PCA

Singular Value Decomposition (SVD) is a powerful matrix factorization technique used across machine learning, computer vision, and data science. From transforming non-square matrices to enabling PCA without explicitly computing the covariance matrix, SVD simplifies complex transformations into elegant geometric steps. This blog unpacks its meaning, mechanics, and visual intuition with real-world applications.

Kernel PCA extends traditional PCA by enabling nonlinear dimensionality reduction using the kernel trick. It projects data into a higher-dimensional space, making complex patterns more separable and preserving structure during reduction.

Principal Component Analysis (PCA) is a powerful technique to reduce dimensionality while preserving essential data variance. It helps tackle the curse of dimensionality, simplifies complex datasets, and enhances model performance by extracting key features. This post breaks down PCA step-by-step, from geometric intuition and variance maximization to real-world applications and limitations.

Explore eigen decomposition through special matrices like diagonal, orthogonal, and symmetric. Understand matrix composition and how PCA leverages eigenvalues and eigenvectors to reduce dimensionality, reveal hidden patterns, and transform data. This post breaks down complex concepts into simple, visual, and intuitive insights for data science and machine learning.

Eigenvectors and eigenvalues reveal how matrices reshape space. From understanding linear transformations to exploring rotation axes and dimensionality reduction in PCA, this post dives into the heart of matrix magic—explained visually, intuitively, and practically.