Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction
Contents
Reducing the number of degrees of freedom, overarching view
Preprocessing our data
More preprocessing
Simple preprocessing examples, Franke function and regression
Simple preprocessing examples, breast cancer data and classification, Support Vector Machines
More on Cancer Data, now with Logistic Regression
Why should we think of reducing the dimensionality
Basic ideas of the Principal Component Analysis (PCA)
Introducing the Covariance and Correlation functions
Correlation Function and Design/Feature Matrix
Covariance Matrix Examples
Correlation Matrix
Correlation Matrix with Pandas
Correlation Matrix with Pandas and the Franke function
Rewriting the Covariance and/or Correlation Matrix
Towards the PCA theorem
The Algorithm before the Theorem
Writing our own PCA code
Compute the sample mean and center the data
Compute the sample covariance
Diagonalize the sample covariance matrix to obtain the principal components
Classical PCA Theorem
Proof of the PCA Theorem
PCA Proof continued
The final step
Geometric Interpretation and link with Singular Value Decomposition
Principal Component Analysis
PCA and scikit-learn
Back to the Cancer Data
More on the PCA
Incremental PCA
Randomized PCA
Kernel PCA
LLE
Other techniques
Geometric Interpretation and link with Singular Value Decomposition
This material will be added by mid January 2020.
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