Efficient Mining of Association Rules Based on Formal Concept Analysis

Lakhal, Lotfi; Stumme, Gerd

doi:10.1007/11528784_10

Cited by 63 publications

(51 citation statements)

References 33 publications

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“…The sequence of chosen candidates c 1 , ..., c k represents the path from the root to the extent {z | S + ∪ {c 1 , ..., c k } → {z}}. Thus a path with S + is just a generator (Lakhal & Stumme, 2005) of the extent. Unlike a set enumeration tree, some control to avoid duplicated generations of the same extents is needed, as there exist several generators for the same extents.…”

Section: Prunings With Right and Left Candidatesmentioning

confidence: 99%

“…Such an implicit concept will be useful in discovering "Crossover Group of Pages" for instance. Suppose we have several concepts with their extents of large numbers of pages so that they are visible by applying standard effective mining engines as Lakhal & Stumme, 2005;Uno et al, 2004;Wang et al, 2003) for instances. These pages are not necessarily connected by links, as we consider here a page-term relationship only.…”

Section: Introductionmentioning

confidence: 99%

“…As is well known, each intent of concept just corresponds to a closed itemset of an association rule (Bastide et al, 2000). Many nice algorithms Lakhal & Stumme, 2005;Uno et al, 2004;Wang et al, 2003) for finding frequent closed itemsets have been developed successfully. However, since our targets are non-frequent, we cannot apply them at least directly.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Pinpoint Clustering of Web Pages and Mining Implicit Crossover Concepts

Haraguchi¹,

Okubo²

2010

Web Intelligence and Intelligent Agents

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Section: Prunings With Right and Left Candidatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Pinpoint Clustering of Web Pages and Mining Implicit Crossover Concepts

Haraguchi¹,

Okubo²

2010

Web Intelligence and Intelligent Agents

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“…Mining times are typically long: this is demonstrated in [26], where the Twister Map-Reduce framework [8] is used to parallelize computational effort. However, in many cases some notion of Formal Concept (FC) importance might yield a better ordering, for example in knowledge discovery [17], information retrieval [21], and social networking analysis [22] applications. In this paper we leverage FC disjointness (as an embodiment of importance) along with lectic ordering to propose a new multiplestarting point approach, RRFCA, that improves mining and searching speed.…”

Section: Introductionmentioning

confidence: 99%

Formal Concept Analysis via Atomic Priming

Fréin

2013

Formal Concept Analysis

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Formal Concept Analysis (FCA) looks to decompose a matrix of objectsattributes into a set of sparse matrices capturing the underlying structure of a formal context. We propose a Rank Reduction (RR) method to prime approximate FCAs, namely RRFCA. While many existing FCA algorithms are complete, lectic ordering of the lattice may not minimize search/decomposition time. Initially, RRFCA decompositions are not unique or complete; however, a set of good closures with high support is learned quickly, and then, made complete. RRFCA has its novelty in that we propose a new multiplicative two-stage method. First, we describe the theoretical foundations underpinning our RR approach. Second, we provide a representative exemplar, showing how RRFCA can be implemented. Further experiments demonstrate that RRFCA methods are efficient, scalable and yield time-savings. We demonstrate the resulting methods lend themselves to parallelization.Key words: Formal Concept Analysis, Rank Reduction, Factorization. IntroductionFormal Concept Analysis (FCA) leverages the notion of a concept, an objectattribute building block of a binary relational dataset, and its ranking in a concept hierarchy to mine data-sets [25]. One short-coming is that concepts are mined according to lectic ordering and not concept importance or support in the formal context. Lectic ordering recommends itself on account of its thoroughness [10] [24,13]. The theoretical and empirical complexity of various approaches is compared by Kuznetsov in [16]. Computational complexity is the main measure for comparing algorithms: Kuznetsov and Obiedkov focus on the properties of the data ensemble, namely sparsity, the primary complexity inducing characteristic of the decomposition. Aside from sparsity, the main bottlenecks are memory and processing constraints. Ganter's algorithm computes concepts iteratively based on the previous concept, without incurring exponential memory requirements, by exploiting lectic ordering. CloseByOne produces many concepts in each iteration. Bordat's algorithm, described in [3], introduces a data structure to store previously found concepts, which results in considerable timesavings. This approach is made more efficient in [2] by removing the need for a structure of exponential size.A significant short-coming of batch approaches is that the entire lattice must be reconstructed if the database changes. Here, we look to the memory and computation challenge by using rank reduction method and disjointness to select good starting-intents for FCA.The justification goes as follows: all concepts are not equal in a binary relational dataset. FC support (the extent to which it overlaps with the formal context) and its expressiveness (FC disjointness given a set of FCs), may be different for FCs. NextClosure's lectic ordering does not consider these concerns. To address this, we prime NextClosure with multiple starting-intents by taking reduced rank approximations of the binary relation using Nonnegative Matrix Factorization (NMF) [18]. Lectic order...

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“…The authors categorized these papers according to the 10 categories as defined in the ISO 12207 software engineering standard and visualize them in a concept lattice. In Lakhal et al (2005), a survey on FCA-based association rule mining techniques is given.…”

Section: Introductionmentioning

confidence: 99%

Formal Concept Analysis in Knowledge Discovery: A Survey

Poelmans

Elzinga²,

Viaene

et al. 2010

Lecture Notes in Computer Science

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Abstract.In this paper, we analyze the literature on Formal Concept Analysis (FCA) using FCA. We collected 702 papers published between 2003-2009 mentioning Formal Concept Analysis in the abstract. We developed a knowledge browsing environment to support our literature analysis process. The pdf-files containing the papers were converted to plain text and indexed by Lucene using a thesaurus containing terms related to FCA research. We use the visualization capabilities of FCA to explore the literature, to discover and conceptually represent the main research topics in the FCA community. As a case study, we zoom in on the 140 papers on using FCA in knowledge discovery and data mining and give an extensive overview of the contents of this literature.

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Efficient Mining of Association Rules Based on Formal Concept Analysis

Cited by 63 publications

References 33 publications

Pinpoint Clustering of Web Pages and Mining Implicit Crossover Concepts

Pinpoint Clustering of Web Pages and Mining Implicit Crossover Concepts

Formal Concept Analysis via Atomic Priming

Formal Concept Analysis in Knowledge Discovery: A Survey

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