Time series clustering is the process of grouping time series with respect to their similarity or characteristics. Previous approaches usually combine a specific distance measure for time series and a standard clustering method. However, these approaches do not take the similarity of the different subsequences of each time series into account, which can be used to better compare the time series objects of the dataset. In this paper, we propose a novel technique of time series clustering based on two clustering stages. In a first step, a least squares polynomial segmentation procedure is applied to each time series, which is based on a growing window technique that returns different-length segments. Then, all the segments are projected into same dimensional space, based on the coefficients of the model that approximates the segment and a set of statistical features. After mapping, a first hierarchical clustering phase is applied to all mapped segments, returning groups of segments for each time series. These clusters are used to represent all time series in the same dimensional space, after defining another specific mapping process. In a second and final clustering stage, all the time series objects are grouped. We consider internal clustering quality to automatically adjust the main parameter of the algorithm, which is an error threshold for the segmenta- tion. The results obtained on 84 datasets from the UCR Time Series Classification Archive have been compared against two state-of-the-art methods, showing that the performance of this methodology is very promising.
Many of the proposals for time series clustering are based on the combination of a distance measure and a clustering algorithm. First, we will analyse the most important distance measures proposed for time series comparison, and then we will introduce the clustering methods that can be applied based on them Further information about time series clustering can be found in @cite_37 or @cite_56 .
@cite_37 @cite_56
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Sequential time series clustering is a technique used to extract important features from time series data. The method can be shown to be the process of clustering in the delay-vector space formalism used in the Dynamical Systems literature. Recently, the startling claim was made that sequential time series clustering is meaningless. This has important consequences for a significant amount of work in the literature, since such a claim invalidates these work’s contribution. In this paper, we show that sequential time series clustering is not meaningless, and that the problem highlighted in these works stem from their use of the Euclidean distance metric as the distance measure in the delay-vector space. As a solution, we consider quite a general class of time series, and propose a regime based on two types of similarity that can exist between delay vectors, giving rise naturally to an alternative distance measure to Euclidean distance in the delay-vector space. We show that, using this alternative distance measure, sequential time series clustering can indeed be meaningful. We repeat a key experiment in the work on which the “meaningless” claim was based, and show that our method leads to a successful clustering outcome. The startling claim was made that sequential time series clustering is meaningless. This has important consequences for a significant amount of work in the literature, since such a claim invalidates this work's contribution. In this paper, we show that sequential time series clustering is not meaningless, and that the problem highlighted in these works stem from their use of the Euclidean distance metric as the distance measure in the subsequence vector space. As a solution, we consider quite a general class of time series, and propose a regime based on two types of similarity that can exist between subsequence vectors, which give rise naturally to an alternative distance measure to Euclidean distance in the subsequence vector space. We show that, using this alternative distance measure, sequential time series clustering can indeed be meaningful. We repeat a key experiment in the work on which the "meaningless" claim was based, and show that our method leads to a successful clustering outcome. Time series clustering has become an increasingly important research topic over the past decade. Most existing methods for time series clustering rely on distances calculated from the entire raw data using the Euclidean distance or Dynamic Time Warping distance as the distance measure. However, the presence of significant noise, dropouts, or extraneous data can greatly limit the accuracy of clustering in this domain. Moreover, for most real world problems, we cannot expect objects from the same class to be equal in length. As a consequence, most work on time series clustering only considers the clustering of individual time series "behaviors," e.g., individual heart beats or individual gait cycles, and contrives the time series in some way to make them all equal in length. However, contriving the data in such a way is often a harder problem than the clustering itself. In this work, we show that by using only some local patterns and deliberately ignoring the rest of the data, we can mitigate the above problems and cluster time series of different lengths, i.e., cluster one heartbeat with multiple heartbeats. To achieve this we exploit and extend a recently introduced concept in time series data mining called shapelets. Unlike existing work, our work demonstrates for the first time the unintuitive fact that shapelets can be learned from unlabeled time series. We show, with extensive empirical evaluation in diverse domains, that our method is more accurate than existing methods. Moreover, in addition to accurate clustering results, we show that our work also has the potential to give insights into the domains to which it is applied. The most widely used measures of time series proximity are the Euclidean distance and dynamic time warping. The latter can be derived from the distance introduced by Maurice Frechet in 1906 to account for the proximity between curves. The major limitation of these proximity measures is that they are based on the closeness of the values regardless of the similarity w.r.t. the growth behavior of the time series. To alleviate this drawback we propose a new dissimilarity index, based on an automatic adaptive tuning function, to include both