Orthogonal Linear Discriminant Analysis (OLDA)

Orthogonal Linear Discriminant Analysis (OLDA) is a fundamental data analysis method particularly suitable for dimensionality reduction of high-dimensional datasets. This technique leverages linear algebra principles to project original data into a new feature space where distances between same-class samples are minimized while maximizing inter-class separation. Implementation typically involves calculating scatter matrices (within-class and between-class scatter), followed by orthogonal transformation using eigenvalue decomposition or SVD to obtain projection vectors. The orthogonal constraint ensures mutually independent features in the reduced space, which can be coded using libraries like scikit-learn's decomposition module or custom MATLAB scripts employing QR decomposition. Widely applied in statistics, machine learning, and pattern recognition domains, OLDA has demonstrated practical effectiveness in real-world applications by preserving critical discriminatory information while reducing computational complexity.