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Boulicaut, Jean-François; Bykowski, Artur; Rigotti, Christophe

doi:10.1023/a:1021571501451

Cited by 195 publications

(5 citation statements)

References 8 publications

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“…Reduction of formal contexts can be achieved by removing noise or outliers from the data. Noise refers to the data that does not fit in a grouping or concept when the difference is not important to a given purpose and it can drastically increase the number of concepts generated (Boulicaut et al, 2003, Pensa & Boulicaut, 2005, Andrews & Orphanides, 2010. Noise is most common in real data such as surveys, logs, documents collections, when values can be biased, missing or when some mistake was introduced in the data.…”

Section: Fault-tolerancementioning

confidence: 99%

“…The notion of fault-tolerant FCA was introduced by Pensa and Boulicaut (2005) to allow a certain number of 'exceptions' to occur in a concept. Based on the idea of "free-sets" (Boulicaut et al, 2003), the method seeks to find maximal rectangles of true values in the context bounded by δ exceptions (outliers). The resulting "purified" context is less likely to generate extra concepts to represent these exceptions in data and therefore it simplifies the concept lattice.…”

Section: Fault-tolerancementioning

confidence: 99%

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Browsing Large Concept Lattices through Tree Extraction and Reduction Methods

Melo

Le-Grand

Aufaure

2013

International Journal of Intelligent Information Technologies

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Browsing concept lattices from Formal Concept Analysis (FCA) becomes a problem as the number of concepts can grow significantly with the number of objects and attributes. Interpreting the lattice through direct graph-based visualisation of the Hasse diagram rapidly becomes difficult and more synthetic representations are needed. In this work the authors propose an approach to simplify concept lattices by extracting and visualising trees derived from them. The authors further simplify the browse-able trees with two reduction methods: fault-tolerance and concept clustering.

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Section: Fault-tolerancementioning

confidence: 99%

Section: Fault-tolerancementioning

confidence: 99%

Browsing Large Concept Lattices through Tree Extraction and Reduction Methods

Melo

Le-Grand

Aufaure

2013

International Journal of Intelligent Information Technologies

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“…One of the most popular data mining task concerns the constraint-based discovery of itemsets and association rules from transactional data [1,3,9,14]. In the so-called inductive database approach [6], a database integrates raw data with knowledge extracted from raw data, materialized under the form of patterns into an unified framework [4].…”

Section: Introductionmentioning

confidence: 99%

“…Crossing-over queries returning transactions satisfying some association rules are of this kind: transactions are itemsets that have to be supersets of some extracted itemsets. Another application where inclusion tests are used is the regeneration of the frequent itemsets from their so-called condensed representations [3]. Other examples of post-processing are given in [13].…”

Section: Introductionmentioning

confidence: 99%

Optimizing subset queries

Masson

Robardet

Boulicaut

2004

Proceedings of the 2004 ACM Symposium on Applied Computing

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Storing sets and querying them (e.g., subset queries that provide all supersets of a given set) is known to be difficult within relational databases. We consider that being able to query efficiently both transactional data and materialized collections of sets by means of standard query language is an important step towards practical inductive databases. Indeed, data mining query languages like MINE RULE extract collections of association rules whose components are sets into relational tables. Post-processing phases often use extensively subset queries and cannot be efficiently processed by SQL servers. In this paper, we propose a new way to handle sets from relational databases. It is based on a data structure that partially encodes the inclusion relationship between sets. It is an extension of the hash group bitmap key proposed by Morzy et al. [8]. Our experiments show an interesting improvement for these useful subset queries.

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“…In [39], an efficient post-processing method is presented to prune redundant rules by virtue of the property of Galois connection, which inherently constrains rules with respect to objects. At present, itemsets have been widely investigated [40,41], and various itemsets and their generating algorithms for specific association rules mining have been proposed, such as expressive generalized itemsets [42], free itemsets [43], disjunction-free itemsets [44,45], non-derivable itemsets [46,47], disjunctive closed itemsets [48], etc. In fact, we notice that frequent itemsets or closed itemsets are rooted to the co-occurrence relation among items; from the mathematical point of view, topology may be a more suitable tool to express the relation among items, because a topology for the set is used to express a relation among subsets, subsets of the set are granulated as members of the topology, and the topology for the set is generated by its topology base; this means that the base for the topology is the basic relation among elements of the set.…”

mentioning

confidence: 99%

Efficient Associate Rules Mining Based on Topology for Items of Transactional Data

Pei

Zhang³

et al. 2023

Mathematics

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A challenge in association rules’ mining is effectively reducing the time and space complexity in association rules mining with predefined minimum support and confidence thresholds from huge transaction databases. In this paper, we propose an efficient method based on the topology space of the itemset for mining associate rules from transaction databases. To do so, we deduce a binary relation on itemset, and construct a topology space of itemset based on the binary relation and the quotient lattice of the topology according to transactions of itemsets. Furthermore, we prove that all closed itemsets are included in the quotient lattice of the topology, and generators or minimal generators of every closed itemset can be easily obtained from an element of the quotient lattice. Formally, the topology on itemset represents more general associative relationship among items of transaction databases, the quotient lattice of the topology displays the hierarchical structures on all itemsets, and provide us a method to approximate any template of the itemset. Accordingly, we provide efficient algorithms to generate Min-Max association rules or reduce generalized association rules based on the lower approximation and the upper approximation of a template, respectively. The experiment results demonstrate that the proposed method is an alternative and efficient method to generate or reduce association rules from transaction databases.

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Untitled

Cited by 195 publications

References 8 publications

Browsing Large Concept Lattices through Tree Extraction and Reduction Methods

Browsing Large Concept Lattices through Tree Extraction and Reduction Methods

Optimizing subset queries

Efficient Associate Rules Mining Based on Topology for Items of Transactional Data

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