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.
A handful of efforts have considered joins on time series, achieving speedup by (in addition to the use of MapReduce) converting the data to lower-dimensional representations such as PAA @cite_37 or SAX @cite_168 and exploiting lower bounds and or Locality Sensitive Hashing (LSH) to prune some calculations. However, the methods are very complex, with many (10-plus) parameters to adjust. As @cite_37 acknowledge with admirable candor, ". In contrast, our proposed algorithm has zero parameters to set.
@cite_168 @cite_37
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We propose a new method for rapid 3D object indexing that combines feature-based methods with coarse alignment-based matching techniques. Our approach achieves a sublinear complexity on the number of models, maintaining at the same time a high degree of performance for real 3D sensed data that is acquired in largely uncontrolled settings. The key component of our method is to first index surface descriptors computed at salient locations from the scene into the whole model database using the locality sensitive hashing (LSH), a probabilistic approximate nearest neighbor method. Progressively complex geometric constraints are subsequently enforced to further prune the initial candidates and eliminate false correspondences due to inaccuracies in the surface descriptors and the errors of the LSH algorithm. The indexed models are selected based on the MAP rule using posterior probability of the models estimated in the joint 3D-signature space. Experiments with real 3D data employing a large database of vehicles, most of them very similar in shape, containing 1,000,000 features from more than 365 models demonstrate a high degree of performance in the presence of occlusion and obscuration, unmodeled vehicle interiors and part articulations, with an average processing time between 50 and 100 seconds per query The data placement strategy greatly affects the efficiency of MapReduce. The current strategy only takes the map phase into account to optimize the map time. But the ignored shuffle phase may increase the total running time significantly in many jobs. We propose a new data placement strategy, named OPTAS, which optimizes both the map and shuffle phases to reduce their total time. However, the huge search space makes it difficult to find out an optimal data placement instance (DPI) rapidly. To address this problem, an algorithm is proposed which can prune most of the search space and find out an optimal result quickly. The search space firstly is segmented in ascending order according to the potential map time. Within each segment, we propose an efficient method to construct a local optimal DPI with the minimal total time of both the map and shuffle phases. To find the global optimal DPI, we scan the local optimal DPIs in order. We have proven that the global optimal DPI can be found as the first local optimal DPI whose total time stops decreasing, thus further pruning the search space. In practice, we find that at most fourteen local optimal DPIs are scanned in tens of thousands of segments with the pruning strategy. Extensive experiments with real trace data verify not only the theoretic analysis of our pruning strategy and construction method but also the optimality of OPTAS. The best improvements obtained in our experiments can be over 40 compared with the existing strategy used by MapReduce. We consider the problem of processing K-Nearest Neighbor (KNN) queries over large datasets where the index is jointly maintained by a set of machines in a computing cluster. The proposed RankReduce approach uses locality sensitive hashing (LSH) together with a MapReduce implementation, which by design is a perfect match as the hashing principle of LSH can be smoothly integrated in the mapping phase of MapReduce. The LSH algorithm assigns similar objects to the same fragments in the distributed file system which enables a effective selection of potential candidate neighbors which get then reduced to the set of K-Nearest Neighbors. We address problems arising due to the different characteristics of MapReduce and LSH to achieve an efficient search process on the one hand and high LSH accuracy on the other hand. We discuss several pitfalls and detailed descriptions on how to circumvent these. We evaluate RankReduce using both synthetic data and a dataset obtained from Flickr.com demonstrating the suitability of the approach. Locality-sensitive hashing (LSH) has emerged as the dominant algorithmic technique for similarity search with strong performance guarantees in high-dimensional spaces. A drawback of traditional LSH schemes is that they may have , i.e., the recall is less than 100 . This limits the applicability of LSH in settings requiring precise performance guarantees. Building on the recent theoretical "CoveringLSH" construction that eliminates false negatives, we propose a fast and practical covering LSH scheme for Hamming space called . Inheriting the design benefits of CoveringLSH our method avoids false negatives and always reports all near neighbors. Compared to CoveringLSH we achieve an asymptotic improvement to the hash function computation time from @math to @math , where @math is the dimensionality of data and @math is the number of hash tables. Our experiments on synthetic and real-world data sets demonstrate that is comparable (and often superior) to traditional hashing-based approaches for search radius up to 20 in high-dimensional Hamming space.