proximity measures w.r.t. values and w.r.t. behavior. A comparative numerical analysis between the proposed index and the classical distance measures is performed on the basis of two datasets: a synthetic dataset and a dataset from a public health study. In time series mining, one of the interesting tasks that attract many researchers is time series clustering which is classified into two main categories. Whole time series clustering considers how to cluster multiple time series, and the other one is Subsequence Time Series (STS) clustering, a clustering of subparts or subsequences within a single time series. Deplorably, STS clustering is not preferable even though it had widely been used as a subroutine in various mining tasks, e.g., rule discovery, anomaly detection, or classification, due to the recent finding a decade ago that STS clustering problem can produce meaningless results. There have been numerous attempts to resolve this problem but seemed to be unsuccessful. Until the two most recent attempts, they seem to accomplish in producing meaningful results; however, their approaches do need some predefined constraint values, such as the width of the subsequences that are in fact quite subjective and sensitive. Thus, we propose a novel parameter-free clustering technique to eliminate this problem by utilizing a motif discovery algorithm and some statistical principles to properly determine these parameters. Our experimental results from well-known datasets demonstrate the effectiveness of the proposed algorithm in selecting the proper subsequence width, and in turn leading to meaningful and highly accurate results. Time series clustering has been shown effective in providing useful information in various domains. There seems to be an increased interest in time series clustering as part of the effort in temporal data mining research. To provide an overview, this paper surveys and summarizes previous works that investigated the clustering of time series data in various application domains. The basics of time series clustering are presented, including general-purpose clustering algorithms commonly used in time series clustering studies, the criteria for evaluating the performance of the clustering results, and the measures to determine the similarity dissimilarity between two time series being compared, either in the forms of raw data, extracted features, or some model parameters. The past researchs are organized into three groups depending upon whether they work directly with the raw data either in the time or frequency domain, indirectly with features extracted from the raw data, or indirectly with models built from the raw data. The uniqueness and limitation of previous research are discussed and several possible topics for future research are identified. Moreover, the areas that time series clustering have been applied to are also summarized, including the sources of data used. It is hoped that this review will serve as the steppingstone for those interested in advancing this area of research. Clustering time series data using the popular subsequence (STS) technique has been widely used in the data mining and wider communities. Recently the conclusion was made that it is meaningless, based on the findings that it produces (a) clustering outcomes for distinct time series that are not distinguishable from one another, and (b) cluster centroids that are smoothed. More recent work has since showed that (a) could be solved by introducing a lag in the subsequence vector construction process, however we show in this paper that such an approach does not solve (b). Motivating the terminology that a clustering method which overcomes (a) is meaningful, while one which overcomes (a) and (b) is useful, we propose an approach that produces useful time series clustering. The approach is based on restricting the clustering space to extend only over the region visited by the time series in the subsequence vector space. We test the approach on a set of 12 diverse real-world and synthetic data sets and find that (a) one can distinguish between the clusterings of these time series, and (b) that the centroids produced in each case retain the character of the underlying series from which they came. Computing distances between examples is at the core of many learning algorithms for time series. Consequently, a great deal of work has gone into designing effective time series distance measures. We present Jiffy, a simple and scalable distance metric for multivariate time series. Our approach is to reframe the task as a representation learning problem---rather than design an elaborate distance function, we use a CNN to learn an embedding such that the Euclidean distance is effective. By aggressively max-pooling and downsampling, we are able to construct this embedding using a highly compact neural network. Experiments on a diverse set of multivariate time series datasets show that our approach consistently outperforms existing methods. Time series clustering is an active research area with applications in a wide range of fields. One key component in cluster analysis is determining a proper dissimilarity measure between two data objects, and many criteria have been proposed in the literature to assess dissimilarity between two time series. The R package TSclust is aimed to implement a large set of well-established peer-reviewed time series dissimilarity measures, including measures based on raw data, extracted features, underlying parametric models, complexity levels, and forecast behaviors. Computation of these measures allows the user to perform clustering by using conventional clustering algorithms. TSclust also includes a clustering procedure based on p values from checking the equality of generating models, and some utilities to evaluate cluster solutions. The implemented dissimilarity functions are accessible individually for an easier extension and possible use out of the clustering context. The main features of TSclust are described and examples of its use are presented. For more than a decade, time series similarity search has been given a great deal of attention by data mining researchers. As a result, many time series representations and distance measures have been proposed. However, most existing work on time series similarity search relies on shape-based similarity matching. While some of the existing approaches work well for short time series data, they typically fail to produce satisfactory