Implementation of Logistic Regression Algorithm in Machine Learning for Multi-Class Classification

In this documentation, we present an implementation of the logistic regression algorithm in machine learning. This algorithm is designed to classify samples generated from three distinct Gaussian distributions. Specifically, we employ a logistic regression model, which is a widely-used machine learning algorithm for classification problems. The implementation leverages the softmax function for multi-class classification, where we calculate probability distributions across three classes using weighted feature inputs. Through training this model with gradient descent optimization, we can classify sample data into three categories based on given feature values. The training process involves minimizing the cross-entropy loss function through iterative weight updates. This approach enables us to better understand and analyze the differences and relationships between different categories. During the implementation process, we utilized extensive mathematical and statistical knowledge, particularly probability theory and optimization techniques, along with programming skills and tools. Key functions include feature normalization, hypothesis calculation using sigmoid/softmax functions, and gradient computation for parameter updates. This implementation provides deeper insights into the application of logistic regression in machine learning, offering more accurate and reliable methods for solving classification problems.