Author(s): Yeh, Michael Chin-Chia | Advisor(s): Keogh, Eamonn | Abstract: The last decade has seen a flurry of research on all-pairs-similarity-search (or, self-join) for text, DNA, and a handful of other datatypes, and these systems have been applied to many diverse data mining problems. Surprisingly, however, little progress has been made on addressing this problem for time series subsequences. In this thesis, we have introduced a near universal time series data mining tool called matrix profile which solves the all-pairs-similarity-search problem and caches the output in an easy-to-access fashion. The proposed algorithm is not only parameter-free, exact and scalable, but also applicable for both single and multidimensional time series. By building time series data mining methods on top of matrix profile, many time series data mining tasks (e.g., motif discovery, discord discovery, shapelet discovery, semantic segmentation, and clustering) can be efficiently solved. Because the same matrix profile can be shared by a diverse set of time series data mining methods, matrix profile is versatile and computed-once-use-many-times data structure. We demonstrate the utility of matrix profile for many time series data mining problems, including motif discovery, discord discovery, weakly labeled time series classification, and representation learning on domains as diverse as seismology, entomology, music processing, bioinformatics, human activity monitoring, electrical power-demand monitoring, and medicine. We hope the matrix profile is not the end but the beginning of many more time series data mining projects.
In a series of papers, Vahdatpour and colleagues introduce an MTS motif discovery tool and apply it to a variety of medical monitoring applications @cite_123 . Their approach is based on computing time series motifs for each individual dimension and using clustering to stitch" together various dimensions. However, even when the motifs are quite obvious, the problems are small and simple, and at most three irrelevant dimensions are considered, they never achieved greater than 85 be sure, this is much better than the 17 given that seven parameters need to be tuned to achieve this result, accuracy is likely to be further compromised in more challenging data sets.
@cite_123
34835763 2006761268 2772177579 2019654077
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. 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. 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. 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.