Spatial indexing for scalability in FCA

The paper provides evidence that spatial indexing structures offer faster resolution of Formal Concept Analysis queries than B-Tree/Hash methods. We show that many Formal Concept Analysis operations, computing the contingent and extent sizes as well as listing the matching objects, enjoy improved performance with the use of spatial indexing structures such as the RD-Tree. Speed improvements can vary up to eighty times faster depending on the data and query. The motivation for our study is the application of Formal Concept Analysis to Semantic File Systems. In such applications millions of formal objects must be dealt with. It has been found that spatial indexing also provides an effective indexing technique for more general purpose applications requiring scalability in Formal Concept Analysis systems. The coverage and benchmarking are presented with general applications in mind.

A new indexing method for high dimensional dataset

Indexing high dimensional datasets has attracted extensive attention from many researchers in the last decade. Since R-tree type of index structures are known as suffering curse of dimensionality problems, Pyramid-tree type of index structures, which are based on the B-tree, have been proposed to break the curse of dimensionality. However, for high dimensional data, the number of pyramids is often insufficient to discriminate data points when the number of dimensions is high. Its effectiveness degrades dramatically with the increase of dimensionality. In this paper, we focus on one particular issue of curse of dimensionality; that is, the surface of a hypercube in a high dimensional space approaches 100% of the total hypercube volume when the number of dimensions approaches infinite. We propose a new indexing method based on the surface of dimensionality. We prove that the Pyramid tree technology is a special case of our method. The results of our experiments demonstrate clear priority of our novel method.