Discovering association rules is one of the most important task in data mining. Many efficient algorithms have been proposed in the literature. The most noticeable are Apriori, Mannila's algorithm, Partition, Sampling and DIC, that are all based on the Apriori mining method: pruning the subset lattice (itemset lattice). In this paper we propose an efficient algorithm, called Close, based on a new mining method: pruning the closed set lattice (closed itemset lattice). This lattice, which is a sub-order of the subset lattice, is closely related to Wille's concept lattice in formal concept analysis. Experiments comparing Close to an optimized version of Apriori showed that Close is very efficient for mining dense and/or correlated data such as census style data, and performs reasonably well for market basket style data.

We apply mathematical concept analysis to the problem of reengineering configurations. Concept analysis will reconstruct a taxonomy of concepts from a relation between objects and attributes. We use concept analysis to infer configuration structures from existing source code. Our tool NORA/RECS will accept source code, where configuration-specific code pieces are controlled by the preprocessor. The algorithm will compute a so-called concept lattice, which —when visually displayed — offers remarkable insight into the structure and properties of possible configurations. The lattice not only displays tine-grained dependencies between configurations, but also visualizes the overall quality of configuration structures according to software engineering principles. In a second step, interferences between configurations can be analyzed in order to restructure or simplify configurations. Interferences showing up in the lattice indicate high coupling and low cohesion between configuration concepts. Source files can then be simplified according to the lattice structure. Finally, we show how governing expressions can be simplified by utilizing an isomorphism theorem of mathematical concept analysis.

. For a given TBox of a terminological KR system, the classification algorithm computes (a representation of) the subsumption hierarchy of all concepts introduced in the TBox. In general, this hierarchy does not contain sufficient information to derive all subsumption relationships between conjunctions of these concepts. We show how a method developed in the area of "formal concept analysis " for computing minimal implication bases can be used to determine a minimal representation of the subsumption hierarchy between conjunctions of concepts introduced in a TBox. To this purpose, the subsumption algorithm must be extended such that it yields (sufficient information about) a counterexample in cases where there is no subsumption relationship. For the concept language ALC, this additional requirement does not change the worst-case complexity of the subsumption algorithm. One advantage of the extended hierarchy is that it is a lattice, and not just a partial ordering. 1 Introduction In kn...

Galois lattices are introduced as a device to provide a general representation for two mode social network data. It is shown that Galois lattices yield a single visual image of such data in cases where most alternative models produce dual images. The inzage provided by the Galois lattice produces, moreover, an inzage that can suggest useful insights about the structuralprop-erties of the data. An example, based on data from Davis, Gardner, and Gardner (1 941), is used to spell out in detail the kinds of struc-tural insights that can be gained from this approach. In addi-tion, other potential applications are suggested. 1.

. This paper presents concept lattices as a natural representation of class hierarchies in object-oriented databases and frame based knowledge representations. We show how to extend concept lattices by uncertainty in the form of conditional probabilities. We illustrate that uncertain reasoning within the hierarchical structure of concept lattices can be performed efficiently and makes uncertain conclusions more precise. 1 Introduction The aim of this paper is to integrate uncertainty into class hierarchies of objectoriented databases and frame based knowledge representations. Extensional subclass relationships and disjointness statements are characteristic of class hierarchies. They can naturally be represented by concept lattices (see e.g. [14]). A concept is a pair consisting of a set of objects and a set of properties that all these objects share. The concept order is based on a coupled extensional and intensional order. For our purpose it is sufficient to concentrate just on the...

In this paper we outline our approach to discover and understand multi-dimensional correlations among regulatory security certification requirements in the context of a complex software system. A thorough understanding of these correlations is necessary to assure that diverse constraints imposed by numerous certification requirements are adequate for collectively contributing to emergent security properties in a highly interconnected socio-technical environment. We elaborate on methodological support to discover an exhaustive set of applicable certification requirements in a given operational scenario of the target software system. We then describe techniques to systematically understand the multi-dimensional correlations among these requirements with application to security risk assessment. The case study of applying our approach to a regulatory certification process of The United States Department of Defense (DoD) is presented.

Abstract. The effective construction of many association rule bases requires the computation of both frequent closed and frequent generator itemsets (FCIs/FGs). However, these two tasks are rarely combined. Most of the existing solutions apply levelwise breadth-first traversal, though depth-first traversal, depending on data characteristics, is often superior. Hence, we address here a hybrid algorithm that combines the two different traversals. The proposed algorithm, Eclat-Z, extracts frequent itemsets (FIs) in a depth-first way. Then, the algorithm filters FCIs and FGs among FIs in a levelwise manner, and associates the generators to their closures. In Eclat-Z we present a generic technique for extending an arbitrary FI-miner algorithm in order to support the generation of minimal non-redundant association rules too. Experimental results indicate that Eclat-Z outperforms pure levelwise methods in most cases. 1

ABSTRACT: Data structures comprising many binary variables can be represented graphically in various ways. Depending on the purpose different plots might be useful. Here two ways of showing associations between variables and implications between variables are discussed. The methods are based on conditional independence graphs and lattices of maximal cluster-property pairs. Applications to multivariate samples and network data are briefly discussed. 1.

Abstract. Two variations of an algorithm by Alan Day for reducing a list of implications regarding redundancy are given, with a new simple justification. All three algorithms have the property that the list can be reduced in place-at no extra memory cost- that will be useful for large applications and databases.

Security breaches most often occur due to a cascading effect of failure among security constraints that collectively contribute to overall secure system behavior in a socio-technical environment. Therefore, during security certification activities, analysts must systematically take into account the nexus of causal chains that exist among security constraints imposed by regulatory requirements. Numerous regulatory requirements specified in natural language documents or listed in spreadsheets/databases do not facilitate such analysis. The work presented in this paper, outlines a step-wise methodology to discover and understand the multidimensional correlations among regulatory requirements for the purpose of understanding the potential for risk due to non-compliance during system operation. Our lattice algebraic computational model helps estimate the collective adequacy of diverse security constraints imposed by regulatory requirements and their interdependencies with each other in a bounded scenario of investigation. Abstractions and visual metaphors combine human intuition with metrics available from the methodology to improve the understanding of risk based on the level of compliance with regulatory requirements. In addition, a problem domain ontology that classifies and categorizes regulatory requirements from multiple dimensions of a socio-technical environment promotes a common understanding among stakeholders during certification and accreditation activities. A preliminary empirical investigation of our theoretical propositions has been conducted in the domain of The