MATLAB Implementation of Logistic Regression Statistical Algorithm

This paper primarily explores the MATLAB implementation of the logistic regression statistical algorithm, including the modeling process, output variable prediction, and prediction error analysis. The dataset used originates from the Ionosphere database in the UCI Machine Learning Repository, containing 351 statistical instances with a binary output variable that indicates whether radar returns from the ionosphere are good or bad. The dataset comprises 32 feature values that provide deeper insights into the data characteristics. The implementation code includes data preprocessing steps, feature normalization, and logistic regression parameter estimation using maximum likelihood methods. In this study, we utilize the preprocessed data provided in the compressed package to conduct experiments, effectively demonstrating the application and implementation process of logistic regression. The MATLAB code implements key algorithms such as the cost function calculation using cross-entropy loss, gradient descent for parameter optimization, and prediction accuracy assessment through confusion matrix analysis. The implementation also includes functionality for calculating prediction probabilities using the sigmoid function and performing error analysis through metrics like precision, recall, and F1-score. The code structure follows a systematic approach: data loading and validation, feature scaling using z-score normalization, hypothesis function implementation with vectorized operations, and iterative parameter updates through optimization algorithms. Special attention is given to handling class imbalance and implementing regularization techniques to prevent overfitting. The final implementation provides comprehensive results including classification reports and receiver operating characteristic (ROC) curve analysis for model performance evaluation.