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The set of frequent closed itemsets uniquely determines the exact frequency of all itemsets, yet it can be orders of magnitude smaller than the set of all frequent itemsets. In this paper, we present CHARM, an efficient algorithm for mining all frequent closed itemsets. It enumerates closed sets using a dual itemset-tidset search tree, using an efficient hybrid search that skips many levels. It also uses a technique called diffsets to reduce the memory footprint of intermediate computations. Finally, it uses a fast hash-based approach to remove any "nonclosed" sets found during computation. We also present CHARM-L, an algorithm that outputs the closed itemset lattice, which is very useful for rule generation and visualization. An extensive experimental evaluation on a number of real and synthetic databases shows that CHARM is a state-of-the-art algorithm that outperforms previous methods. Further, CHARM-L explicitly generates the frequent closed itemset lattice.

Efficient algorithms for mining closed itemsets and their lattice structure

Web-based applications greatly increase information availability and ease of access, which is optimal for public information. The distribution and sharing of information via the Web that must be accessed in a selective way, such as electronic commerce transactions, require the definition and enforcement of security controls, ensuring that information will be accessible only to authorized entities. Different approaches have been proposed that address the problem of protecting information in a Web system. However, these approaches typically operate at the file-system level, independently of the data that have to be protected from unauthorized accesses. Part of this problem is due to the limitations of HTML, historically used to design Web documents. The extensible markup language (XML), a markup language promoted by the World Wide Web Consortium (W3C), is de facto the standard language for the exchange of information on the Internet and represents an important opportunity to provide fine-grained access control. We present an access control model to protect information distributed on the Web that, by exploiting XML's own capabilities, allows the definition and enforcement of access restrictions directly on the structure and content of the documents. We present a language for the specification of access restrictions, which uses standard notations and concepts, together with a description of a system architecture for access control enforcement based on existing technology. The result is a flexible and powerful security system offering a simple integration with current solutions.

A fine-grained access control system for XML documents

Recently concept lattices became widely used tools for intelligent data analysis. In this paper, several algorithms that generate the set of all formal concepts and diagram graphs of concept lattices are considered. Some modifications of wellknown algorithms are proposed. Algorithmic complexity of the algorithms is studied both theoretically (in the worst case) and experimentally. Conditions of preferable use of some algorithms are given in terms of density/sparseness of underlying formal contexts. Principles of comparing practical performance of algorithms are discussed.

/pdf/comparing-performance-of-algorithms-for-generating-concept-1ybmrj3kxe.pdf

Comparing performance of algorithms for generating concept lattices

A graph is just a bunch of points with lines between some of them, like a map of cities linked by roads. A rather simple notion. Nevertheless, the theory of graphs has broad and important applications, because so many things can be modeled by graphs. For example, planar graphs — graphs in which none of the lines cross are— important in designing computer chips and other electronic circuits. Also, various puzzles and games are solved easily if a little graph theory is applied.

A Theory of Graphs

http://perso.ens-lyon.fr/eric.thierry/Graphes2007/lattice-generation.pdf

A fast algorithm for building lattices

This paper presents an incremental algorithm to compute the covering graph of the lattice generated by a family B of subsets of a totally ordered set X. The implementation of this algorithm has O (((|X| + |B|).|B|).|F|) time complexity, where F is the number of elements in the lattice. This improves the complexity of the previous algorithms which is roughly in O(Min(|X|, |B|)3.|F|). This algorithm may be used in many applications in computer sciences such as the computations of Galois (concept) lattice, the maximal antichains lattice or the Dedekind-MacNeille completion of a partial order. All these lattices can be computed incrementally using this algorithm without increasing time complexity.

A fast incremental algorithm for building lattices

Efficient implementation of type inclusion is an important feature of object oriented programming languages with multiple inheritance. The idea is to associate to each type a subset of a set S={1,...,k} such that type inclusion coincides with subset inclusion. Such an embedding of types into 2S (the lattice of all subsets of S) is called a bit-vector encoding of the type hierarchy. In this paper, we show that most known bit-vector encoding methods can be inserted on a general theoretical framework using graph coloration, namely the notion of a simple encoding. We use the word simple because all these methods are heuristics for the general bit-vector encoding problem, known as the 2-dimension problem. First we provide a correct algorithm for partial orders based on simple encoding, improving the algorithm of Krall, Vitek, and Horspool (1997). Second we show that finding an optimal simple encoding is an NP-hard problem. We end with a discussion on some practical issues.

Encoding of Multiple Inheritance Hierarchies and Partial Orders

Given a set Un={0,1,...,n−1}, a collection $\mathcal{M}$ of subsets of Un that is closed under intersection and contains Un is known as a Moore family. The set of Moore families for a given n, denoted by Mn, increases very quickly with n, thus |M3| is 61 and |M4| is 2480. In [1] the authors determined the number for n=6 and stated a 24h- computation-time. Thus, the number for n=7 can be considered as an extremely difficult technical challenge. In this paper, we introduce a counting strategy for determining the number of Moore families for n=7 and we give the exact value : 14 087 648 235 707 352 472. Our calculation is particularly based on the enumeration of Moore families up to an isomorphism for n ranging from 1 to 6.

Counting of moore families for n=7

Type inclusion tests consist in determining whether a type is a subtype of another. An efficient implementation of type inclusion is an important feature of object oriented programming languages.A well-known method to achieve these tests is to associate to each type a subset of a set S = {1, . . . , k} such that type inclusion coincides with subset inclusion. Such an embedding of types into 2S (the lattice of all subsets of S) is called a bit-vector encoding of the type hierarchy. These encodings are known for several interesting features. Bit-vector encodings are perfectly appropriate for hierarchies with single subtyping as well as hierarchies with multiple subtyping. Subset inclusion tests can be performed very efficiently.Several works have studied bit-vector encodings froma theoretical point of view ([6, 7, 10, 14, 16, 18, 19]) and froma practical point of view ([3, 8, 9, 17]), in particular in order to minimize the size of the encoding, i.e. the size of S.In this article, we present a new algorithmw hich computes bit-vector encodings for single subtyping hierarchies, also called tree hierarchies.Our algorithm is simple, it computes the bit-vector encoding very quickly and gives good results for the size of the encoding. In particular, we have significantly improved the best bounds known for the encoding sizes of some benchmarks presented in [9].

Olivier Raynaud

Papers

A fast algorithm for building lattices

A fast incremental algorithm for building lattices

Encoding of Multiple Inheritance Hierarchies and Partial Orders

Counting of moore families for n=7

A Quasi Optimal Bit-Vector Encoding of Tree Hierarchies. Application to Efficient Type Inclusion Tests