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Efficient Mining Of Association Rules Using Closed Itemset Lattices
 INFORMATION SYSTEMS
, 1999
"... 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 ..."
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Cited by 157 (11 self)
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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 suborder 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.
Reengineering of Configurations Based on Mathematical Concept Analysis
 ACM Transactions on Software Engineering and Methodology
, 1996
"... 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 ..."
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Cited by 61 (7 self)
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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 configurationspecific code pieces are controlled by the preprocessor. The algorithm will compute a socalled concept lattice, which —when visually displayed — offers remarkable insight into the structure and properties of possible configurations. The lattice not only displays tinegrained 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.
Computing the Least Common Subsumer w.r.t. a Background Terminology
 Journal of Applied Logic
, 2004
"... Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive DLs whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to reuse concepts defined in such terminologies and still support the definition of new concepts ..."
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Cited by 50 (12 self)
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Methods for computing the least common subsumer (lcs) are usually restricted to rather inexpressive DLs whereas existing knowledge bases are written in very expressive DLs. In order to allow the user to reuse concepts defined in such terminologies and still support the definition of new concepts by computing the lcs, we extend the notion of the lcs of concept descriptions to the notion of the lcs w.r.t. a background terminology.
Using Galois lattices to represent network data
 Sociological methodology
, 1993
"... 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, m ..."
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Cited by 33 (9 self)
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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 structuralproperties 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 structural insights that can be gained from this approach. In addition, other potential applications are suggested. 1.
Computing a Minimal Representation of the Subsumption Lattice of All Conjunctions of Concepts Defined in a Terminology
 Proc. Intl. KRUSE Symposium
, 1995
"... . 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 conjuncti ..."
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Cited by 31 (1 self)
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. 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 worstcase 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...
Efficient Vertical Mining of Frequent Closures and Generators
, 2009
"... The effective construction of many association rule bases requires the computation of both frequent closed and frequent generator itemsets (FCIs/FGs). However, only few miners address both concerns, typically by applying levelwise breadthfirst traversal. As depthfirst traversal is known to be sup ..."
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Cited by 11 (6 self)
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The effective construction of many association rule bases requires the computation of both frequent closed and frequent generator itemsets (FCIs/FGs). However, only few miners address both concerns, typically by applying levelwise breadthfirst traversal. As depthfirst traversal is known to be superior, we examine here the depthfirst FCI/FGmining. The proposed algorithm, Touch, deals with both tasks separately, i.e., uses a wellknown vertical method, Charm, to extract FCIs and a novel one, TalkyG, to extract FGs. The respective outputs are matched in a postprocessing step. Experimental results indicate that Touch is highly efficient and outperforms its levelwise competitors.
Discovering and Understanding Multidimensional Correlations among Certification Requirements with application to Risk Assessment
, 2007
"... In this paper we outline our approach to discover and understand multidimensional 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 ..."
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Cited by 8 (5 self)
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In this paper we outline our approach to discover and understand multidimensional 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 sociotechnical 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 multidimensional 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.
An Efficient Hybrid Algorithm for Mining Frequent . . .
 PALACK´Y UNIVERSITY, OLOMOUC
, 2008
"... 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 breadthfirst traversal, though depthfirst traversal, ..."
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Cited by 5 (1 self)
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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 breadthfirst traversal, though depthfirst traversal, depending on data characteristics, is often superior. Hence, we address here a hybrid algorithm that combines the two different traversals. The proposed algorithm, EclatZ, extracts frequent itemsets (FIs) in a depthfirst way. Then, the algorithm filters FCIs and FGs among FIs in a levelwise manner, and associates the generators to their closures. In EclatZ we present a generic technique for extending an arbitrary FIminer algorithm in order to support the generation of minimal nonredundant association rules too. Experimental results indicate that EclatZ outperforms pure levelwise methods in most cases.
Uncertain Reasoning in Concept Lattices
 In Proc. of the 3 rd European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, volume 946 of LNCS/LNAI
, 1995
"... . This paper presents concept lattices as a natural representation of class hierarchies in objectoriented 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 withi ..."
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Cited by 5 (4 self)
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. This paper presents concept lattices as a natural representation of class hierarchies in objectoriented 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...
Structural plots of multivariate binary data
 Journal of Social Structure
"... 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 cond ..."
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Cited by 1 (0 self)
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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 clusterproperty pairs. Applications to multivariate samples and network data are briefly discussed. 1.