Big Data Concept

1. Introduction In the era of big data, machine learning models increasingly rely on handling complex, multi-dimensional datasets. From images and videos to time-series signals and natural language embeddings, these datasets often exceed the capabilities of traditional vector or matrix representations. Tensors, as multi-dimensional arrays, provide a powerful framework for organizing and processing such data efficiently. This chapter explores tensor-based computation, focusing on how tensor operations enable the manipulation of high-dimensional data in machine learning contexts. We will cover fundamental concepts, key operations, implementations in popular frameworks, applications, decompositions, and practical examples. Tensors generalize scalars, vectors, and matrices to higher dimensions, allowing for natural representation of real-world data structures. For instance, a color image can be represented as a 3D tensor (height × width × channels), while a video adds a time dimension, ...