Computing iceberg concept lattices with Titanic

Abstract

International audienceWe introduce the notion of iceberg concept lattices and show their use in knowledge discovery in databases. Iceberg lattices are a conceptual clustering method, which is well suited for analyzing very large databases. They also serve as a condensed representation of frequent itemsets, as starting point for computing bases of association rules, and as a visualization method for association rules. Iceberg concept lattices are based on the theory of Formal Concept Analysis, a mathematical theory with applications in data analysis, information retrieval, and knowledge discovery. We present a new algorithm called TITANIC for computing (iceberg) concept lattices. It is based on data mining techniques with a level-wise approach. In fact, TITANIC can be used for a more general problem: Computing arbitrary closure systems when the closure operator comes along with a so-called weight function. The use of weight functions for computing closure systems has not been discussed in the literature up to now. Applications providing such a weight function include association rule mining, functional dependencies in databases, conceptual clustering, and ontology engineering. The algorithm is experimentally evaluated and compared with Ganter's Next-Closure algorithm. The evaluation shows an important gain in efficiency, especially for weakly correlated data

Efficient Mining of Association Rules Based on Formal Concept Analysis

“…Titanic [45] -as introduced above in detail -continues the tradition of the Close family. It computes in a level-wise manner all frequent key sets, and in the same step their closures.…”

“…This is especially important when the database is too large for main memory, as each disk access significantly increases computation time. A theoretical and experimental analysis of this behavior is given in [45], further experimental results are provided in [40].…”

Query-Based Multicontexts for Knowledge Base Browsing: An Evaluation

“…She would like to get an overview of the researchers working on this -use an iceberg concept lattice -use conceptual scaling -select the context objects and attributes to be used for the displaying of the lattice 5 -define queries to create object and attribute sets and their incidence relation The first technique is based on frequent item sets. Using the TITANIC algorithm (see [9]), it is possible to construct the lattice of the frequent item sets of the formal context. Setting a threshold on the number of publications would reduce the size of the lattice to be displayed.…”

Making Use of Empty Intersections to Improve the Performance of CbO-Type Algorithms

“…Such approaches include ice-berg lattices [1], nesting lattices [2], creating sub-contexts [3], fault-tolerance [4,5], expandable concept trees [6], rough concepts [7] and approximation [8]. However, there will always be the need for faster performance of the fundamental operations in FCA, such as the computation of formal concepts.…”