An Extension to Basis-Hypervectors for Learning from Circular Data in Hyperdimensional Computing

Abstract

Hyperdimensional Computing (HDC) is a computation framework based on properties of high-dimensional random spaces. It is particularly useful for machine learning in resourceconstrained environments, such as embedded systems and IoT, as it achieves a good balance between accuracy, efficiency and robustness. The mapping of information to the hyperspace, named encoding, is the most important stage in HDC. At its heart are basis-hypervectors, responsible for representing the smallest units of meaningful information. In this work we present a detailed study on basis-hypervector sets, which leads to practical contributions to HDC in general: 1) we propose an improvement for level-hypervectors, used to encode real numbers; 2) we introduce a method to learn from circular data, an important type of information never before addressed in machine learning with HDC. Empirical results indicate that these contributions lead to considerably more accurate models for both classification and regression with circular data.

Classification using Hyperdimensional Computing: A~Review~with~Comparative Analysis

“…Random selections starts by generating the initial hypervector l i and the final hypervector l f as random hypervectors, in addition to a random vector Φ with elements sampled uniformly between 0 and 1 [36]. To create the remaining level hypervectors l l , an interpolation process is employed.…”

“…This encoding generates a set of hypervectors characterized by circular correlation [36,37], using a similar technique as random selection level hypervectors, achieved through mapping the data onto a circular hyperspace. Circular basis hypervectors find wide applications, particularly in the analysis of cyclic data, such as seasonal weather patterns and financial data.…”