Most time series data mining algorithms use similarity search as a core subroutine, and thus the time taken for similarity search is the bottleneck for virtually all time series data mining algorithms. The difficulty of scaling search to large datasets largely explains why most academic work on time series data mining has plateaued at considering a few millions of time series objects, while much of industry and science sits on billions of time series objects waiting to be explored. In this work we show that by using a combination of four novel ideas we can search and mine truly massive time series for the first time. We demonstrate the following extremely unintuitive fact; in large datasets we can exactly search under DTW much more quickly than the current state-of-the-art Euclidean distance search algorithms. We demonstrate our work on the largest set of time series experiments ever attempted. In particular, the largest dataset we consider is larger than the combined size of all of the time series datasets considered in all data mining papers ever published. We show that our ideas allow us to solve higher-level time series data mining problem such as motif discovery and clustering at scales that would otherwise be untenable. In addition to mining massive datasets, we will show that our ideas also have implications for real-time monitoring of data streams, allowing us to handle much faster arrival rates and/or use cheaper and lower powered devices than are currently possible.

Time series shapelets are a recent promising concept in time series data mining. Shapelets are time series snippets that can be used to classify unlabeled time series. Shapelets not only provide interpretable results, which are useful for domain experts and developers alike, but shapelet-based classifiers have been shown by several independent research groups to have superior accuracy on many datasets. Moreover, shapelets can be seen as generalizing the lazy nearest neighbor classifier to an eager classifier. Thus, as a deployed classification tool, shapelets can be many orders of magnitude faster than any rival with comparable accuracy. Although shapelets are a useful concept, the current literature bemoans the fact that shapelet discovery is a time-consuming task. In spite of several efforts to speed up shapelet discovery algorithms, including the use of specialist hardware, the current state-of-the-art algorithms are still intractable on large datasets. In this work, we propose a fast shapelet discovery algorithm that outperforms the current state-of-the-art by two or three orders of magnitude, while producing models with accuracy that is not perceptibly different.

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Abstract-Given the pervasiveness of time series data in all human endeavors, and the ubiquity of clustering as a data mining application, it is somewhat surprising that the problem of time series clustering from a single stream remains largely unsolved. Most work on time series clustering considers the clustering of individual time series, e.g., gene expression profiles, individual heartbeats or individual gait cycles. The few attempts at clustering time series streams have been shown to be objectively incorrect in some cases, and in other cases shown to work only on the most contrived datasets by carefully adjusting a large set of parameters. In this work, we make two fundamental contributions. First, we show that the problem definition for time series clustering from streams currently used is inherently flawed, and a new definition is necessary. Second, we show that the Minimum Description Length (MDL) framework offers an efficient, effective and essentially parameter-free method for time series clustering. We show that our method produces objectively correct results on a wide variety of datasets from medicine, zoology and industrial process analyses.

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Abstract. Data streams have recently attracted attention for their applicability to numerous domains including credit fraud detection, network intrusion detection, and click streams. Stream clustering is a technique that performs cluster analysis of data streams that is able to monitor the results in real time. A data stream is continuously generated sequences of data for which the characteristics of the data evolve over time. A good stream clustering algorithm should recognize such evolution and yield a cluster model that conforms to the current data. In this paper, we propose a new technique for stream clustering which supports five evolutions that are appearance, disappearance, selfevolution, merge and split.

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