Vanessa Freitas Silva

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
Seasonal and daily variations of gaseous emissions from naturally ventilated dairy cattle barns are important figures for the establishment of effective and specific mitigation plans. The present study aimed to measure methane (CH4) and ammonia (NH3) emissions in three naturally ventilated dairy cattle barns covering the four seasons for two consecutive years. In each barn, air samples from five indoor locations were drawn by a multipoint sampler to a photoacoustic infrared multigas monitor, along with temperature and relative humidity. Milk production data were also recorded. Results showed seasonal differences for CH4 and NH3 emissions in the three barns with no clear trends within years. Globally, diel CH4 emissions increased in the daytime with high intra-hour variability. The average hourly CH4 emissions (g h-1 livestock unit- 1 (LU)) varied from 8.1 to 11.2 and 6.2 to 20.3 in the dairy barn 1, from 10.1 to 31.4 and 10.9 to 22.8 in the dairy barn 2, and from 1.5 to 8.2 and 13.1 to 22.1 in the dairy barn 3, respectively, in years 1 and 2. Diel NH3 emissions highly varied within hours and increased in the daytime. The average hourly NH3 emissions (g h-1 LU-1) varied from 0.78 to 1.56 and 0.50 to 1.38 in the dairy barn 1, from 1.04 to 3.40 and 0.93 to 1.98 in the dairy barn 2, and from 0.66 to 1.32 and 1.67 to 1.73 in the dairy barn 3, respectively, in years 1 and 2. Moreover, the emission factors of CH4 and NH3 were 309.5 and 30.6 (g day- 1 LU-1), respectively, for naturally ventilated dairy cattle barns. Overall, this study provided a detailed characterization of seasonal and daily gaseous emissions variations highlighting the need for future longitudinal emission studies and identifying an opportunity to better adequate the existing mitigation strategies according to season and daytime.

Abstract
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.

Abstract
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 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 way 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. This article is categorized under: Fundamental Concepts of Data and Knowledge > Data Concepts Fundamental Concepts of Data and Knowledge > Knowledge Representation