PCA - created from Mind Map

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Step 1: Covariance /Covariance Matrix of the dataset

Motivation for PCA

Step 0: Standarize dataset of dim(d)

What is covariance for two variable

Covariance for Multivariate

What is covariance matrix

Step 2:Calulate Eigenvalue/Eigenvector of covariance matrix of the dataset

Why we use covariance matrix: because it captures the relationship of the data

What is eigenvalue & eigenvector

Why we calculate eigenvalue & eigenvector of the covariance matrix

Step3: Sort the eigenvalues by decresing order to rank the eigenvectors

later to rotate data alongside the axis of the eigenvectors: create new axis

it captures the variances of the data: first eigenvector is the direction of greatest variance of the dataset

All matrix has a property of eigenstuff

each eigenvalue captures a propotion of ori variance

Step 4: Select k eigenvectors which correspond to the k largest eigenvalues

k is the dim of new feature space

Step 5: Comput projection matrix; from the k selected eigenvectors, construct a projection matrix

Step 6: transform; tranform the original dataset with d dim with projection matrix W, obtain new k-dimension feature space