Feature Selection and Regularization in Multi-Class Classification: An Empirical Study of One-vs-Rest Logistic Regression with Gradient Descent Optimization and L1 Sparsity Constraints

Multi-class wine classification presents fundamental trade-offs between model accuracy, feature dimensionality, and interpretability - critical factors for production deployment in analytical chemistry. This paper presents a comprehensive empirical study of One-vs-Rest logistic regression on the UCI Wine dataset (178 samples, 3 cultivars, 13 chemical features), comparing from-scratch gradient descent implementation against scikit-learn's optimized solvers and quantifying L1 regularization effects on feature sparsity. Manual gradient descent achieves 92.59 percent mean test accuracy with smooth convergence, validating theoretical foundations, though scikit-learn provides 24x training speedup and 98.15 percent accuracy. Class-specific analysis reveals distinct chemical signatures with heterogeneous patterns where color intensity varies dramatically (0.31 to 16.50) across cultivars. L1 regularization produces 54-69 percent feature reduction with only 4.63 percent accuracy decrease, demonstrating favorable interpretability-performance trade-offs. We propose an optimal 5-feature subset achieving 62 percent complexity reduction with estimated 92-94 percent accuracy, enabling cost-effective deployment with 80 dollars savings per sample and 56 percent time reduction. Statistical validation confirms robust generalization with sub-2ms prediction latency suitable for real-time quality control. Our findings provide actionable guidelines for practitioners balancing comprehensive chemical analysis against targeted feature measurement in resource-constrained environments.