數據科學矩陣方法(英文授課)
Matrix Methods in Data Science
| 節 | 週二 | 週四 |
|---|---|---|
3 10:10–11:00 | 數據科學矩陣方法(英文授課) EC122（光復） 2 節連堂 | |
4 11:10–12:00 | ||
8 16:30–17:20 | 數據科學矩陣方法(英文授課) EC122（光復） |
* 根據陽明交大上課時間表所列
This course extends matrix methods in Linear Algebra to cover their applications to data science, including data analysis, signal processing, and machine learning. It shall equip students with the required matrix methods on which data science depends.
1. Linear Algebra
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Mid-term x 2 -- 50% Final x 1 -- 30 % Homework (including computer assignments) – 20% Project (??)
Highlights of Linear Algebra
1. The four fundamental subspaces 2. Orthogonal matrices and subspaces 3. Eigenvalues and eigenvectors 4. Symmetric positive definite matrices 5. Singular value and singular vectors in SVD 6. Principle components and best low rank matrices 7. Rayleigh quotients and generalized eigenvalues 8. Norms of vectors, functions, and matrices 9. Factoring matrices and tensors
Computations with Large Matrices
1. Least squares 2. Three bases for the column space 3. Randomized linear algebra
Low Rank and Compressed Sensing
1. Changes in the inverse of matrices from changes in them 2. Interlacing eigenvalues and low rank signals 3. Rapidly decaying singular values 4. Compressed sensing and matrix completion
Special Matrices
1. Fourier transforms 2. Shift matrices and circulant matrices 3. The kronecker product 4. Sine and Cosine transforms from Kronecker sums 5. Toeplitz matrices and shift invariant filters 6. Graphs and Laplacians 7. Clustering by spectral methods and k-means 8. Completing rank one matrices 9. The orthogonal procrustes problem 10. Distance matrices
Optimization
1. Minimum problems: convexity and Newton’s Method 2. Lagrange multipliers 3. Linear programming, game theory, and duality 4. Gradient descent 5. Stochastic gradient descent and ADAM
Learning form data
1. The construction of deep neural networks 2. Convolutional neural nets 3. Backpropagation and the chain rule 4. Hyperparameters
| 週次 | 主題 |
|---|---|
| 第 1 週 | Highlights of Linear Algebra |
| 第 2 週 | Highlights of Linear Algebra |
| 第 3 週 | Highlights of Linear Algebra |
| 第 4 週 | Computations with Large Matrices |
| 第 5 週 | Computations with Large Matrices |
| 第 6 週 | Computations with Large Matrices |
| 第 7 週 | Low Rank and Compressed Sensing |
| 第 8 週 | Low Rank and Compressed Sensing |
| 第 9 週 | Low Rank and Compressed Sensing |
| 第 10 週 | Special Matrices |
| 第 11 週 | Special Matrices |
| 第 12 週 | Special Matrices |
| 第 13 週 | Optimization |
| 第 14 週 | Optimization |
| 第 15 週 | Optimization |
| 第 16 週 | Learning form data |
| 第 17 週 | Learning form data |
| 第 18 週 | Learning form data |
Text: “Linear Algebra and Learning from Data,” Gilbert Strang, 1st Ed., published by Wellesley-Cambridge Press, 2019. Online resources: https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/
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