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.
The work of @cite_176 is the closest in spirit to our work. Their work was the first to note the detrimental impact of irrelevant dimensions on multidimensional motif search, and they introduced a method that is shown to be somewhat robust for a small number of , but irrelevant dimensions, or one noisy irrelevant dimension. However, the algorithm introduced is . Even in an ideal case, with just six dimensions, they report ". The idea is attractive for its simplicity, but it requires all (or at least ) of the dimensions to be relevant, as the algorithm is brittle to even a handful of irrelevant dimensions. ddd Moreover, both the speed and accuracy of Tanaka's algorithm depend on careful tuning of five parameters.
@cite_176
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We analyze a sublinear RA@?SFA (randomized algorithm for Sparse Fourier analysis) that finds a near-optimal B-term Sparse representation R for a given discrete signal S of length N, in time and space poly(B,log(N)), following the approach given in [A.C. Gilbert, S. Guha, P. Indyk, S. Muthukrishnan, M. Strauss, Near-Optimal Sparse Fourier Representations via Sampling, STOC, 2002]. Its time cost poly(log(N)) should be compared with the superlinear @W(NlogN) time requirement of the Fast Fourier Transform (FFT). A straightforward implementation of the RA@?SFA, as presented in the theoretical paper [A.C. Gilbert, S. Guha, P. Indyk, S. Muthukrishnan, M. Strauss, Near-Optimal Sparse Fourier Representations via Sampling, STOC, 2002], turns out to be very slow in practice. Our main result is a greatly improved and practical RA@?SFA. We introduce several new ideas and techniques that speed up the algorithm. Both rigorous and heuristic arguments for parameter choices are presented. Our RA@?SFA constructs, with probability at least 1-@d, a near-optimal B-term representation R in time poly(B)log(N)log(1 @d) @e^2log(M) such that @?S-R@?"2^2=<(1+@e)@?S-R"o"p"t@?"2^2. Furthermore, this RA@?SFA implementation already beats the FFTW for not unreasonably large N. We extend the algorithm to higher dimensional cases both theoretically and numerically. The crossover point lies at N 70,000 in one dimension, and at N 900 for data on a NxN grid in two dimensions for small B signals where there is noise. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). In many image or video retrieval systems, the search for similar objects in the database includes a spatial access method to a multidimensional feature space. This step is generally considered as a problem independent of the features and the similarity type. The well known multidimensional nearest neighbor search has also been widely studied by the database community as a generic method. We propose a novel strategy dedicated to pseudo-invariant features retrieval and more specifically applied to content based copy identification. The range of a query is computed during the search according to deviation statistics between original and observed features. Furthermore, this approximate search range is directly mapped onto a Hilbert space-filling curve, allowing an efficient access to the database. Experimental results give excellent response times for very large databases both on synthetic and real data. This work is used in a TV monitoring system including more than 13000 hours of video in the reference database. Abstract We propose a novel approach to solving the approximate k-nearest neighbor search problem in metric spaces. The search structure is based on a navigable small world graph with vertices corresponding to the stored elements, edges to links between them, and a variation of greedy algorithm for searching. The navigable small world is created simply by keeping old Delaunay graph approximation links produced at the start of construction. The approach is very universal, defined in terms of arbitrary metric spaces and at the same time it is very simple. The algorithm handles insertions in the same way as queries: by finding approximate neighbors for the inserted element and connecting it to them. Both search and insertion can be done in parallel requiring only local information from the structure. The structure can be made distributed. The accuracy of the probabilistic k-nearest neighbor queries can be adjusted without rebuilding the structure. The performed simulation for data in the Euclidean spaces shows that the structure built using the proposed algorithm has small world navigation properties with log 2 ( n ) insertion and search complexity at fixed accuracy, and performs well at high dimensionality. Simulation on a CoPHiR dataset revealed its high efficiency in case of large datasets (more than an order of magnitude less metric computations at fixed recall) compared to permutation indexes. Only 0.03 of the 10 million 208-dimensional vector dataset is needed to be evaluated to achieve 0.999 recall (virtually exact search). For recall 0.93 processing speed 2800 queries s can be achieved on a dual Intel X5675 Xenon server node with Java implementation.