This paper explores the mathematical underpinnings of key classification algorithms used in machine learning, providing an in-depth analysis of their models, assumptions, and applications. The study delves into linear models such as Logistic Regression, and Support Vector Machines (SVM), as well as non-linear models like Decision Trees and Neural Networks. The goal is to offer a comprehensive understanding of the mathematical structures that enable these algorithms to classify data effectively.

Classification algorithms are at the heart of machine learning, driving the ability of machines to make decisions based on data. These algorithms, whether linear or non-linear, are powered by sophisticated mathematical models that allow them to process, interpret, and classify data efficiently. Understanding the mathematical underpinnings of these algorithms is crucial for anyone looking to delve deeper into machine learning, as it provides insights into how these models function, their inherent assumptions, and the contexts in which they perform best. This paper aims to explore these mathematical foundations, providing a detailed analysis of both linear and non-linear models. By examining algorithms like Logistic Regression, Support Vector Machines (SVM), Decision Trees, and Neural Networks, we seek to uncover the mathematical structures that enable effective data classification.