Finding repeated patterns or motifs in a time series is an important unsupervised task that has still a number of open issues, starting by the definition of motif. In this paper, we revise the notion of motif support, characterizing it as the number of patterns or repetitions that define a motif. We then propose GENMOTIF, a genetic algorithm to discover motifs with support which, at the same time, is flexible enough to accommodate other motif specifications and task characteristics. GENMOTIF is an anytime algorithm that easily adapts to many situations: searching in a range of segment lengths, applying uniform scaling, dealing with multiple dimensions, using different similarity and grouping criteria, etc. GENMOTIF is also parameter-friendly: it has only two intuitive parameters which, if set within reasonable bounds, do not substantially affect its performance. We demonstrate the value of our approach in a number of synthetic and real-world settings, considering traffic volume measurements, accelerometer signals, and telephone call records.
Other algorithms have been proposed for the task of time series subsequence clustering @cite_6 @cite_26 . Though this task and the one of finding motifs with support have common aspects, they are conceptually different. Time series subsequence clustering aims at obtaining a good and compact representation of the whole time series while, as shown in @cite_26 , ignoring some data. However, motif discovery aims at finding characteristic patterns (with support) that do not necessarily need to reliably and compactly represent the full time series. In fact, the segments used to derive the motifs can actually represent a tiny part of the time series (i.e., @math , as mentioned in the main text).
@cite_26 @cite_6
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Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of this work were the poor scalability of the motif discovery algorithm, and the inability to discover motifs in the presence of noise.Here we address these limitations by introducing a novel algorithm inspired by recent advances in the problem of pattern discovery in biosequences. Our algorithm is probabilistic in nature, but as we show empirically and theoretically, it can find time series motifs with very high probability even in the presence of noise or "don't care" symbols. Not only is the algorithm fast, but it is an anytime algorithm, producing likely candidate motifs almost immediately, and gradually improving the quality of results over time. The problem of locating motifs in real-valued, multivariate time series data involves the discovery of sets of recurring patterns embedded in the time series. Each set is composed of several non-overlapping subsequences and constitutes a motif because all of the included subsequences are similar. The ability to automatically discover such motifs allows intelligent systems to form endogenously meaningful representations of their environment through unsupervised sensor analysis. In this paper, we formulate a unifying view of motif discovery as a problem of locating regions of high density in the space of all time series subsequences. Our approach is efficient (sub-quadratic in the length of the data), requires fewer user-specified parameters than previous methods, and naturally allows variable length motif occurrences and non-linear temporal warping. We evaluate the performance of our approach using four data sets from different domains including on-body inertial sensors and speech. 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 motifs are approximately repeating patterns in real-valued time series data. They are useful for exploratory data mining and are often used as inputs for various time series clustering, classification, segmentation, rule discovery, and visualization algorithms. Since the introduction of the first motif discovery algorithm for univariate time series in 2002, multiple efforts have been made to generalize motifs to the multidimensional case. In this work, we show that these efforts, which typically attempt to find motifs on all dimensions, will not produce meaningful motifs except in the most contrived situations. We explain this finding and introduce mSTAMP, an algorithm that allows meaningful discovery of multidimensional motifs. Beyond producing objectively and subjectively meaningful results, our algorithm has a host of additional advantages, including being much faster, requiring fewer parameters and supporting streaming data. We demonstrate the utility of our mSTAMP-based motif discovery framework on domains as diverse as audio processing, industry, and sports analytics. Time series motifs are pairs of individual time series, or subsequences of a longer time series, which are very similar to each other. As with their discrete analogues in computational biology, this similarity hints at structure which has been conserved for some reason and may therefore be of interest. Since the formalism of time series motifs in 2002, dozens of researchers have used them for diverse applications in many different domains. Because the obvious algorithm for computing motifs is quadratic in the number of items, more than a dozen approximate algorithms to discover motifs have been proposed in the literature. In this work, for the first time, we show a tractable exact algorithm to find time series motifs. As we shall show through extensive experiments, our algorithm is up to three orders of magnitude faster than brute-force search in large datasets. We further show that our algorithm is fast enough to be used as a subroutine in higher level data mining algorithms for anytime classification, near-duplicate detection and summarization, and we consider detailed case studies in domains as diverse as electroencephalograph interpretation and entomological telemetry data mining. Time series motifs are repeated patterns in long and noisy time series. Motifs are typically used to understand the dynamics of the source because repeated patterns with high similarity evidentially rule out the presence of noise. Recently, time series motifs have also been used for clustering, summarization, rule discovery