Linear Discriminant Analysis (LDA) in Real-Life: Dimensionality Reduction in a Real-Estate Dataset

Linear Discriminant Analysis (LDA) is a supervised learning technique used for dimensionality reduction in classification problems by identifying the linear combination of features that best separates different classes. The goal is to project a high-dimensional dataset onto a lower-dimensional space while preserving the characteristics that ensure maximum class separability. The method operates under key assumptions, including that the data is linearly separable, follows a Gaussian distribution, and has a shared covariance matrix across all classes. Mathematically, LDA approximates the Bayes Classifier by estimating prior probabilities, class means, and a shared covariance to calculate a discriminant function for assigning observations to the most probable class.