Pedro Manuel Ribeiro

Abstract
Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often adapt univariate approaches or rely on assumptions specific to certain domains or problems, presenting limitations. A recent promising alternative is to map multivariate time series into high-level network structures such as multiplex networks, with past work relying on connecting successive time series components with interconnections between contemporary timestamps. In this work, we first define a novel cross-horizontal visibility mapping between lagged timestamps of different time series and then introduce the concept of multilayer horizontal visibility graphs. This allows describing cross-dimension dependencies via inter-layer edges, leveraging the entire structure of multilayer networks. To this end, a novel parameter-free topological measure is proposed and common measures are extended for the multilayer setting. Our approach is general and applicable to any kind of multivariate time series data. We provide an extensive experimental evaluation with both synthetic and real-world datasets. We first explore the proposed methodology and the data properties highlighted by each measure, showing that inter-layer edges based on cross-horizontal visibility preserve more information than previous mappings, while also complementing the information captured by commonly used intra-layer edges. We then illustrate the applicability and validity of our approach in multivariate time series mining tasks, showcasing its potential for enhanced data analysis and insights.

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.

Abstract
With the huge amount of data that has been collected over time, many methods are being developed to allow better understanding and forecasting in several domains. Time series analysis is a powerful tool to achieve this goal. Despite being a well-established area, there are some gaps, and new methods are emerging to overcome these limitations, such as visibility graphs. Visibility graphs allow the analyses of times series as complex networks and make possible the use of more advanced techniques from another well-established area, network science. In this paper, we present two new efficient approaches for computing natural visibility graphs from times series, one for online scenarios in.O(n log n) and the other for offline scenarios in.O(nm), the latter taking advantage of the number of different values in the time series (m).

Abstract

Abstract
When the available data for a target domain is limited, transfer learning (TL) methods leverage related data-rich source domains to train and evaluate models, before deploying them on the target domain. However, most TL methods assume fixed levels of labeled and unlabeled target data, which contrasts with real-world scenarios where both data and labels arrive progressively over time. As a result, evaluations based on these static assumptions may not reflect how methods perform in practice. To support a more realistic assessment of TL methods in dynamic settings, we propose an evaluation framework that (1) simulates varying data availability over time, (2) creates multiple domains via resampling of a given dataset and (3) introduces inter-domain variability through controlled transformations, e.g., including time-dependent covariate and concept shifts. These capabilities enable the systematic simulation of a large number of variants of the experiments, providing deeper insights into how algorithms may behave when deployed. We demonstrate the usefulness of the proposed framework by performing a case study on a proprietary real-world suite of card payment datasets. To support reproducibility, we also apply the framework on the publicly available Bank Account Fraud (BAF) dataset. By providing a methodology for evaluating TL methods over time and in different data availability conditions, our framework supports a better understanding of model behavior in real-world environments, which enables more informed decisions when deploying models in new domains.