Реферат: This paper examines the comparison of time series of a set of concepts based on the formation of weighted directed graphs of the mutual influences of time series concepts on each other. The graph vertices correspond to the concepts, and the weighted arcs correspond to the values of the influence of one concept on another. The graph structure can be characterized using the spectrum of the eigenvalues of the graph's Laplace matrix, which corresponds to the heat equation. For this purpose, a heat kernel matrix is formed; the time derivative of the heat kernel matrix is determined by the Laplace matrix. The coefficients of the Taylor series expansion of the heat content of the heat kernel can be used to represent the graph structure. The paper presents relations for determining the Mahalanobis distance between feature vectors—heat kernel invariants—which can be used for pattern recognition. The topicality of the problem is to increase the uniqueness of identification when recognizing time series by taking into account both the spectrum of eigenvalues of the Laplace matrix of the graph and the eigenvectors. The goal of this paper is to explore the possibility of using the coefficients of the power series expansion of the heat content of the constructed graph as feature vectors—characteristics of the graph's properties. The novelty of the methods presented in this paper lies in the fact that, unlike the spectral embedding method, it explores the possibility of comparing graphs (images) based on the Mahalanobis distance between invariants constructed from the thermal content decomposition coefficients. An algorithm for minimizing the Mahalanobis distance between graph vertices is proposed, based on learning the Mahalanobis matrix. By comparing graphs corresponding to time series of a set of concepts, it is possible to compare time series.

Библиографическая ссылка: Chukanov S. , Belik A.G. , Tsyganenko V.N.
Time series matching based on comparison of corresponding graphs
XIX Международная научно-техническая конференция «Динамика систем, механизмов и машин» 11-13 Nov 2025