Scalable and Interpretable Machine Learning with Tensor Decomposition

High-dimensional data is prevalent in modern machine learning applications, necessitating efficient methods for representation, compression, and analysis. Tensor factorization techniques provide a powerful framework for handling such data, enabling structured decomposition and extraction of meaningful latent patterns. This paper presents a comprehensive survey of tensor decomposition methods, including CANDECOMP/PARAFAC (CP), Tucker, Tensor Train (TT), and Hierarchical Tucker (HT) decompositions, with an emphasis on their mathematical foundations and computational properties. We explore their applications in machine learning, ranging from dimensionality reduction and model compression to recommendation systems and graph analytics. Additionally, we discuss recent advancements in scalable and adaptive tensor methods, covering online, sparse, and randomized approaches. The integration of tensor-based techniques with deep neural networks, explainable AI, and quantum computing is also examined, highlighting emerging research trends. Finally, we outline key challenges and future directions, including scalability improvements, automated rank selection, and fairness considerations in tensor-based models. With their growing impact on artificial intelligence, tensor decomposition techniques continue to shape the development of more efficient, interpretable, and scalable machine learning models.