The Application of Linear Algebra in Machine Learning

Abstract

In the realm of machine learning, incorporating linear algebraic methods has become indispensable, serving as a foundational element in developing and refining various algorithms. This study explores the significant impact of linear algebra on machine learning applications, highlighting its fundamental principles and practical implications. It delves into key concepts such as vector spaces, matrices, eigenvalues, and eigenvectors, which form the mathematical basis of well-established machine learning models. The research provides a comprehensive overview of how linear algebra contributes to tasks such as classification, regression analysis, and dimensionality reduction. It also investigates how linear algebra simplifies data representation and processing, enabling effective handling of large datasets and identification of meaningful patterns. Additionally, the study explores specific machine learning applications like Word/Vector Embedding, Image Compression, and Movie Recommendation systems, demonstrating the critical role of linear algebra. Through case studies and practical examples, the study illustrates how a deep understanding of linear algebra empowers machine learning practitioners to develop robust and scalable solutions. Beyond theoretical frameworks, this research has practical implications for practitioners, researchers, and educators seeking a deeper understanding of the relationship between machine learning and linear algebra. By elucidating these connections, the study contributes to ongoing efforts to improve the efficacy and efficiency of machine learning applications.