Principal Component Analysis

Principal Component Analysis (PCA) is a fundamental Unsupervised Learning technique used for Dimensionality Reduction and Feature Extraction in Data Science. It operates through an Orthogonal Transformation that converts a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called Principal Components. Mathematically, this is achieved by computing the Eigenvectors and Eigenvalues of the Covariance Matrix or by performing Singular Value Decomposition (SVD). The first component accounts for the largest possible Variance in the data, and each succeeding component has the highest variance possible under the constraint that it is orthogonal to the preceding components. PCA is widely implemented in libraries such as Scikit-learn and is essential for Data Visualization, noise reduction, and mitigating the Curse of Dimensionality before training Machine Learning models.