and compression as features. For all such purposes, many high quality motifs of various lengths are desirable and thus, originates the problem of enumerating motifs for a wide range of lengths. Existing algorithms find motifs for a given length. A trivial way to enumerate motifs is to run one of the algorithms for the whole range of lengths. However, such parameter sweep is computationally infeasible for large real datasets. In this paper, we describe an exact algorithm, called MOEN, to enumerate motifs. The algorithm is an order of magnitude faster than the naive algorithm. The algorithm frees us from re-discovering the same motif at different lengths and tuning multiple data-dependent parameters. The speedup comes from using a novel bound on the similarity function across lengths and the algorithm uses only linear space unlike other motif discovery algorithms. We describe three case studies in entomology and activity recognition where MOEN enumerates several high quality motifs. 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. As one of the most essential data mining tasks, finding frequently occurring patterns, i.e., motif discovery, has drawn a lot of attention in the past decade. Despite successes in speedup of motif discovery algorithms, most of the existing algorithms still require predefined parameters. The critical and most cumbersome one is time series motif length since it is difficult to manually determine the proper length of the motifs-even for the domain experts. In addition, with variability in the motif lengths, ranking among these motifs becomes another major problem. In this work, we propose a novel algorithm using compression ratio as a heuristic to discover meaningful motifs in proper lengths. The ranking of these various length motifs relies on an ability to compress time series by its own motif as a hypothesis. Furthermore, other than being an anytime algorithm, our experimental evaluation also demonstrates that our proposed method outperforms existing works in various domains both in terms of speed and accuracy. One significant task in time series mining research area is motif discovery which is the first step needed to be done in finding interesting patterns in time series sequence. Recently, many motif discovery algorithms have been proposed in place of the untenable brute-force algorithm, to improve its time complexity. However, those motif discovery algorithms still need a predefined sliding window length that must be known a priori. In this paper, we present a novel motif discovery algorithm that requires no window length parameter. This sliding window length is sensitive in that a small difference in the value can lead to huge difference of motif results. The proposed algorithm automatically returns suitable motif lengths from all possible sliding window lengths; in other words, our algorithm efficiently reduces a large set of possibilities of the sliding window lengths down to a few truly-interesting variable-length motifs. Discovering motifs in sequence databases has been receiving abundant attentions from both database and data mining communities, where the motif is the most correlated pair of subsequences in a sequence object. Motif discovery is expensive for emerging applications which may have very long sequences (e.g., million observations per sequence) or the queries arrive rapidly (e.g., per 10 seconds). Prior works cannot offer fast correlation computations and prune subsequence pairs at the same time, as these two techniques require different orderings on examining subsequence pairs. In this work, we propose a novel framework named Quick-Motif which adopts a two-level approach to enable batch pruning at the outer level and enable fast correlation calculation at the inner level. We further propose two optimization techniques for the outer and the inner level. In our experimental study, our method is up to 3 orders of magnitude faster than the state-of-the-art methods. Discovering recurring patterns in time series data is a fundamental problem for temporal data mining. This paper addresses the problem of locating subdimensional motifs in real-valued, multivariate time series, which requires the simultaneous discovery of sets of recurring patterns along with the corresponding relevant dimensions. While many approaches to motif discovery have been developed, most are restricted to categorical data, univariate time series, or multivariate data in which the temporal patterns span all of the dimensions. In this paper, we present an expected linear-time algorithm that addresses a generalization of multivariate pattern discovery in which each motif may span only a subset of the dimensions. To validate our algorithm, we discuss its theoretical properties and empirically evaluate it using several data sets including synthetic data and motion capture data collected by an on-body iner- tial sensor. 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. We consider the problem of finding rules relating patterns in a time series to other patterns in that series, or patterns in one series to patterns in another series. A simple example is a rule such as "a period of low telephone call activity is usually followed by a sharp rise in call volume". Examples of rules relating two or more time series are "if the Microsoft stock price goes up and Intel falls, then IBM goes up the next day," and "if Microsoft goes up strongly for one day, then declines strongly on the next day, and on the same days Intel stays about level, then IBM stays about level." Our emphasis is in the discovery of local patterns in multivariate time series, in contrast to traditional time series analysis which largely focuses on global models. Thus, we search for rules whose conditions refer to patterns in time series. However, we do not want to define beforehand which patterns are to be used; rather, we want the patterns to be formed from the data in the context of rule discovery. We describe adaptive methods for finding rules of the above type from time-series data. The methods are based on discretizing the sequence by methods resembling vector quantization. We first form subsequences by sliding a