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Time series pattern identification by hierarchical community detection
Abstract
Identifying time series patterns is of great importance for many real-world problems in a variety of scientific fields. Here, we present a method to identify time series patterns in multiscale levels based on the hierarchical community representation in a complex network. The construction method transforms the time series into a network according to its segments’ correlation. The constructed network’s quality is evaluated in terms of the largest correlation threshold that reaches the largest main component’s size. The presence of repeated hierarchical patterns is then captured through network metrics, such as the modularity along the community detection process. We show the benefits of the proposed method by testing in one artificial dataset and two real-world time series applications. The results indicate that the method can successfully identify the original data’s hierarchical (micro and macro) characteristics.
... Temporal auto-correlation dependencies: The evolution of multivariate time series changes dynamically over time and is mainly reflected in auto-correlations and trends (Anghinoni et al., 2021). For example, in the bird migration case, factors affecting these correlations can include inadequate food and subsequent starvation, too little energy to travel, bad weather conditions, and others Visser et al. (2009). ...
... Temporal auto-correlation dependency. The evolution of multivariate time series changes dynamically over time and patterns are quasi-periodical on different scales of years and days (Anghinoni et al., 2021). Additionally, sensor malfunctions and failures, transmission errors, and other factors can mean the recorded time series carries noise (Han & Wang, 2013). ...
Background
Multivariate time series data generally contains missing values, which can be an obstacle to subsequent analysis and may compromise downstream applications. One challenge in this endeavor is the presence of the missing values brought about by sensor failure and transmission packet loss. Imputation is the usual remedy in such circumstances. However, in some multivariate time series data, the complex correlation and temporal dependencies, coupled with the non-stationarity of the data, make imputation difficult.
Mehods
To address this problem, we propose a novel model for multivariate time series imputation called CGCNImp that considers both correlation and temporal dependency modeling. The correlation dependency module leverages neural Granger causality and a GCN to capture the correlation dependencies among different attributes of the time series data, while the temporal dependency module relies on an attention-driven long short term memory (LSTM) and a time lag matrix to learn its dependencies. Missing values and noise are addressed with total variation reconstruction.
Results
We conduct thorough empirical analyses on two real-world datasets. Imputation results show that CGCNImp achieves state-of-the-art performance when compared to previous methods.
... The theoretical aspects considered here cover a broad spectrum of topics such as collective dynamics of excitable systems, cluster dynamics [1], interplay of noise and feedback [2], subdiffusive behavior [5], spreading phenomena on networks [8], coarsening [9], multipartite networks, partial synchrony [11], and time-delayed interactions [13,14]. In a series of works, complex networks are successfully employed as tools for detecting artificially inserted data [3], community detection [4,12], identification of time series patterns [6], and modeling a voter dynamics [15]. ...
... Anghinoni et al. [6] present a method for the identification of time series patterns using complex networks tools. The method first transforms the time series into a network according to the correlation between the different segments of the time-series. ...
This special issue presents a series of 33 contributions in the area of dynamical networks and their applications. Part of the contributions is devoted to theoretical and methodological aspects of dynamical networks, such as collective dynamics of excitable systems, spreading processes, coarsening, synchronization, delayed interactions, and others. A particular focus is placed on applications to neuroscience and Earth science, especially functional climate networks. Among the highlights, various methods for dealing with noise and stochastic processes in neuroscience are presented. A method for constructing weighted networks with arbitrary topologies from a single dynamical node with delayed feedback is introduced. Also, a generalization of the concept of geodesic distances, a path-integral formulation of network-based measures is developed, which provides fundamental insights into the dynamics of disease transmission. The contributions from the Earth science application field substantiate predictive power of climate networks to study challenging Earth processes and phenomena.
... However, there are less common cases in which some nodes are scattered between communities, or it is not visible from the graph how close the two communities are. This issue motivates us to further analyze the MST to optimize the clustering result using several community detection methods which have been developed [99][100][101][102][103]. Of these, the Louvain method is applicable across a wide range of domains [104][105][106][107]. Thus, we apply this method to our MST in order to obtain optimal communities. ...
