Search

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.

In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are translating solitons for the inverse mean curvature flow. In particular, we prove the existence of non-cylindrical ruled translating solitons, which contrast with the Euclidean setting., Comment: 22 pages, 4 figures. Final version

In this paper, we classify the nondegenerate ruled surfaces in the three-dimensional Lorentz-Minkowski space that are homothetic self-similar solutions for the inverse mean curvature flow. This classification shows the existence of two classes of non-cylindrical homothetic solitons: one with lightlike rulings and another one with non-lightlike rulings., Comment: 26 pages, 6 figures. Final version, to appear in the Bulletin of the Brazilian Mathematical Society, New Series. arXiv admin note: substantial text overlap with arXiv:2308.11457

The architecture, engineering and construction (AEC) sector extensively uses documents supporting product and process development. As part of this, organisations should handle big data of hundreds, or even thousands, of technical documents strongly linked together, including CAD design of industrial plants, equipment purchase orders, quality certificates, and part material analysis. However, analysing such records is daunting for users because it gets complicated to sift through hundreds of documents to establish valuable relationships. This paper addresses how knowledge extracted from linked engineering documents contributes to industrial digitalisation under IT/OT convergence. The proposed GraphLED is a system tasked with data processing, graph-based modelling, and colourful visualisation of related documents. The graph-based approach ensures an improved understanding of linked information because the graph structure offers a promising tool to model the underlying data properties of engineering documents. Preliminary system validation indicates quality improvements are possible in the OCR-based data (85.9% of ambiguous text data removed). This work has the potential to benefit the industry by improving the reliability and resilience of industrial production systems through automated summaries of large quantities of documents and their linkage.

Understanding the properties of time-indexed multivariate data has been a predominant topic mainly to address open issues in multivariate time series analysis. Usually, the methodologies used to analyze multivariate time series are based on adapting approaches for univariate settings or on assumptions and parameters for specific problems. A different strategy uses complex network to obtain an additional and reduced representation of temporal and causal properties of the time series data. Recent strategies involve mapping multivariate time series into high-level network structures, specifically into multiplex networks representing interconnections between contemporary timestamps of different time series components. In this work, we propose a new mapping method that takes advantage of the entire structure of multilayer networks. We introduce the multilayer horizontal visibility graph that is based on the new concept of cross-horizontal visibility between lagged timestamps of different components, which allows describing the cross-dimension dependencies via inter-layer edges. We use a set of existing topological measures of multilayer networks as well as a novel measure to evaluate and validate our approach, which is parameter-free, does not require data pre-processing and is applicable to any kind of multivariate time series data. We provide an extensive experimental evaluation, where we explore the proposed topological measures, showing that the inter-layer edges based on cross-horizontal visibility preserve more information about the time series data after the mappings, information that would inevitably be lost using mapping methods that result in single-layer and multiplex structures. We also verify that the information mapped by the inter-layer edges is not enough on its own, but that it complements the data information captured by the commonly used intra-layer edges.

There is nowadays a constant flux of data being generated and collected in all types of real world systems. These data sets are often indexed by time, space or both requiring appropriate approaches to analyze the data. In univariate settings, time series analysis is a mature and solid field. However, in multivariate contexts, time series analysis still presents many limitations. In order to address these issues, the last decade has brought approaches based on network science. These methods involve transforming an initial time series data set into one or more networks, which can be analyzed in depth to provide insight into the original time series. This review provides a comprehensive overview of existing mapping methods for transforming time series into networks for a wide audience of researchers and practitioners in machine learning, data mining and time series. Our main contribution is a structured review of existing methodologies, identifying their main characteristics and their differences. We describe the main conceptual approaches, provide authoritative references and give insight into their advantages and limitations in a unified notation and language. We first describe the case of univariate time series, which can be mapped to single layer networks, and we divide the current mappings based on the underlying concept: visibility, transition and proximity. We then proceed with multivariate time series discussing both single layer and multiple layer approaches. Although still very recent, this research area has much potential and with this survey we intend to pave the way for future research on the topic.

Being able to capture the characteristics of a time series with a feature vector is a very important task with a multitude of applications, such as classification, clustering or forecasting. Usually, the features are obtained from linear and nonlinear time series measures, that may present several data related drawbacks. In this work we introduce NetF as an alternative set of features, incorporating several representative topological measures of different complex networks mappings of the time series. Our approach does not require data preprocessing and is applicable regardless of any data characteristics. Exploring our novel feature vector, we are able to connect mapped network features to properties inherent in diversified time series models, showing that NetF can be useful to characterize time data. Furthermore, we also demonstrate the applicability of our methodology in clustering synthetic and benchmark time series sets, comparing its performance with more conventional features, showcasing how NetF can achieve high-accuracy clusters. Our results are very promising, with network features from different mapping methods capturing different properties of the time series, adding a different and rich feature set to the literature.