Principal Component Analysis
Principal Component Analysis (PCA) is a dimensionality reduction technique that transforms high-dimensional data into a lower-dimensional form while preserving as much of the original data’s variance as possible. PCA achieves this by creating new, uncorrelated variables called principal components , which are linear combinations of the original variables. These principal components capture the directions of maximum variance in the data, with the first few components typically containing most of the information. How PCA Works Standardize the Data : Center and scale the data so that each feature has a mean of zero and a variance of one. This step ensures that features with larger scales don’t dominate the results. Compute the Covariance Matrix : Calculate the covariance matrix to understand how features vary with respect to each other. Calculate Eigenvalues and Eigenvectors : Determine the eigenvalues and eigenvectors of the covariance matrix. Eigenvectors define the directions (...
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