Multilayer quantile graph for multivariate time series analysis and dimensionality reduction Vanessa Freitas Silva, Maria Eduarda Silva, Pedro Ribeiro and Fernando Silva 2024

Abstract

In recent years, there has been a surge in the prevalence of high- and multidimensional temporal data across various scientific disciplines. These datasets are characterized by their vast size and challenging potential for analysis. Such data typically exhibit serial and cross-dependency and possess high dimensionality, thereby introducing additional complexities to conventional time series analysis methods. To address these challenges, a recent and complementary approach has emerged, known as network-based analysis methods for multivariate time series. In univariate settings, quantile graphs have been employed to capture temporal transition properties and reduce data dimensionality by mapping observations to a smaller set of sample quantiles. To confront the increasingly prominent issue of high dimensionality, we propose an extension of quantile graphs into a multivariate variant, which we term “Multilayer Quantile Graphs”. In this innovative mapping, each time series is transformed into a quantile graph, and inter-layer connections are established to link contemporaneous quantiles of pairwise series. This enables the analysis of dynamic transitions across multiple dimensions. In this study, we demonstrate the effectiveness of this new mapping using synthetic and benchmark multivariate time series datasets. We delve into the resulting network’s topological structures, extract network features, and employ these features for original dataset analysis. Furthermore, we compare our results with a recent method from the literature. The resulting multilayer network offers a significant reduction in the dimensionality of the original data while capturing serial and cross-dimensional transitions. This approach facilitates the characterization and analysis of large multivariate time series datasets through network analysis techniques.

Keywords

Multivariate time series; Quantile graphs; Multilayer networks; Dimensionality reduction

Digital Object Identifier (DOI)

doi 10.1007/s41060-024-00561-6

Publication in PDF format

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Software

software

Journal/Conference/Book

International Journal of Data Science and Analytics

Reference (text)

Vanessa Freitas Silva, Maria Eduarda Silva, Pedro Ribeiro and Fernando Silva. Multilayer quantile graph for multivariate time series analysis and dimensionality reduction. In International Journal of Data Science and Analytics, Springer, May, 2024.

Bibtex

@article{ribeiro-IJDSA2024,
  author = {Vanessa Freitas Silva and  Maria Eduarda Silva and  Pedro Ribeiro and Fernando Silva},
  title = {Multilayer quantile graph for multivariate time series analysis and dimensionality reduction},
  doi = {10.1007/s41060-024-00561-6},
  journal = {International Journal of Data Science and Analytics},
  publisher = {Springer},
  month = {May},
  year = {2024}
}