Harnessing Tensor Decomposition for High-Dimensional Machine Learning

Tensor decomposition has gained significant attention in machine learning due to its ability to efficiently represent and process high-dimensional data. As a natural extension of matrix factorization, tensor decomposition provides powerful tools for dimensionality reduction, feature extraction, and structured learning in multi-modal datasets. This paper provides a comprehensive overview of tensor decomposition techniques, including CAN-DECOMP/PARAFAC (CP), Tucker, Tensor Train (TT), and Hierarchical Tucker (HT) decompositions, highlighting their applications in deep learning, natural language processing, recommender systems, and computer vision. We discuss the computational challenges associated with tensor decomposition, such as scalability, optimization difficulties, and rank selection, along with recent advancements aimed at improving efficiency. The integration of tensor decomposition with deep learning architectures has led to notable improvements in model compression, multi-modal learning, and attention mechanisms. Additionally, emerging fields such as quantum machine learning and neuroscience are beginning to leverage tensor methods for novel applications. Despite these advancements, open challenges remain in areas such as automatic rank estimation, interpretable decomposition models, and scalable distributed implementations. This paper outlines future research directions, emphasizing the need for more robust and adaptive tensor decomposition frameworks. As machine learning continues to evolve, tensor decomposition is expected to play an increasingly important role in building efficient, interpretable, and scalable AI models.