We employ graph-based methods to examine the connectedness between cryptocurrencies of different market caps over time. By applying denoising and detrending techniques inherited from Random Matrix Theory and the concept of the so-called Market Component, we are able to extract new insights from historical return and volatility time series. Notably, our analysis reveals that changes in volatility-based network structure can be used to identify major events that have, in turn, impacted the cryptocurrency market. Additionally, we find that these structures reflect investors’ sentiments, including emotions like fear and greed. Using metrics such as PageRank, we discover that certain minor coins unexpectedly exert a disproportionate influence on the market, while the largest cryptocurrencies such as BTC and ETH seem less influential. We suggest that our findings have practical implications for investors in different ways: Firstly, helping them to avoid major market disruptions such as crashes, to safeguard their investments, and to capitalize on opportunities for high returns; Secondly, sharpening and optimizing the portfolios thanks to the understanding of cryptocurrencies’ connectedness.
... However, there are less common cases in which some nodes are scattered between communities, or it is not visible from the graph how close the two communities are. This issue motivates us to further analyze the MST to optimize the clustering result using several community detection methods which have been developed [99][100][101][102][103]. Of these, the Louvain method is applicable across a wide range of domains [104][105][106][107]. Thus, we apply this method to our MST in order to obtain optimal communities. ...
We analyze the correlation between different assets in the cryptocurrency market throughout different phases, specifically bearish and bullish periods. Taking advantage of a fine-grained dataset comprising 34 historical cryptocurrency price time series collected tick-by-tick on the HitBTC exchange, we observe the changes in interactions among these cryptocurrencies from two aspects: time and level of granularity. Moreover, the investment decisions of investors during turbulent times caused by the COVID-19 pandemic are assessed by looking at the cryptocurrency community structure using various community detection algorithms. We found that finer-grain time series describes clearer the correlations between cryptocurrencies. Notably, a noise and trend removal scheme is applied to the original correlations thanks to the theory of random matrices and the concept of Market Component, which has never been considered in existing studies in quantitative finance. To this end, we recognized that investment decisions of cryptocurrency traders vary between bearish and bullish markets. The results of our work can help scholars, especially investors, better understand the operation of the cryptocurrency market, thereby building up an appropriate investment strategy suitable to the prevailing certain economic situation.
Given the nature of time series and their vast applications, it is essential to find clustering algorithms that depict their real-life properties. Among the features that can hugely effect the options available for time series are overlapping and hierarchical properties. In this paper a novel approach to analyze time series with such features is introduced. Using the two concepts of network construction and link community detection, we have attempted to analyze and identify the mentioned properties of time series using data that is often gathered first hand. The proposed algorithm has been applied using both recent and common similarity measures on ten synthetic time series with hierarchal and overlapping features, alongside various distance measures. When testing the proposed approach, the element-centric measure of similarity indicated a clear increased accuracy for this algorithm, showing the highest accuracy when used alongside the Dynamic Time Warping distance measure. Moreover, the proposed algorithm has been very successful in identifying and forming communities for both large and small time series, thus solving another one of the main issues previous algorithms tended to have.
Community detection has attracted a lot of attention in recent decades for understanding structures and functions of complex networks. A plethora of exhaustive studies have proved that community detection methods based only on topology information tend to obtain poor community partition results. Several methods that utilize prior information to improve performance are proposed. However, most of the previous work ignores the influence of the noise from prior information. Prior information can be uncertain, imprecise, or even noisy. The reliability of prior information is a crucial factor, as wrong prior information may propagate throughout the whole network, reducing community detection effectiveness. In this paper, by combining particle cooperation and competition with distance dynamics, we propose a novel algorithm for community detection in error-prone environments (PCCDD), which helps to make full use of prior information. Finally, we conduct extensive experiments on artificial and real-world networks compared with state-of-the-art algorithms. Experimental results show that the PCCDD algorithm improves the accuracy of community detection and has good robustness in error-prone environments for detecting and preventing error propagation. Moreover, the algorithm can also be applied well to large-scale networks with unbalanced community structures due to linear time complexity.
