In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: This paper develops the idea of membership function assignment for OWL (Web Ontology Language) ontology elements in order to subsequently generate fuzzy rules from this ontology. The task of membership function assignment for OWL ontology elements had already been partially described, but this concerned the case , when several OWL ontologies of the same domain were available, and they were merged into a single ontology. The purpose of this paper is to present the way of membership function assignment for OWL ontology elements in the case, when there is the only one available ontology. Fuzzy rules, generated from the OWL ontology, are necessary for supplement of the SWES (Semantic Web Expert System) knowledge base. SWES is an expert system, which will be able to extract knowledge from OWL ontologies , found in the Web, and will serve as a universal expert for the user.

Output: Membership Function Assignment for Elements of Single OWL Ontology


Input: Consider Input: We introduce a new spatial data structure for high dimensional data called the approximate principal direction tree (APD tree) that adapts to the intrinsic dimension of the data. Our algorithm ensures vector-quantization accuracy similar to that of computationally-expensive PCA trees with similar time-complexity to that of loweraccuracy RP trees. APD trees use a small number of powermethod iterations to find splitting planes for recursively partitioning the data. As such they provide a natural trade-off between the running-time and accuracy achieved by RP and PCA trees. Our theoretical results establish a) strong performance guarantees regardless of the convergence rate of the powermethod and b) that O(log d) iterations suffice to establish the guarantee of PCA trees when the intrinsic dimension is d. We demonstrate this trade-off and the efficacy of our data structure on both the CPU and GPU.

Output: Approximate Principal Direction Trees


Input: Consider Input: Asynchronous parallel implementations for stochastic optimization have received huge successes in theory and practice recently. Asynchronous implementations with lock-free are more efficient than the one with writing or reading lock. In this paper, we focus on a composite objective function consisting of a smooth convex function f and a block separable convex function, which widely exists in machine learning and computer vision. We propose an asynchronous stochastic block coordinate descent algorithm with the accelerated technology of variance reduction (AsySBCDVR), which are with lock-free in the implementation and analysis. AsySBCDVR is particularly important because it can scale well with the sample size and dimension simultaneously. We prove that AsySBCDVR achieves a linear convergence rate when the function f is with the optimal strong convexity property, and a sublinear rate when f is with the general convexity. More importantly, a near-linear speedup on a parallel system with shared memory can be obtained.


Output: Asynchronous Stochastic Block Coordinate Descent with Variance Reduction