Hyperdimensional Bayesian Time Mapping (HyperBaT): A Probabilistic Approach to Time Series Mapping of Non-Identical Sequences

Abstract

A common problem in time series analysis is mapping the related elements between two sequences as they progress in time. Methods such as dynamic time warping (DTW) have good performance in mapping time series signals with repeated (warped) elements relative to a reference signal. However, there is not an adequate method for mapping time series signals with inserted or deleted elements. This paper introduces hyperdimensional Bayesian time mapping (HyperBaT), a machine learning algorithm that maps two time sequence signals that may contain inserted, deleted, or warped elements. In addition, HyperBaT estimates the common underlying signal shared between the two sequences. The algorithm is presented in a general context so that it can be used in a variety of applications. There are many relevant areas, including speech processing, genetic sequencing, electronic warfare, communications, and radar processing that process signals containing inserted or deleted elements. In this paper, the performance of HyperBaT and DTW are compared using simulated signals containing inserts. For sequence mapping and classification, the performance of HyperBaT exceeds that of DTW in nearly all test cases. As an experimental example, HyperBaT is used to map radio frequency side-channel signals emitted from the processor of a computing device, in order to track control flow execution and monitor for malicious activity. Another experimental example uses HyperBaT for speaker identification.