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WIREs Data Mining Knowl Discov
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Time series analysis via network science: Concepts and algorithms

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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
An example of a general (a) multilayer network with five nodes V = {0,1,2,3,4} and two aspects, which have the corresponding elementary‐layers sets L1 = {A, B} and L2 = {X, Y}; (b) multiplex network with five nodes V = {0,1,2,3,4} and one aspect. In both figures, solid lines represent intra‐layer edges and dashed lines represent inter‐layer edges
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A representation of (a) a simple directed graph and (b) a simple undirected weighted graph
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Overview of our survey. Taxonomy of algorithms for mapping time series into complex networks based on the dimensionality of time series, resulting network structure, mapping concept, and main mapping methods
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Illustration of multiplex natural visibility graph algorithm for a toy multivariate time series
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(a) Illustrative example of a toy bivariate time series (Y1,t, Y2,t) and its ordinal pattern definitions and evolution. We show an embedding in a three‐dimensional space using a time delay τ = 2 and the schematic illustration of the OPTN analysis of the two series of ordinal patterns with a unidirectional coupling Y1,t → Y2,t with a coupling delay of h = 1. The time‐lagged conditional co‐occurrences of the patterns and are indicated by dashed arrows. (b) The network generated by the ordinal partition transition algorithm proposed in Ruan et al. (2019)
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(a) Illustrative example of a toy three‐dimensional series (Y1,t, Y2,t, Y3,t). (b) First‐order differences and corresponding ordinal patterns
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Illustrative example of the correlation network algorithm. On the left side we present the plot of a toy multivariate time series and on the right side the network generated by the correlation algorithm (using contemporaneous cross‐correlation). The different colors represent the time series. Higher correlation values result in edges in the network with larger weights represented by thicker lines
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Illustrative example of ordinal partition transition network algorithm. On the left side we illustrate the method of embedding with window size w = 3 and lag τ = 2 and the method of find its ordinal pattern, based in the amplitude rank of its elements. On the right side we show the resulting networks
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Illustrative example of the quantile graph algorithm for Q = 4. On the left panel we present the plot of a toy time series and on the right panel the network generated by the quantile graph algorithm. The different colors in the time series plot represent the regions corresponding to the different quantiles. In the network, edges with larger weights represented by thicker lines correspond to the repeated transitions between quantiles
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On the left side, we present the plot of a toy time series and, on the right side, the network generated by the natural visibility algorithm. The purple lines in the time series plot represent the lines of visibility (and hence the edges of the graph) between data points
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(a) Illustrative example of limited penetrable visibility graph algorithm where the limit l = 1. The purple lines show the edges between points that have direct visibility (as in NVG, l = 0) and the blue dashed lines are the extra edges imposed by LPVG algorithm, where two points can be seen with only one higher intermediate point. (b) Illustrative example of parametric natural visibility graph algorithm with comparison with NVG algorithm
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Illustrative example of directed horizontal visibility algorithm and corresponding out‐degree (), in‐degree (), and total‐degree (ki). On the left side, we present the plot of a toy time series and, on the right side, the network generated by the directed horizontal visibility algorithm. The green directed lines represent the directed horizontal lines of visibility between data points
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On the left side, we present the plot of a toy time series and, on the right side, the network generated by the horizontal visibility algorithm. The green lines represent the horizontal lines of visibility between the data points and the purple lines the natural visibility, to comparison
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Fundamental Concepts of Data and Knowledge > Knowledge Representation
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