Building Linear Discriminant Functions Using Minimum Squared Error Criterion (MSE Criterion) Through Training Sample Sets

This study employs the Minimum Squared Error Criterion (MSE Criterion) to establish linear discriminant functions through training sample sets, representing a fundamental classification algorithm widely used in machine learning. The algorithm learns patterns from pre-labeled data to categorize new data points into distinct classes. The training dataset utilized in this research comprises three key feature dimensions: 1) Gender classification (male/female), 2) SONA academic discipline indicators, and 3) UPS academic performance scores. In code implementation, these features are typically organized as feature vectors X = [x1, x2, x3] where x1 encodes gender, x2 represents subject area, and x3 contains UPS scores. Through systematic analysis of these multi-dimensional features, we derive an optimized linear discriminant function that classifies new data points in test sets. Specifically, the function takes the form f(x) = w^T*x + b, where weight vector w and bias term b are computed through MSE minimization using matrix pseudoinverse operations (implemented via numpy.linalg.pinv). This discriminant function effectively partitions test data into distinct categories and enables accurate prediction of new data classifications. The algorithm finds extensive applications across multiple domains including computer vision (image recognition) and natural language processing (text categorization). From a programming perspective, the MSE solution involves constructing a design matrix from training features, computing the pseudoinverse, and deriving optimal parameters through normal equations. This study provides comprehensive understanding of the algorithm's theoretical foundations and practical implementations, enabling effective application to real-world classification problems. The code typically involves feature normalization, matrix operations for weight calculation, and threshold-based decision functions for final classification.