SVD LU QR Saddle Points

49:00

19. Saddle Points Continued Maxmin Principle

52:13

20. Definitions and Inequalities

55:01

21. Minimizing a Function Step by Step

53:45

22. Gradient Descent - Downhill to a Minimum

52:44

23. Accelerating Gradient Descent Use Momentum

49:02

24. Linear Programming and Two-Person Games

53:34

25. Stochastic Gradient Descent

53:03

26. Structure of Neural Nets for Deep Learning

53:17

27. Backpropagation - Find Partial Derivatives

52:38

30. Completing a Rank-One Matrix Circulants

49:53

31. Eigenvectors of Circulant Matrices - Fourier Matrix

52:37

32. ImageNet is a Convolutional Neural Network CNN The Convolution Rule

47:19

33. Neural Nets and the Learning Function

56:08

34. Distance Matrices Procrustes Problem

29:17

35. Finding Clusters in Graphs

34:49

36. Alan Edelman and Julia Language

38:12

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