Learning encoding phasors with fractional power encoding

Hyperdimensional Computing (HDC), also Hyperdimensional Computing (HD), also known as Vector Symbolic Architectures (VSA), operates in high-dimensional vector spaces for symbolic processing. Within HD, Fractional Power Encoding (FPE), also referred to as Random Fourier Features, is a method that creates randomized data representations by exponentiating random base vectors. In this paper, we evaluate the application of FPE for classification tasks. We focus on the Fourier Holographic Reduced Representation (FHRR) within this framework. We investigate the use of various probability distributions for sampling to generate the basis hypervectors for FPE. Our findings indicate that distributions from the generalized hyperbolic family, such as Laplace, Cauchy, Student-t, and Gaussian, are more effective in capturing information during encoding. Furthermore, we propose two novel models for classification. Each model begins by determining an optimal bandwidth to achieve high accuracy. The first model, inspired by Fourier Series, generates an encoding by accumulating different bandwidths. Both models employ Stochastic Gradient Descent (SGD) to learn encodings tailored to specific applications. This approach enables the models to generate application-specific kernels, resulting in higher accuracy. Our models outperforms the current state-of-the-art in Hyperdimensional Computing in 121 datasets on accuracy, memory usage, training time and inference time allowing for achieving better results in embedded devices. Furthermore our results outperform Support Vector Machines (SVM) on accuracy.