The number of spatiotemporal data sets has increased rapidly in the last years, which demands robust and fast methods to extract information from this kind of data. Here, we propose a network-based model, called Chronnet, for spatiotemporal data analysis. The network construction process consists of dividing a geometric space into grid cells represented by nodes connected chronologically. Strong links in the network represent consecutive recurrent events between cells. The chronnet construction process is fast, making the model suitable to process large data sets. Using artificial and real data sets, we show how chronnets can capture data properties beyond simple statistics, like frequent patterns, spatial changes, outliers, and spatiotemporal clusters. Therefore, we conclude that chronnets represent a robust tool for the analysis of spatiotemporal data sets.
Temporal network mining tasks are usually hard problems. This is because we need to face not only a large amount of data but also its non-stationary nature. In this paper, we propose a method for temporal network pattern representation and pattern change detection following the reductionist approach. The main idea is to model each stable (durable) state of a given temporal network as a community in a sampled static network and the temporal state change is represented by the transition from one community to another. For this purpose, a reduced static single-layer network, called a target network, is constructed by sampling and rearranging the original temporal network. Our approach provides a general way not only for temporal networks but also for data stream mining in topological space. Simulation results on artificial and real temporal networks show that the proposed method can group different temporal states into different communities with a very reduced amount of sampled nodes.
The advent of the digital era provided a fertile ground for the development of virtual societies, complex systems influencing real-world dynamics. Understanding online human behavior and its relevance beyond the digital boundaries is still an open challenge. Here we show that online social interactions during a massive voting event can be used to build an accurate map of real-world political parties and electoral ranks for Italian elections in 2018. We provide evidence that information flow and collective attention are often driven by a special class of highly influential users, that we name “augmented humans”, who exploit thousands of automated agents, also known as bots, for enhancing their online influence. We show that augmented humans generate deep information cascades, to the same extent of news media and other broadcasters, while they uniformly infiltrate across the full range of identified groups. Digital augmentation represents the cyber-physical counterpart of the human desire to acquire power within social systems.
Addressing fake news requires a multidisciplinary effort
The official air-quality statistic reported that Beijing had a 9.9% decline in the annual concentration of PM2.5 in 2016. While this statistic offered some relief for the inhabitants of the capital, we present several analyses based on Beijing's PM2.5 data of the past 4 years at 36 monitoring sites along with meteorological data of the past 7 years. The analyses reveal the air pollution situation in 2016 was not as rosy as the 9.9% decline would convey, and improvement if any was rather uncertain. The paper also provides an assessment on the city's PM2.5 situation in the past 4 years.
Computational propaganda deploys social or political bots to try to shape, steer and manipulate online public discussions and influence decisions. Collective behaviour of populations of social bots has not been yet widely studied, though understanding of collective patterns arising from interactions between bots would aid social bot detection. Here we show that there are significant differences in collective behaviour between population of bots and population of humans as detected from their Twitter activity. Using a large dataset of tweets we have collected during the UK EU referendum campaign, we separated users into population of bots and population of humans based on the length of sequences of their high-frequency tweeting activity. We show that while pairwise correlations between users are weak they co-exist with collective correlated states, however the statistics of correlations and co-spiking probability differ in both populations. Our results demonstrate that populations of social bots and human users in social media exhibit collective properties similar to the ones found in social and biological systems placed near a critical point.
Revealing complicated behaviors from time series constitutes a fundamental problem of continuing interest and it has attracted a great deal of attention from a wide variety of fields on account of its significant importance. The past decade has witnessed a rapid development of complex network studies, which allow to characterize many types of systems in nature and technology that contain a large number of components interacting with each other in a complicated manner. Recently, the complex network theory has been incorporated into the analysis of time series and fruitful achievements have been obtained. Complex network analysis of time series opens up new venues to address interdisciplinary challenges in climate dynamics, multiphase flow, brain functions, ECG dynamics, economics and traffic systems.
In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined to test the method’s reliability. Many different mea-sures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view.
From time series to complex networks: The visibility graph. Available from: https://www.researchgate.net/publication/301232812_From_time_series_to_complex_networks_The_visibility_graph [accessed Jun 29, 2017].
