The Mathematics Behind Principal Component Analysis
Mathematics Behind PCA Principal Component Analysis (PCA) is a dimensionality reduction technique used in machine learning and statistics to transform a dataset with many correlated variables into a smaller set of uncorrelated variables called principal components . Steps behind Principal Component Analysis. Step 1: Take the whole dataset consisting of d+1 dimensions and ignore the labels such that our new dataset becomes d dimensional. Step 2: Compute the mean of every dimension of the whole dataset. Step 3: Mean Center the Data Step 4: Compute the sample covariance matrix Step 5: Compute Eigenvalues Step 6: Compute Eigenvectors Step 7: Principal Components Step 8: Projection Practice Problems Matrix 1: The "E-Commerce Customer" Data This matrix represents customer behavior on a shopping website. It’s perfect for teaching Customer Segmentation . Features: Number of Visits, Items in Cart, Total Spend (normalized). Identify whic...