High-Dimensional Vector Spaces in Machine Learning constitute a mathematical framework wherein data instances and feature representations exist within Euclidean spaces characterized by dimensions exceeding the number of samples or standard linear boundaries. This domain relies formally on Linear Algebra axioms, specifically focusing on vector embeddings where semantic proximity is quantified via metric-preserving operations such as dot products and cosine similarity under high-dimensional geometry laws like concentration of measure. As a foundational subfield within Representation Learning and Dimensionality Analysis, it provides the necessary theoretical bedrock for defining feature manifolds that enable effective non-linear mapping strategies in subsequent architectures.
Every discrete image or continuous function is formally defined as a point within a high-dimensional vector space where each axis corresponds to a specific basis element (pixel for finite grids, Dira…