Network based time series analysis has made considerable achievements in the recent years. By mapping mono/multivariate time series into networks, one can investigate both it's microscopic and macroscopic behaviors. However, most proposed approaches lead to the construction of static networks consequently providing limited information on evolutionary behaviors. In the present paper we propose a method called visibility graph based time series analysis, in which series segments are mapped to visibility graphs as being descriptions of the corresponding states and the successively occurring states are linked. This procedure converts a time series to a temporal network and at the same time a network of networks. Findings from empirical records for stock markets in USA (S&P500 and Nasdaq) and artificial series generated by means of fractional Gaussian motions show that the method can provide us rich information benefiting short-term and long-term predictions. Theoretically, we propose a method to investigate time series from the viewpoint of network of networks.
Our understanding of a variety of phenomena in physics, biology and economics
crucially depends on the analysis of multivariate time series. While a wide
range of tools and techniques for time series analysis already exist, the
increasing availability of massive data structures calls for new approaches for
multidimensional signal processing. We present here a non-parametric method to
analyse multivariate time series, based on the mapping of a multidimensional
time series into a multilayer network, which allows to extract information on a
high dimensional dynamical system through the analysis of the structure of the
associated multiplex network. The method is simple to implement, general,
scalable, does not require ad hoc phase space partitioning, and is thus
suitable for the analysis of large, heterogeneous and non-stationary time
series. We show that simple structural descriptors of the associated multiplex
networks allow to extract and quantify nontrivial properties of coupled chaotic
maps, including the transition between different dynamical phases and the onset
of various types of synchronization. As a concrete example we then study
financial time series, showing that a multiplex network analysis can
efficiently discriminate crises from periods of financial stability, where
standard methods based on time-series symbolization often fail.
In this paper, we propose a technique for time series clustering using community detection in complex networks. Firstly, we present a method to transform a set of time series into a network using different distance functions, where each time series is represented by a vertex and the most similar ones are connected. Then, we apply community detection algorithms to identify groups of strongly connected vertices (called a community) and, consequently, identify time series clusters. Still in this paper, we make a comprehensive analysis on the influence of various combinations of time series distance functions, network generation methods and community detection techniques on clustering results. Experimental study shows that the proposed network-based approach achieves better results than various classic or up-to-date clustering techniques under consideration. Statistical tests confirm that the proposed method outperforms some classic clustering algorithms, such as k-medoids, diana, median-linkage and centroid-linkage in various data sets. Interestingly, the proposed method can effectively detect shape patterns presented in time series due to the topological structure of the underlying network constructed in the clustering process. At the same time, other techniques fail to identify such patterns. Moreover, the proposed method is robust enough to group time series presenting similar pattern but with time shifts and/or amplitude variations. In summary, the main point of the proposed method is the transformation of time series from time-space domain to topological domain. Therefore, we hope that our approach contributes not only for time series clustering, but also for general time series analysis tasks.
The multiscale phenomenon widely exists in nonlinear complex systems. One efficient way to characterize complex systems is to measure time series and then extract information from the measurements. We propose a reliable method for constructing a multiscale complex network from multivariate time series. In particular, for a given multivariate time series, we first perform a coarse-grained operation to define temporal scales and then reconstruct the multivariate phase-space for each scale to infer multiscale complex networks. In addition, we develop a novel clustering coefficient entropy to assess the derived multiscale complex networks, aiming to characterize the coupled dynamical characteristics underlying multivariate time series. We apply our proposed approach to the analysis of multivariate time series measured from gas-liquid two-phase flow experiments. The results yield novel insights into the inherent coupled flow behavior underlying a realistic multiphase flow system. Bridging multiscale analysis and complex network provides a fascinating methodology for probing multiscale complex behavior underlying complex systems.
Uncovering complex oil-water flow structure represents a challenge in diverse scientific disciplines. This challenge stimulates us to develop a new distributed conductance sensor for measuring local flow signals at different positions and then propose a novel approach based on multi-frequency complex network to uncover the flow structures from experimental multivariate measurements. In particular, based on the Fast Fourier transform, we demonstrate how to derive multi-frequency complex network from multivariate time series. We construct complex networks at different frequencies and then detect community structures. Our results indicate that the community structures faithfully represent the structural features of oil-water flow patterns. Furthermore, we investigate the network statistic at different frequencies for each derived network and find that the frequency clustering coefficient enables to uncover the evolution of flow patterns and yield deep insights into the formation of flow structures. Current results present a first step towards a network visualization of complex flow patterns from a community structure perspective.
