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65
Comparing performance of algorithms for generating concept lattices
- J.EXPT.THEOR.ARTIF.INTELL.??(2002)1–28
, 2002
"... 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 well-known algorithms are proposed. Algorithmic complexity of ..."
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Cited by 133 (11 self)
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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 well-known 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.
Computing Iceberg Concept Lattices with TITANIC
, 2002
"... We introduce the notion of iceberg concept lattices... ..."
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Cited by 112 (15 self)
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We introduce the notion of iceberg concept lattices...
Efficient Algorithms for Mining Closed Itemsets and Their Lattice Structure
- IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
, 2005
"... 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 u ..."
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Cited by 85 (7 self)
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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 hashbased 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.
Exploiting the potential of concept lattices for information retrieval with CREDO
- JOURNAL OF UNIVERSAL COMPUTER SCIENCE
, 2004
"... The recent advances in Formal Concept Analysis (FCA) together with the major changes faced by modern Information Retrieval (IR) provide new unprecedented challenges and opportunities for FCA-based IR applications. The main advantage of FCA for IR is the possibility of creating a conceptual represe ..."
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Cited by 48 (2 self)
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The recent advances in Formal Concept Analysis (FCA) together with the major changes faced by modern Information Retrieval (IR) provide new unprecedented challenges and opportunities for FCA-based IR applications. The main advantage of FCA for IR is the possibility of creating a conceptual representation of a given document collection in the form of a document lattice, which may be used both to improve the retrieval of specific items and to drive the mining of the collection’s contents. In this paper, we will examine the best features of FCA for solving IR tasks that could not be easily addressed by conventional systems, as well as the most critical aspects for building FCA-based IR applications. These observations have led to the development of CREDO, a system that allows the user to query Web documents and see retrieval results organized in a browsable concept lattice. This is the second major focus of the paper. We will show that CREDO is especially useful for quickly locating the documents corresponding to the meaning of interest among those retrieved in response to an ambiguous query, or for mining the contents of the documents that reference a given entity. An on-line version of the system is available for testing at
Generating All The Minimal Separators Of A Graph
, 1999
"... We present an efficient algorithm which computes the set of minimal separators of a graph in O(n³) time per separator, thus gaining a factor of n² on the current best-time algorithms for this problem. Our process is based on a new structural result, derived from the work of Kloks and Kratsch on list ..."
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Cited by 34 (8 self)
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We present an efficient algorithm which computes the set of minimal separators of a graph in O(n³) time per separator, thus gaining a factor of n² on the current best-time algorithms for this problem. Our process is based on a new structural result, derived from the work of Kloks and Kratsch on listing all the minimal separators of a graph.
AddIntent: A new incremental algorithm for constructing concept lattices
- Lecture Notes in Computer Science Vol 2961
, 2004
"... Abstract. An incremental concept lattice construction algorithm, called AddIntent, is proposed. In experimental comparison, AddIntent outperformed a selection of other published algorithms for most types of contexts and was close to the most efficient algorithm in other cases. The current best estim ..."
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Cited by 26 (0 self)
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Abstract. An incremental concept lattice construction algorithm, called AddIntent, is proposed. In experimental comparison, AddIntent outperformed a selection of other published algorithms for most types of contexts and was close to the most efficient algorithm in other cases. The current best estimate for the algorithm’s upper bound complexity to construct a concept lattice L whose context has a set of objects G, each of which possesses at most max(|g ′ |) attributes, is O(|L||G | 2 max(|g ′ |)). 1
Reasoning about Sets using Redescription Mining
- KDD'05
, 2005
"... Redescription mining is a newly introduced data mining problem that seeks to find subsets of data that afford multiple definitions. It can be viewed as a generalization of association rule mining, from finding implications to equivalences; as a form of conceptual clustering, where the goal is to ide ..."
