Hyperdimensional Regression: Potentials and insights into Hadamard Matrix - Based Encoding For Predictive Analysis

Abstract

The use of Hadamard matrices for hypervector generation within hyperdimensional computing (HDC) offers a transformative and efficient approach to data encoding, significantly reducing the dimensionality of hypervectors. Unlike traditional encoding methods that often require hypervectors with dimensions exceeding 10,000, Hadamard-based encoding creates a more compact representation while maintaining key properties for robust data processing. The inherent binary orthogonality of Hadamard matrices ensures effective and distinct data representation, supporting high-performance classification and regression tasks within HDC frameworks. Our analysis demonstrates that hypervectors generated through Hadamard matrices achieve competitive performance, particularly on datasets with normal or near-normal distributions, when compared to advanced machine learning models. The compact nature of these hypervectors enhances computational efficiency without sacrificing accuracy. However, the method’s performance diminishes on datasets that deviate substantially from normality. This work underscores the value of Hadamard-based encoding in HDC, combining dimensionality reduction with effective data processing capabilities.