results when the sequence is long. For long sequences, it is more appropriate to consider the similarity based on the higher-level structures. In this work, we present a histogram-based representation for time series data, similar to the "bag of words" approach that is widely accepted by the text mining and information retrieval communities. We performed extensive experiments and show that our approach outperforms the leading existing methods in clustering, classification, and anomaly detection on dozens of real datasets. We further demonstrate that the representation allows rotation-invariant matching in shape datasets. Time-Series clustering is one of the important concepts of data mining that is used to gain insight into the mechanism that generate the time-series and predicting the future values of the given time-series. Time-series data are frequently very large and elements of these kinds of data have temporal ordering. The clustering of time series is organized into three groups depending upon whether they work directly on raw data either in frequency or time domain, indirectly with the features extracted from the raw data or with model built from raw data. In this paper, we have shown the survey and summarization of previous work that investigated the clustering of time series in various application domains ranging from science, engineering, business, finance, economic, health care, to government. Recent papers have claimed that the result of K-means clustering for time series subsequences (STS clustering) is independent of the time series that created it. Our paper revisits this claim. In particular, we consider the following question: Given several time series sequences and a set of STS cluster centroids from one of them (generated by the K-means algorithm), is it possible to reliably determine which of the sequences produced these cluster centroids? While recent results suggest that the answer should be NO, we answer this question in the affirmative.We present cluster shape distance, an alternate distance measure for time series subsequence clusters, based on cluster shapes. Given a set of clusters, its shape is the sorted list of the pairwise Euclidean distances between their centroids. We then present two algorithms based on this distance measure, which match a set of STS cluster centroids with the time series that produced it. While the first algorithm creates DQG reuse this term more smaller "fingerprints" for the sequences, the second is more accurate. In our experiments with a dataset of 10 sequences, it produced a correct match 100 of the time.Furthermore, we offer an analysis that explains why our cluster shape distance provides a reliable way to match STS clusters to the original sequences, whereas cluster set distance fails to do so. Our work establishes for the first time a strong relation between the result of K-means STS clustering and the time series sequence that created it, despite earlier predictions that this is not possible. In the last decade there has been an explosion of interest in mining time series data. Literally hundreds of papers have introduced new algorithms to index, classify, cluster and segment time series. In this work we make the following claim. Much of this work has very little utility because the contribution made (speed in the case of indexing, accuracy in the case of classification and clustering, model accuracy in the case of segmentation) offer an amount of “improvement” that would have been completely dwarfed by the variance that would have been observed by testing on many real world datasets, or the variance that would have been observed by changing minor (unstated) implementation details. To illustrate our point, we have undertaken the most exhaustive set of time series experiments ever attempted, re-implementing the contribution of more than two dozen papers, and testing them on 50 real world, highly diverse datasets. Our empirical results strongly support our assertion, and suggest the need for a set of time series benchmarks and more careful empirical evaluation in the data mining community. During last decade, tremendous efforts have been devoted to the research of time series classification. Indeed, many previous works suggested that the simple nearest-neighbor classification is effective and difficult to beat. However, we usually need to determine the distance metric (e.g., Euclidean distance and Dynamic Time Warping) for different domains, and current evidence shows that there is no distance metric that is best for all time series data. Thus, the choice of distance metric has to be done empirically, which is time expensive and not always effective. To automatically determine the distance metric, in this paper, we investigate the distance metric learning and propose a novel Convolutional Nonlinear Neighbourhood Components Analysis model for time series classification. Specifically, our model performs supervised learning to project original time series into a transformed space. When classifying, nearest neighbor classifier is then performed in this transformed space. Finally, comprehensive experimental results demonstrate that our model can improve the classification accuracy to some extent, which indicates that it can learn a good distance metric. Clustering problems are central to many knowledge discovery and data mining tasks. However, most existing clustering methods can only work with fixed-dimensional representations of data patterns. In this paper we study the clustering of data patterns that are represented as sequences or time series possibly of different lengths. We propose a model-based approach to this problem using mixtures of autoregressive moving average (ARMA) models. We derive an expectation-maximization (EM) algorithm for learning the mixing coefficients as well as the parameters of component models. Experiments were conducted on simulated and real datasets. Results show that our method compares favorably with another method recently proposed by others for similar time series clustering problems. Given the pervasiveness of time series data in all human endeavors, and the ubiquity of clustering as a data mining application, it is somewhat surprising that the problem of time series clustering from a single stream remains largely unsolved. Most work on time series clustering considers the clustering of individual time series, e.g., gene expression profiles, individual heartbeats or individual gait cycles. The few