  In recent years, there has been a surge in the prevalence of high- and
multi-dimensional 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 a synthetic
multivariate time series dataset. 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.