Complex networks are a unified form of rep-resenting complex systems. Through this representation is possible to study dynamical systems and make time series analysis using network techniques. One common charac-teristic of many real world time series is the periodicity. Detecting these periods is interesting because it permits to forecast the series behavior. Some techniques have been proposed to search for these periods but many of them fail to deal with noisy data. In this paper, we present an algorithm for periodicity detection in noisy data based on community detection. First, the method transforms a time series by dividing it into intervals that are represented by vertices. Then, we apply community detection in order to cluster highly connected ranges. These clusters of vertices represent periodic changes in the series and can be used to detect periodicity. The efficiency of the proposed method is illustrated in a meteorological case study where we detected periodicity in a noisy temperature data.
There are many types of autoregressive patterns in financial time series, and they form a transmission process. Here, we define autoregressive patterns quantitatively through an econometrical regression model. We present a computational algorithm that sets the autoregressive patterns as nodes and transmissions between patterns as edges, and then converts the transmission process of autoregressive patterns in a time series into a network. We utilised daily Shanghai (securities) composite index time series to study the transmission characteristics of autoregressive patterns. We found statistically significant evidence that the financial market is not random and that there are similar characteristics between parts and whole time series. A few types of autoregressive sub-patterns and transmission patterns drive the oscillations of the financial market. A clustering effect on fluctuations appears in the transmission process, and certain non-major autoregressive sub-patterns have high media capabilities in the financial time series. Different stock indexes exhibit similar characteristics in the transmission of fluctuation information. This work not only proposes a distinctive perspective for analysing financial time series but also provides important information for investors.
There are now several algorithms with which one can generate a complex network representation of a time series. The basic motivation of these methods is that by performing such a transformation one can then apply a range of techniques from complex network science to the analysis and quantification of features of the time series. We will review our favorites among these techniques and then focus on what the current techniques do not do well - capture deterministic dynamical information directly. We will propose an alternative technique, the ordinal partition network transform, to do precisely this. By constructing networks from connectivity patterns among ordinal partitions of the time series we provide a parameter-free approach to study the dynamical evolution of the system directly. We show that the ordinal networks generated in this way from experimental time series data have statistical properties which provide a useful (and novel) characterisation of the underlying system.
This paper investigates political homophily on Twitter. Using a combination of machine learning and social network analysis we classify users as Democrats or as Republicans based on the political content shared. We then investigate political homophily both in the network of reciprocated and nonreciprocated ties. We find that structures of political homophily differ strongly between Democrats and Republicans. In general, Democrats exhibit higher levels of political homophily. But Republicans who follow official Republican accounts exhibit higher levels of homophily than Democrats. In addition, levels of homophily are higher in the network of reciprocated followers than in the nonreciprocated network. We suggest that research on political homophily on the Internet should take the political culture and practices of users seriously.
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related to the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.
This paper presents a new approach for analysing structural properties of
time series from complex systems. Starting from the concept of recurrences in
phase space, the recurrence matrix of a time series is interpreted as the
adjacency matrix of an associated complex network which links different points
in time if the evolution of the considered states is very similar. A critical
comparison of these recurrence networks with similar existing techniques is
presented, revealing strong conceptual benefits of the new approach which can
be considered as a unifying framework for transforming time series into complex
networks that also includes other methods as special cases.
It is demonstrated that there are fundamental relationships between the
topological properties of recurrence networks and the statistical properties of
the phase space density of the underlying dynamical system. Hence, the network
description yields new quantitative characteristics of the dynamical complexity
of a time series, which substantially complement existing measures of
recurrence quantification analysis.
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks. Comment: Review article. 103 pages, 42 figures, 2 tables. Two sections expanded + minor modifications. Three figures + one table + references added. Final version published in Physics Reports
Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail. We discuss the main requirements that permit a feasible system-theoretic interpretation of network topology in terms of dynamically invariant phase-space properties. Possible artifacts induced by disregarding these requirements are pointed out and systematically studied. Finally, a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed.
Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.
