Multivariate Time Series Clustering based on Graph Convolutional Network

The time series clustering is one of the important research contents in the time series data mining. Since the dimension of time series is common high, the performance of direct raw time series data clustering is not ideal. How to improve the clustering performance of time series is the main research point of this paper. Firstly, use Locality Preserving Projection (LPP) to time series samples for dimensionality reduction; secondly, carry out clustering ensemble to the lowdimension data; finally, compare the clustering performance with the existing methods such as Principal Component Analysis (PCA) and Piecewise Aggregate Approximation (PAA). Experiment results show that the proposed method is superior to the compared methods.

In recent past, there is an increased interest in time series clustering research, particularly for finding useful similar trends in multivariate time series in various applied areas such as environmental research, finance, and crime. Clustering multivariate time series has potential for analyzing large volume of crime data at different time points as law enforcement agencies are interested in finding crime trends of various police administration units such as states, districts and police stations so that future occurrences of similar incidents can be overcome. Most of the traditional time series clustering algorithms deals with only univariate time series data and for clustering high dimensional data, it has to be transformed into single dimension using a dimension reduction technique. The conventional time series clustering techniques do not provide desired results for crime data set, since crime data is high dimensional and consists of various crime types with different weight age. In this paper, a novel approach based on dynamic time wrapping and parametric Minkowski model has been proposed to find similar crime trends among various crime sequences of different crime locations and subsequently use this information for future crime trends prediction. Analysis on Indian crime records show that the proposed technique generally outperforms the existing techniques in clustering of such multivariate time series data.

Subsequence clustering of multivariate time series is a useful tool for discovering repeated patterns in temporal data. Once these patterns have been discovered, seemingly complicated datasets can be interpreted as a temporal sequence of only a small number of states, or clusters. However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Here we propose a new method of model-based clustering, which we call Toeplitz Inverse Covariance-based Clustering (TICC). Each cluster in the TICC method is defined by a correlation network, or Markov random field (MRF), characterizing the interdependencies between different observations in a typical subsequence of that cluster. Based on this graphical representation, TICC simultaneously segments and clusters the time series data. We solve the TICC problem through a scalable algorithm that is able to efficiently solve for tens of millions of observations. We validate our approach by comparing TICC to several state-of-the-art baselines in a series of synthetic experiments, and we then demonstrate on an automobile dataset how TICC can be used to learn interpretable clusters in real-world scenarios.

This paper proposes a novel time series data mining and analysis framework inspired by ancient Chinese culture I-Ching. The proposed method converts the time series into symbol spaces by employing the concepts and principles of I-Ching. Algorithms are addressed to explore and identify temporal patterns in the resulting symbol spaces. Using the analysis framework, major topics of time series data mining regarding time series clustering, association rules of temporal patterns, and transition of hidden Markov process can be analyzed. Dynamic patterns are derived and adopted to investigate the occurrence of special events existing in the time series. A case study is illustrated to demonstrate the effectiveness and usefulness of the proposed analysis framework. Key words: Time series, data mining, Chinese I-Ching.

Much of the world’s supply of data is in the form of time series. Furthermore, as we shall see, many types of data can be meaningfully converted into ”time series”, including text, DNA, video, images etc. The last decade has seen an explosion of interest in mining time series data from the academic community. There has been significant work on algorithms to classify, cluster, segment, index, discover rules, visualize, and detect anomalies/novelties in time series. In this talk I will summarize the latest advances in mining time series data, including: – New representations of time series data. – New algorithms/definitions. – The migration from static problems to online problems. – New areas and applications of time series data mining. I will end the talk with a discussion of “what’s left to do” in time series data mining.

Much of the world’s supply of data is in the form of time series. Furthermore, as we shall see, many types of data can be meaningfully converted into ”time series”, including text, DNA, video, images etc. The last decade has seen an explosion of interest in mining time series data from the academic community. There has been significant work on algorithms to classify, cluster, segment, index, discover rules, visualize, and detect anomalies/novelties in time series.In this talk I will summarize the latest advances in mining time series data, including:– New representations of time series data.– New algorithms/definitions.– The migration from static problems to online problems.– New areas and applications of time series data mining.I will end the talk with a discussion of “what’s left to do” in time series data mining.KeywordsTime SeriesData MiningKnowledge DiscoveryTime Series DataAcademic CommunityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The novel Time Series Data Mining (TSDM) framework is applied to analyzing financial time series. The TSDM framework adapts and innovates data mining concepts to analyzing time series data. In particular, it creates a set of methods that reveal hidden temporal patterns that are characteristic and predictive of time series events. This contrasts with other time series analysis techniques, which typically characterize and predict all observations. The TSDM framework and concepts are reviewed, and the applicable TSDM method is discussed. Finally, the TSDM method is applied to time series generated by a basket of financial securities. The results show that statistically significant temporal patterns that are both characteristic and predictive of events in financial time series can be identified.

