▬▬ Papers / Resources ▬▬▬
Colab Notebook: https://colab.research.google.com/drive/1n_kdyXsA60djl-nTSUxLQTZuKcxkMA83?usp=sharing
Peter Bloem PCA Blog: https://peterbloem.nl/blog/pca
PCA for DS book: https://pca4ds.github.io/basic.html
PCA Book: http://cda.psych.uiuc.edu/statistical_learning_course/Jolliffe%20I.%20Principal%20Component%20Analysis%20(2ed.,%20Springer,%202002)(518s)_MVsa_.pdf
Lagrange Multipliers: https://ekamperi.github.io/mathematics/2020/11/01/principal-component-analysis-lagrange-multiplier.html
PCA Mathematical derivation #1: https://www.quora.com/Why-does-PCA-choose-covariance-matrix-to-get-the-principal-components-of-features-X
PCA Mathematical derivation #2: https://towardsdatascience.com/principal-component-analysis-part-1-the-different-formulations-6508f63a5553
PCA Mathematical derivation #3: https://rich-d-wilkinson.github.io/MATH3030/4.2-pca-a-formal-description-with-proofs.html
PCA Mathematical derivation #4: https://stats.stackexchange.com/questions/32174/pca-objective-function-what-is-the-connection-between-maximizing-variance-and-m/136072#136072
PCA Mathematical derivation #5: https://medium.com/@bishikh90/geometrical-and-mathematical-interpretation-principal-component-analysis-52f39a924b40
Eigenvectors and Eigenvalues: https://sebastianraschka.com/Articles/2015_pca_in_3_steps.html
Image Sources:
- Eigenfaces: https://towardsdatascience.com/eigenfaces-recovering-humans-from-ghosts-17606c328184
- Hyperplane: https://www.analyticsvidhya.com/blog/2021/07/svm-and-pca-tutorial-for-beginners/
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▬▬ Timestamps ▬▬▬▬▬▬▬▬▬▬▬
00:00 Introduction
00:26 Used Literature
00:41 Example dataset
02:47 Variance
03:52 Projecting data
04:14 Variance as measure of information
05:15 Scree Plot
05:53 Principal Components
06:14 PCA on images
07:00 Reconstruction based on eigenfaces
07:35 Orthogonal Basis
08:12 Kernel PCA
08:45 Finding principal components
09:28 Distance minimization vs. Variance maximization
10:45 Covariance Matrix
11:35 Correlation vs. Covariance
11:50 Covariance examples
12:50 Linear Algebra Basics
14:22 Eigenvectors and Eigenvalues
15:30 Eigenvector Equation
16:10 Spectral Theorem
16:40 Connection between Eigenvectors and Principal Components
17:23 [STEP 1]: Centering the Data
17:54 [STEP 2]: Calculate Covariance Matrix
18:25 [STEP 3]: Eigenvalue Decomposition
19:05 How to find eigenvectors?
19:17 The truth :O
19:27 Singular value decomposition
20:21 Why eigendecomposition at all?
20:45 [STEP 4]: Projection onto PCs
21:12 Orthogonal Eigenvectors
21:49 Dimensionality Reduction Projection
22:11 [CODE]
24:52 Summary Table
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