We construct complex networks from pseudoperiodic time series, with each cycle represented by a single node in the network. We investigate the statistical properties of these networks for various time series and find that time series with different dynamics exhibit distinct topological structures. Specifically, noisy periodic signals correspond to random networks, and chaotic time series generate networks that exhibit small world and scale free features. We show that this distinction in topological structure results from the hierarchy of unstable periodic orbits embedded in the chaotic attractor. Standard measures of structure in complex networks can therefore be applied to distinguish different dynamic regimes in time series. Application to human electrocardiograms shows that such statistical properties are able to differentiate between the sinus rhythm cardiograms of healthy volunteers and those of coronary care patients.
Extracting knowledge from time series provides important tools for many real applications. However, many challenging problems still open due to the stochastic nature of large amount of time series. Considering this scenario, new data mining and machine learning techniques have continuously developed. In this paper, we study time series based on its topological features, observed on a complex network generated from the time series data. Specifically, we present a trend detection algorithm for stochastic time series based on community detection and network metrics. The proposed model presents some advantages over traditional time series analysis, such as adaptive number of classes with measurable strength and better noise absorption. The appealing feature of this work is to pave a new way to represent time series trends by communities of complex networks in topological space instead of physical space (spatial-temporal space or frequency spectral) as traditional techniques do. Experimental results on artificial and real data-sets shows that the proposed method is able to classify the time series into local and global patterns. As a consequence, it improves the predictability on time series.
Time series databases consist of sequences of values that are calculated or retrieved at regular intervals of time. The values or the events are measured at equal intervals of time (hourly, weekly, yearly etc). Time series data is very large in size having high dimensionality and is updated at regular intervals of time. Mining of the time series data is considered as an important analysis approach in large number of application areas like medicine, fraud detection, stock market etc. There has been a huge amount of research going in the field of time series data mining.
Time series is one of the popular data types that can be found in many domains such as business, medical, meteorological fields, etc. Identifying potential trends in time series is important because it imparts knowledge about what has taken place in the past and what will take place in time to come. Trend analysis in the time series is the practice of collecting and attempting to spot patterns. Various data mining techniques such as clustering, classification, regression, etc. can be used to expose those trends. In this work, we developed a framework to analyze the time series data, which cluster time series according to their similarity. We also introduced a merging algorithm to represent each cluster using a representative series. Trends are detected in a series using Modified Mann-Kendall test.
This paper reviews the recent advances in bridging time series analysis and complex network theory. We first introduce the main representative approaches of mapping time series into complex networks with their potential and advantages in applications in a variety of fields, and also report the latest methods to feature complex networks with typical time series after multi-scaling transformation, and to estimate and identify the uncertain connectivity of a complex network. As an example, we show an amplitude-temporal method to fast detect arrhythmia with the indicator of the average degree of associated networks.
Detecting overlapping communities is essential to analyzing and exploring natural networks such as social networks, biological networks, and citation networks. However, most existing approaches do not scale to the size of networks that we regularly observe in the real world. In this paper, we develop a scalable approach to community detection that discovers overlapping communities in massive real-world networks. Our approach is based on a Bayesian model of networks that allows nodes to participate in multiple communities, and a corresponding algorithm that naturally interleaves subsampling from the network and updating an estimate of its communities. We demonstrate how we can discover the hidden community structure of several real-world networks, including 3.7 million US patents, 575,000 physics articles from the arXiv preprint server, and 875,000 connected Web pages from the Internet. Furthermore, we demonstrate on large simulated networks that our algorithm accurately discovers the true community structure. This paper opens the door to using sophisticated statistical models to analyze massive networks.
Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of1, 2, 3, 4. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins5, 6, industrial sectors7 and groups of people8, 9) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.
Recent works show that complex network theory may be a powerful tool in time series analysis. We propose in this paper a reliable procedure for constructing complex networks from the correlation matrix of a time series. An original stock time series, the corresponding return series and its amplitude series are considered. The degree distribution of the original series can be well fitted with a power law, while that of the return series can be well fitted with a Gaussian function. The degree distribution of the amplitude series contains two asymmetric Gaussian branches. Reconstruction of networks from time series is a common problem in diverse research. The proposed strategy may be a reasonable solution to this problem.
The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m approximately n and d approximately log n, in which case our algorithm runs in essentially linear time, O (n log(2) n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on-line retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 x 10(6) edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.
We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.
Temporal network pattern identification by community modelling
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