Time series clustering via matrix profile and community detection

The previous decade has brought a remarkable increase of the interest in applications that deal with querying and mining of time series data. Many of the research efforts in this context have focused on introducing new representation methods for dimensionality reduction or novel similarity measures for the underlying data. In the vast majority of cases, each individual work introducing a particular method has made specific claims and, aside from the occasional theoretical justifications, provided quantitative experimental observations. However, for the most part, the comparative aspects of these experiments were too narrowly focused on demonstrating the benefits of the proposed methods over some of the previously introduced ones. In order to provide a comprehensive validation, we conducted an extensive experimental study re-implementing eight different time series representations and nine similarity measures and their variants, and testing their effectiveness on 38 time series data sets from a wide variety of application domains. In this article, we give an overview of these different techniques and present our comparative experimental findings regarding their effectiveness. In addition to providing a unified validation of some of the existing achievements, our experiments also indicate that, in some cases, certain claims in the literature may be unduly optimistic.

One of the main challenging subjects of data mining is fuzzy-clustering time series in real-world applications. Its reason can be time-series data characteristics that include high dimensional, large volume and existence of temporal ordering in data. So far, many studies have performed about issues such as addressing time-series data high dimension and applying a different effect of each dimension in clustering results. In many of the recent published resources, feature-weighting process in time-series data has employed as one effective way to overcome mentioned problems. Appropriate weight's assignment can discuss as one challenge in mentioned resources. Hence, aim of this paper is optimization of the feature-weighting process in time series clustering task. For this aim, a technique is proposed based on the combination of two fundamental concepts, including features effect-based weighting and optimization in order to optimize weight's assignment in time series clustering. Proposed technique is made possibility use of the merits of two concepts in order to improving performance fuzzy-clustering task in time-series data. Fuzzy Particle Swarm Optimization (FPSO) is used as a population-based technique for optimization of feature-weighting process and enhancing performance of clustering. Proposed technique is evaluated based on three indexes validity that includes Partition Coefficient (PC), Partition Entropy (PE) and Davios-Bouldin (DB). Experimental results are indicated that our proposed technique is efficient and can represent encouraging results. Also, clustering results by population-based a proposed technique is demonstrated the improvement of performance of fuzzy-clustering time series than other conventional techniques.

With the increasing use of time series data, particularly in critical applications and high-risk decision-making contexts, understanding and improving the explainability of time-series clustering(TSC) techniques is essential. While machine learning models excel in processing time series data, their explainability often needs enhancement, challenging human comprehension and trust. Time series data clustering, as an unsupervised learning method, extracts valuable patterns from complex datasets without prior knowledge, spanning various domains like biology and finance. However, the complexity of clustering models and their opaque decision-making processes raise concerns about understanding and trusting the results. Research in this area aims to enhance the explainability of TSC by developing new interpretation methods that not only ensure the accuracy of clustering results but also make them user-friendly and comprehensible to human users. This is crucial for overcoming challenges related to understanding and trusting the decision-making processes and outcomes of the model. In this study, we embarked on two significant endeavors: (a) We explored the use of explainable artificial intelligence (XAI) for TSC for the first time, conducting a comprehensive literature review. (b) We subdivided the research field through innovative classification methods, categorizing the explainability methods of TSC into three main categories: data preprocessing techniques based on time series data, single or hybrid methods based model training, and instance-based visualization algorithm applications. This analytical framework aims to elucidate how the explainability of TSC can be enhanced across these three dimensions, thereby improving its credibility. Our work not only opens new research avenues but also provides robust strategies for enhancing the explainability and credibility of TSC methods.

Specification, estimation, and analysis of macroeconomic models: Ray C. Fair. Cambridge, MA: Harvard University Press, 1984. 479 pp. $35.00 ISBN 0-674-83180-2

Graph convolutional network – Long short term memory neural network- multi layer perceptron- Gaussian progress regression model: A new deep learning model for predicting ozone concertation

With the diversification of applications and the diversity of users, the era of big data is always producing various new types of data, such as graph data, time series data, and spatial data. When predicting the future trend of the system, we always need to learn from the historical working state, and time series data plays a huge value in this aspect. Hardware resources are becoming cheaper, computing power has made major breakthroughs, and multi-machine and multi-core scenarios have become commonplace. At present, the focus of large-scale time series data processing is either focused on data collection and storage, or on single-machine processing, which has been unable to meet the existing needs. In response to this problem, this paper designs and implements a distributed large-scale time series processing and analysis system based on the Spark platform. The system framework is mainly divided into storage layer, operator layer and algorithm layer. At the storage layer, the system completes the organization and indexing of large-scale time series data based on HDFS and Hive. At the operator layer, the system provides users with basic operations commonly used for time series data on the Spark platform, and allows users to directly use these operators to implement custom time series related processing algorithms. At the algorithm level, the system implements some commonly used time series analysis algorithms in the Spark platform, including time series similarity query, clustering and prediction, so that users can directly use these algorithms to analyze time series. Finally, the feasibility and practicability of this system are verified by testing the performance and function of the system.

Most algorithms for mining or indexing time series data do not operate directly on the original data, but instead they consider alternative representations that include transforms, quantization, approximation, and multi-resolution abstractions. Choosing the best representation and abstraction level for a given task/dataset is arguably the most critical step in time series data mining. In this paper, we investigate techniques to discover the natural intrinsic representation model, dimensionality and alphabet cardinality of a time series. The ability to discover these intrinsic features has implications beyond selecting the best parameters for particular algorithms, as characterizing data in such a manner is useful in its own right and an important sub-routine in algorithms for classification, clustering and outlier discovery. We will frame the discovery of these intrinsic features in the Minimal Description Length (MDL) framework. Extensive empirical tests show that our method is simpler, more general and significantly more accurate than previous methods, and has the important advantage of being essentially parameter-free.