Understanding the functioning of a neural system in terms of its underlying circuitry is an important problem in neuroscience. Recent developments in electrophysiology and imaging allow one to simultaneously record activities of hundreds of neurons. Inferring the underlying neuronal connectivity patterns from such multi-neuronal spike train data streams is a challenging statistical and computational problem. This task involves finding significant temporal patterns from vast amounts of symbolic time series data. In this paper we show that the frequent episode mining methods from the field of temporal data mining can be very useful in this context. In the frequent episode discovery framework, the data is viewed as a sequence of events, each of which is characterized by an event type and its time of occurrence and episodes are certain types of temporal patterns in such data. Here we show that, using the set of discovered frequent episodes from multi-neuronal data, one can infer different types of connectivity patterns in the neural system that generated it. For this purpose, we introduce the notion of mining for frequent episodes under certain temporal constraints; the structure of these temporal constraints is motivated by the application. We present algorithms for discovering serial and parallel episodes under these temporal constraints. Through extensive simulation studies we demonstrate that these methods are useful for unearthing patterns of neuronal network connectivity.

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The detection of frequently occurring patterns, also called motifs, in data streams has been recognized as an important task. To find these motifs, we use an advanced event encoding and pattern discovery algorithm. Since a large time series can contain hundreds of motifs, there is a need to support interactive analysis and exploration. In addition, for certain applications, such as data center resource management, service managers want to be able to predict the next day's power consumption from the previous months' data. For this purpose, we introduce four novel visual analytics methods: (1) motif layout, using colored rectangles for visualizing the occurrences and hierarchical relationships of motifs; (2) motif distortion, enlarging or shrinking motifs for visualizing them more clearly; (3) motif merging, combining a number of identical adjacent motif instances to simplify the display; and (4) pattern preserving prediction, using a pattern preserving smoothing and prediction algorithm to provide a reliable prediction for seasonal data. We have applied these methods to three real-world data sets: data center chilling utilization, oil well production, and system resource utilization. The results enable service managers to interactively examine motifs and gain new insights into the recurring patterns to analyze system operations. Using the above methods, we have also predicted both power consumption and server utilization in data centers with a 70-80% accuracy.

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