20. Definitions and Inequalities - Uedu Open

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20. Definitions and Inequalities

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

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English 中文

其他影片 (36)

1 Course Introduction of 18.065 by Professor Strang 2 An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,... 3 Lecture 1: The Column Space of A Contains All Vectors Ax 4 Lecture 2: Multiplying and Factoring Matrices 5 3. Orthonormal Columns in Q Give Q'Q = I 6 4. Eigenvalues and Eigenvectors 7 5. Positive Definite and Semidefinite Matrices 8 6. Singular Value Decomposition (SVD) 9 7. Eckart-Young: The Closest Rank k Matrix to A 10 Lecture 8: Norms of Vectors and Matrices 11 9. Four Ways to Solve Least Squares Problems 12 Lecture 10: Survey of Difficulties with Ax = b 13 Lecture 11: Minimizing ‖x‖ Subject to Ax = b 14 12. Computing Eigenvalues and Singular Values 15 Lecture 13: Randomized Matrix Multiplication 16 14. Low Rank Changes in A and Its Inverse 17 15. Matrices A(t) Depending on t, Derivative = dA/dt 18 16. Derivatives of Inverse and Singular Values 19 Lecture 17: Rapidly Decreasing Singular Values 20 Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points 21 19. Saddle Points Continued, Maxmin Principle 22 20. Definitions and Inequalities 23 Lecture 21: Minimizing a Function Step by Step 24 22. Gradient Descent: Downhill to a Minimum 25 23. Accelerating Gradient Descent (Use Momentum) 26 24. Linear Programming and Two-Person Games 27 25. Stochastic Gradient Descent 28 26. Structure of Neural Nets for Deep Learning 29 27. Backpropagation: Find Partial Derivatives 30 Lecture 30: Completing a Rank-One Matrix, Circulants! 31 31. Eigenvectors of Circulant Matrices: Fourier Matrix 32 Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule 33 33. Neural Nets and the Learning Function 34 34. Distance Matrices, Procrustes Problem 35 35. Finding Clusters in Graphs 36 Lecture 36: Alan Edelman and Julia Language

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

課程影片 (36)

1 Course Introduction of 18.065 by Professor Strang 2 An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,... 3 Lecture 1: The Column Space of A Contains All Vectors Ax 4 Lecture 2: Multiplying and Factoring Matrices 5 3. Orthonormal Columns in Q Give Q'Q = I 6 4. Eigenvalues and Eigenvectors 7 5. Positive Definite and Semidefinite Matrices 8 6. Singular Value Decomposition (SVD) 9 7. Eckart-Young: The Closest Rank k Matrix to A 10 Lecture 8: Norms of Vectors and Matrices 11 9. Four Ways to Solve Least Squares Problems 12 Lecture 10: Survey of Difficulties with Ax = b 13 Lecture 11: Minimizing ‖x‖ Subject to Ax = b 14 12. Computing Eigenvalues and Singular Values 15 Lecture 13: Randomized Matrix Multiplication 16 14. Low Rank Changes in A and Its Inverse 17 15. Matrices A(t) Depending on t, Derivative = dA/dt 18 16. Derivatives of Inverse and Singular Values 19 Lecture 17: Rapidly Decreasing Singular Values 20 Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points 21 19. Saddle Points Continued, Maxmin Principle 22 20. Definitions and Inequalities 23 Lecture 21: Minimizing a Function Step by Step 24 22. Gradient Descent: Downhill to a Minimum 25 23. Accelerating Gradient Descent (Use Momentum) 26 24. Linear Programming and Two-Person Games 27 25. Stochastic Gradient Descent 28 26. Structure of Neural Nets for Deep Learning 29 27. Backpropagation: Find Partial Derivatives 30 Lecture 30: Completing a Rank-One Matrix, Circulants! 31 31. Eigenvectors of Circulant Matrices: Fourier Matrix 32 Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule 33 33. Neural Nets and the Learning Function 34 34. Distance Matrices, Procrustes Problem 35 35. Finding Clusters in Graphs 36 Lecture 36: Alan Edelman and Julia Language