window through the time series, and then cluster these subsequences by using a suitable measure of time-series similarity. The discretized version of the time series is obtained by taking the cluster identifiers corresponding to the subsequence. Once the time-series is discretized, we use simple rule finding methods to obtain rules from the sequence. We present empirical results on the behavior of the method. This paper addresses the problem of activity and event discovery in multi dimensional time series data by proposing a novel method for locating multi dimensional motifs in time series. While recent work has been done in finding single dimensional and multi dimensional motifs in time series, we address motifs in general case, where the elements of multi dimensional motifs have temporal, length, and frequency variations. The proposed method is validated by synthetic data, and empirical evaluation has been done on several wearable systems that are used by real subjects. Time series motifs are repeated segments in a long time series that, if exist, carry precise information about the underlying source of the time series. Motif discovery in time series data has received significant attention in the data mining community since its inception, principally because, motif discovery is meaningful and more likely to succeed when the data is large. 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. For example, raw sensor data from a fitness-tracking application can be expressed as a timeline of a select few actions (i.e., walking, sitting, running). However, discovering these patterns is challenging because it requires simultaneous segmentation and clustering of the time series. Furthermore, interpreting the resulting clusters is difficult, especially when the data is high-dimensional. 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 alternating minimization, using a variation of the expectation maximization (EM) algorithm. We derive closed-form solutions to efficiently solve the two resulting subproblems in a scalable way, through dynamic programming and the alternating direction method of multipliers (ADMM), respectively. 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 sensor dataset how TICC can be used to learn interpretable clusters in real-world scenarios. The all-pairs-similarity-search (or similarity join) problem has been extensively studied for text and a handful of other datatypes. However, surprisingly little progress has been made on similarity joins for time series subsequences. The lack of progress probably stems from the daunting nature of the problem. For even modest sized datasets the obvious nested-loop algorithm can take months, and the typical speed-up techniques in this domain (i.e., indexing, lower-bounding, triangular-inequality pruning and early abandoning) at best produce one or two orders of magnitude speedup. In this work we introduce a novel scalable algorithm for time series subsequence all-pairs-similarity-search. For exceptionally large datasets, the algorithm can be trivially cast as an anytime algorithm and produce high-quality approximate solutions in reasonable time. The exact similarity join algorithm computes the answer to the time series motif and time series discord problem as a side-effect, and our algorithm incidentally provides the fastest known algorithm for both these extensively-studied problems. We demonstrate the utility of our ideas for two time series data mining problems, including motif discovery and novelty discovery. This paper proposes a generalized motif-based method for detecting defects in 16 out of 17 wallpaper groups in 2D patterned texture. It assumes that most patterned texture can be decomposed into lattices and their constituents-motifs. It then utilizes the symmetry property of motifs to calculate the energy of moving subtraction and its variance among different motifs. By learning the distribution of these values over a number of defect-free patterns, boundary conditions for discerning defective and defect-free patterns can be determined. This paper presents the theoretical foundation of the method, and defines the relations between motifs and lattice, from which a new concept called energy of moving subtraction is derived using norm metric measurement between a collection of circular shift matrices of motif and itself. It has been shown in this paper that the energy of moving subtraction amplifies the defect information of the defective motif. Together with its variance, an energy-variance space is further defined where decision boundaries are drawn for classifying defective and defect-free motifs. As the 16 wallpaper groups of patterned fabric can be transformed into three major groups, the proposed method is evaluated over these three major groups, from which 160 defect-free lattices samples are used for defining the decision boundaries, with 140 defect-free and 113 defective samples used for testing. An overall detection success rate of 93.32 is achieved for the proposed method. No other generalized approach can achieve this success rate has been reported before, and hence this result outperforms all other previously published approaches. Mining subtopics from weblogs and analyzing their spatiotemporal patterns have applications in multiple domains. In this paper, we define the novel problem of mining spatiotemporal theme patterns from weblogs and propose a novel probabilistic approach to model the subtopic themes and spatiotemporal theme patterns simultaneously. The proposed model discovers spatiotemporal theme patterns by (1) extracting common themes from weblogs; (2) generating theme life cycles for each given location; and (3) generating theme snapshots for each given time period. Evolution of patterns can be discovered by comparative analysis of theme life cycles and theme snapshots. Experiments on three different data sets show that the proposed approach can discover interesting spatiotemporal theme patterns effectively. The proposed probabilistic model is general and can be used for spatiotemporal text mining on any domain with time and location information. 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.