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Abstract. Trend analysis of time series is an important problem since trend identification enables the prediction of the near future. In streaming time series the problem is more challenging due to the dynamic nature of the data. In this paper, we propose a method to continuously clustering a number of streaming time series based on their trend characteristics. Each streaming time series is transformed to a vector by means of the Piecewise Linear Approximation (PLA) technique. The PLA vector comprises pairs of values (timestamp, trend) denoting the starting time of the trend and the type of the trend (either UP or DOWN) respectively. A distance metric for PLA vectors is introduced. We propose split and merge criteria to continuously update the clustering information. Moreover, the proposed method handles outliers. Performance evaluation results, based on real-life and synthetic data sets, show the efficiency and scalability of the proposed scheme.

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Abstract. Dense subgraph discovery is a key issue in graph mining, due to its importance in several applications, such as correlation analysis, community discovery in the Web, gene co-expression and protein-protein interactions in bioinformatics. In this work, we study the discovery of the top-k dense subgraphs in a set of graphs. After the investigation of the problem in its static case, we extend the methodology to work with dynamic graph collections, where the graph collection changes over time. Our methodology is based on lower and upper bounds of the density, resulting in a reduction of the number of exact density computations. Our algorithms do not rely on user-defined threshold values and the only input required is the number of dense subgraphs in the result (k). In addition to the exact algorithms, an approximation algorithm is provided for top-k dense subgraph discovery, which trades result accuracy for speed. We show that a significant number of exact density computations is avoided, resulting in efficient monitoring of the top-k dense subgraphs.