While analyzing vehicular sensor data, we found that frequently occurring waveforms could serve as features for further analysis, such as rule mining, classification, and anomaly detection. The discovery of waveform patterns, also known as time-series motifs, has been studied extensively; however, available techniques for discovering frequently occurring time-series motifs were found lacking in either efficiency or quality: Standard subsequence clustering results in poor quality, to the extent that it has even been termed 'meaningless'. Variants of hierarchical clustering using techniques for efficient discovery of 'exact pair motifs' find high-quality frequent motifs, but at the cost of high computational complexity, making such techniques unusable for our voluminous vehicular sensor data. We show that good quality frequent motifs can be discovered using bounded spherical clustering of time-series subsequences, which we refer to as COIN clustering, with near linear complexity in time-series size. COIN clustering addresses many of the challenges that previously led to subsequence clustering being viewed as meaningless. We describe an end-to-end motif-discovery procedure using a sequence of pre and post-processing techniques that remove trivial-matches and shifted-motifs, which also plagued previous subsequence-clustering approaches. We demonstrate that our technique efficiently discovers frequent motifs in voluminous vehicular sensor data as well as in publicly available data sets.
Motif discovery from time-series data has been an active topic of research in last decade or so @cite_8 @cite_21 @cite_15 @cite_5 @cite_22 . It is also evident from past work that there are many aspects of this problem which need to be addressed, for example @cite_5 @cite_21 @cite_22 focus on finding out what should be the appropriate width of the time-series motifs, and find the motifs of multiple lengths. Most of these approaches use MK-Motif discovery algorithm @cite_15 underneath, which discovers pairs of subsequences that are similar. in @cite_6 focus on finding another subsequence that is similar to a given subsequence.
@cite_22 @cite_8 @cite_21 @cite_6 @cite_5 @cite_15
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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. 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. 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.