Principal Component Analysis (PCA) | Dimensionality Reduction Techniques (2/5)

Опубликовано: 31 Октябрь 2024
на канале: DeepFindr

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▬▬ Papers / Resources ▬▬▬
Colab Notebook: https://colab.research.google.com/dri...

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...

Lagrange Multipliers: https://ekamperi.github.io/mathematic...

PCA Mathematical derivation #1: https://www.quora.com/Why-does-PCA-ch...

PCA Mathematical derivation #2: https://towardsdatascience.com/princi...

PCA Mathematical derivation #3: https://rich-d-wilkinson.github.io/MA...

PCA Mathematical derivation #4: https://stats.stackexchange.com/quest...

PCA Mathematical derivation #5: / geometrical-and-mathematical-interpretatio...

Eigenvectors and Eigenvalues: https://sebastianraschka.com/Articles...

Image Sources:
Eigenfaces: https://towardsdatascience.com/eigenf...
Hyperplane: https://www.analyticsvidhya.com/blog/...

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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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