Many applications rely on distributed databases. However, only few discovery methods exist to extract patterns without centralizing the data. In fact, this centralization is often less expensive than the communication of extracted patterns from the different nodes. To circumvent this difficulty, this paper revisits the problem of pattern mining in distributed databases by benefiting from pattern sampling. Specifically, we propose the algorithm DDSampling that randomly draws a pattern from a distributed database with a probability proportional to its interest. We demonstrate the soundness of DDSampling and analyze its time complexity. Finally, experiments on benchmark datasets highlight its low communication cost and its robustness. We also illustrate its interest on real-world data from the Semantic Web for detecting outlier entities in DBpedia and Wikidata.
Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and its dual space. Let be a bounded strongly monotone mapping such that For given let be generated by the algorithm: where J is the normalized duality mapping from E into and is a real sequence in (0, 1) satisfying suitable conditions. Then it is proved that converges strongly to the unique point Finally, our theorems are applied to the convex minimization problem.
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