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Cited by 25 (13 self)
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Redescription mining is a newly introduced data mining problem that seeks to find subsets of data that afford multiple definitions. It can be viewed as a generalization of association rule mining, from finding implications to equivalences; as a form of conceptual clustering, where the goal is to identify clusters that afford dual characterizations; and as a form of constructive induction, to build features based on given descriptors that mutually reinforce each other. In this paper, we present the use of redescription mining as an important tool to reason about a collection of sets, especially their overlaps, similarities, and differences. We outline algorithms to mine all minimal (non-redundant) redescriptions underlying a dataset using notions of minimal generators of closed itemsets. We also show the use of these algorithms in an interactive context, supporting constraint-based exploration and querying. Specifically, we showcase a bioinformatics application that empowers the biologist to define a vocabulary of sets underlying a domain of genes and to reason about these sets, yielding significant biological insight.
Building concept (Galois) lattices from parts: Generalizing the incremental methods
- Proceedings of the ICCS’01
, 2001
"... Formal concept analysis and Galois lattices in general are increasingly used as a framework for the resolution of practical problems from software engineering, knowledge engineering and data mining. Recent applications have put the emphasis on the need for both efficient, scalable and flexible al ..."
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Cited by 21 (7 self)
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Formal concept analysis and Galois lattices in general are increasingly used as a framework for the resolution of practical problems from software engineering, knowledge engineering and data mining. Recent applications have put the emphasis on the need for both efficient, scalable and flexible algorithms to build the lattice. Such features are sought in the development of incremental algorithms. However, the major known incremental algorithm lacks clear theoretical foundations and shows some design flaws which strongly affect its practical performances. Our paper presents a general theoretical framework for the assembly of lattices sharing a same set of attributes based on existing theory on subposition of contexts. The framework underlies the design of a generic procedure for lattice assembly from parts, a new lattice building approach which is more general than the existing incremental and batch ones. As an argument for its theoretical strength, we describe the way our procedure reduces to an improved version of the major known incremental algorithm, which both corrects existing bugs and increases its overall efficiency.
Using concept lattices for text retrieval and mining
- IN FORMAL CONCEPT ANALYSIS-STATE OF THE ART, PROC. OF THE FIRST INTERNATIONAL CONFERENCE ON FORMAL CONCEPT ANALYSIS
, 2005
"... The potentials of formal concept analysis (FCA) for information retrieval (IR) have been highlighted by a number of research studies since its inception. With the proliferation of small-size specialised text databases available in electronic format and the advent of Web-based graphical interfaces, ..."
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Cited by 20 (0 self)
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The potentials of formal concept analysis (FCA) for information retrieval (IR) have been highlighted by a number of research studies since its inception. With the proliferation of small-size specialised text databases available in electronic format and the advent of Web-based graphical interfaces, FCA has then become even more appealing and practical for searching text collections. The main advantage of FCA for IR is the possibility of eliciting context, which may be used both to im-prove the retrieval of specic items from a text collection and to drive the mining of its contents. In this paper, we will focus on the unique features of FCA for building contextual IR applications as well as on its most critical aspects. The development of a FCA-based application for mining the web results returned by a major search engine is envisaged as the next big challenge for the field.
Representing a Concept Lattice By a Graph
- Proceedings of Discrete Maths and Data Mining Workshop, 2nd SIAM Conference on Data Mining (SDM'02
, 2004
"... Concept lattices (also called Galois lattices) are an ordering of the maximal rectangles dened by a binary relation. In this paper, we present a new relationship between lattices and graphs: given a binary relation R, we dene an underlying graph GR , and establish a one-to-one correspondence between ..."
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Cited by 18 (13 self)
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Concept lattices (also called Galois lattices) are an ordering of the maximal rectangles dened by a binary relation. In this paper, we present a new relationship between lattices and graphs: given a binary relation R, we dene an underlying graph GR , and establish a one-to-one correspondence between the set of elements of the concept lattice of R and the set of minimal separators of GR .