attempts at clustering time series streams have been shown to be objectively incorrect in some cases, and in other cases shown to work only on the most contrived datasets by carefully adjusting a large set of parameters. In this work, we make two fundamental contributions. First, we show that the problem definition for time series clustering from streams currently used is inherently flawed, and a new definition is necessary. Second, we show that the Minimum Description Length (MDL) framework offers an efficient, effective and essentially parameter-free method for time series clustering. We show that our method produces objectively correct results on a wide variety of datasets from medicine, zoology and industrial process analyses. Spatio-temporal and geo-referenced datasets are growing rapidly, with the rapid development of some technology, such as GPS, satellite systems. At present, many scholars are very interested in the clustering of the trajectory. Existing trajectory clustering algorithms group similar trajectories as a whole and can't distinguish the direction of trajectory. Our key finding is that clustering trajectories as a whole could miss common sub-trajectories and trajectory has direction information. In many applications, discovering common sub-trajectories is very useful. In this paper, we present a trajectory clustering algorithm CTHD (clustering of trajectory based on hausdorff distance). In the CTHD, the trajectory is firstly described by a sequence of flow vectors and partitioned into a set of sub-trajectory. Next the similarity between trajectories is measured by their respective Hausdorff distances. Finally, the trajectories are clustered by the DBSCAN clustering algorithm. The proposed algorithm is different from other schemes using Hausdorff distance that the flow vectors include the position and direction. So it can distinguish the trajectories in different directions. The experimental result shows the phenomenon. Dynamic time warping (DTW), which finds the minimum path by providing non-linear alignments between two time series, has been widely used as a distance measure for time series classification and clustering. However, DTW does not account for the relative importance regarding the phase difference between a reference point and a testing point. This may lead to misclassification especially in applications where the shape similarity between two sequences is a major consideration for an accurate recognition. Therefore, we propose a novel distance measure, called a weighted DTW (WDTW), which is a penalty-based DTW. Our approach penalizes points with higher phase difference between a reference point and a testing point in order to prevent minimum distance distortion caused by outliers. The rationale underlying the proposed distance measure is demonstrated with some illustrative examples. A new weight function, called the modified logistic weight function (MLWF), is also proposed to systematically assign weights as a function of the phase difference between a reference point and a testing point. By applying different weights to adjacent points, the proposed algorithm can enhance the detection of similarity between two time series. We show that some popular distance measures such as DTW and Euclidean distance are special cases of our proposed WDTW measure. We extend the proposed idea to other variants of DTW such as derivative dynamic time warping (DDTW) and propose the weighted version of DDTW. We have compared the performances of our proposed procedures with other popular approaches using public data sets available through the UCR Time Series Data Mining Archive for both time series classification and clustering problems. The experimental results indicate that the proposed approaches can achieve improved accuracy for time series classification and clustering problems. Time series data mining has received much greater interest along with the increase in temporal data sets from different domains such as medicine, finance, multimedia, etc. Representations are important to reduce dimensionality and generate useful similarity measures. High-level representations such as Fourier transforms, wavelets, piecewise polynomial models, etc., were considered previously. Recently, autoregressive kernels were introduced to reflect the similarity of the time series. We introduce a novel approach to model the dependency structure in time series that generalizes the concept of autoregression to local autopatterns. Our approach generates a pattern-based representation along with a similarity measure called learned pattern similarity (LPS). A tree-based ensemble-learning strategy that is fast and insensitive to parameter settings is the basis for the approach. Then, a robust similarity measure based on the learned patterns is presented. This unsupervised approach to represent and measure the similarity between time series generally applies to a number of data mining tasks (e.g., clustering, anomaly detection, classification). Furthermore, an embedded learning of the representation avoids pre-defined features and an extraction step which is common in some feature-based approaches. The method generalizes in a straightforward manner to multivariate time series. The effectiveness of LPS is evaluated on time series classification problems from various domains. We compare LPS to eleven well-known similarity measures. Our experimental results show that LPS provides fast and competitive results on benchmark datasets from several domains. Furthermore, LPS provides a research direction and template approach that breaks from the linear dependency models to potentially foster other promising nonlinear approaches. With the advent of ubiquitous computing, we can easily acquire the locations of moving objects. This paper studies clustering problems for trajectory data that is constrained by the road network. While many trajectory clustering algorithms have been proposed, they do not consider the spatial proximity of objects across the road network. For this kind of data, we propose a new distance measure that reflects the spatial proximity of vehicle trajectories on the road network, and an efficient clustering method that reduces the number of distance computations during the clustering process. Experimental results demonstrate that our proposed method correctly identifies clusters using real-life trajectory data yet reduces the distance computations by up to 80 against the baseline algorithm.