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Current spatial database systems offer limited querying capabilities beyond binary topological relations. This paper introduces a model for projective relations between regions to support other qualitative spatial queries. The relations are ternary because they are based on the collinearity invariant of three points under projective geometry. The model is built on a partition of the plane into separate zones that are obtained from projective properties of two reference objects: Then, by considering the empty/nonempty intersections of a primary object with these zones, the model is able to distinguish between 34 different projective relations. Then, the paper proposes original algorithms for computing the relations under the assumption that regions of the plane are stored as vector polygons in a spatial database. These algorithms run in optimal O(n log n) time. [ABSTRACT FROM AUTHOR]

Relational databases are the most popular repository for structured data, and is thus one of the richest sources of knowledge in the world. In a relational database, multiple relations are linked together via entity-relationship links. Multirelational classification is the procedure of building a classifier based on information stored in multiple relations and making predictions with it. Existing approaches of Inductive Logic Programming (recently, also known as Relational Mining) have proven effective with high accuracy in multirelational classification. Unfortunately, most of them suffer from scalability problems with regard to the number of relations in databases. In this paper, we propose a new approach, called CrossMine, which includes a set of novel and powerful methods for multirelational classification, including 1) tuple ID propagation, an efficient and flexible method for virtually joining relations, which enables convenient search among different relations, 2) new definitions for predicates and decision-tree nodes, which involve aggregated information to provide essential statistics for classification, and 3) a selective sampling method for improving scalability with regard to the number of tuples. Based on these techniques, we propose two scalable and accurate methods for multirelational classification: CrossMine-Rule, a rule-based method and CrossMine-Tree, a decision-tree-based method. Our comprehensive experiments on both real and synthetic data sets demonstrate the high scalability and accuracy of the CrossMine approach. [ABSTRACT FROM AUTHOR]

Incorporating constraints into frequent itemset mining not only improves data mining efficiency, but also leads to concise and meaningful results. In this paper, a framework for closed constrained gradient itemset mining in retail databases is proposed by introducing the concept of gradient constraint into closed itemset mining. A tailored version of CLOSET+, LCLOSET, is first briefly introduced, which is designed for efficient closed itemset mining from sparse databases. Then, a newly proposed weaker but antimonotone measure, top-X average measure, is proposed and can be adopted to prune search space effectively. Experiments show that a combination of LCLOSET and the top-X average pruning provides an efficient approach to mining frequent closed gradient itemsets. [ABSTRACT FROM AUTHOR]