Constructing Iceberg Lattices from Frequent Closures Using Generators

  title={Constructing Iceberg Lattices from Frequent Closures Using Generators},
  author={Laszlo Szathmary and Petko Valtchev and Amedeo Napoli and Robert Godin},
  booktitle={Discovery Science},
Frequent closures (FCIs) and generators (FGs) as well as the precedence relation on FCIs are key components in the definition of a variety of association rule bases. Although their joint computation has been studied in concept analysis, no scalable algorithm exists for the task at present. We propose here to reverse a method from the latter field using a fundamental property of hypergraph theory. The goal is to extract the precedence relation from a more common mining output, i.e. closures and… 

Efficient Vertical Mining of Frequent Closures and Generators

The proposed algorithm, Touch, deals with both FCI/FG-mining separately and is highly efficient and outperforms its levelwise competitors.

Fast Mining of Iceberg Lattices: A Modular Approach Using Generators

A performance comparison of Snow-Touch to its closest competitor, Charm-L, indicates that in the specific case of dense data, the modularity overhead is set by the speed gain of the new task order.

A fast compound algorithm for mining generators, closed itemsets, and computing links between equivalence classes

A new schema that should enable for a more parsimonious computation is proposed and exemplified in the design of Snow-Touch, a concrete FCI/FG/precedence miner that reuses an existing algorithm, Charm, for mining FCIs, and completes it with two original methods for mining FGs and precedence, respectively.

Yet a Faster Algorithm for Building the Hasse Diagram of a Concept Lattice

A novel method is presented that borrows its overall incremental approach from two algorithms in the literature and shows a good improvement with respect to its counterpart both on its theoretical complexity and on its practical performance.

CICLAD: A Fast and Memory-efficient Closed Itemset Miner for Streams

Leveraging in-depth insights into FCI evolution, Ciclad, an intersection-based sliding-window FCI miner combines minimal storage with quick access is designed, which indicates Ciclad's memory imprint is much lower and its performances globally better than competitor methods.

A comprehensive review on updating concept lattices and its application in updating association rules

This article comprehensively introduces basic knowledge regarding updating both concept lattices and AR‐basis with new illustrations, formalization, and examples.


The objective of this research is to extract triadic association rules from a triadic formal context K := (K 1, K 2, K 3, Y) where K 1, K 2 and K 3 respectively represent the sets of objects,

Mining Triadic Association Rules from Ternary Relations

This paper defines new notions and proposes procedures to mine closed tri-sets (triadic concepts) and triadic association rules within the framework of triadic concept analysis.

A Neural-Network Like Logical-Combinatorial Structure of Data and Constructing Concept Lattices

Some algorithms for constructing concept lattice, inferring good maximally redundant and irredundant classification tests are given using a generalization process based on Galois connections and a direct and backward wave of network activity propagation.

An intensive study on rule acquisition in formal decision contexts based on minimal closed label concept lattices

Minimal closed label concept lattice is defined to present limitary decision implications, which not only are easier to be extracted than decided implications, but also have more concise premises than decision rules and granular rules.



On Computing the Minimal Generator Family for Concept Lattices and Icebergs

A novel method for computing the mingen family that, although based on incremental lattice construction, is intended to be run in a batch mode and sheds light on the evolution of the family upon increases in the context attribute set.

An Efficient Hybrid Algorithm for Mining Frequent Closures and Generators

The proposed algorithm, Eclat-Z, extracts fre- quent itemsets (FIs) in a depth-first way, and filters FCIs and FGs among FIs in a levelwise manner, and associates the generators to their closures.

Computing iceberg concept lattices with T

Incremental Transformation of Lattices: A Key to Effective Knowledge Discovery

It is shown that a formal concept lattice L, with explicit generators, constitutes a viable medium for discrete, deterministic, data mining and can be grown from a binary relation R one row, or observation, at a time using a transformation that is based on the mathematical properties of the generators and faces of closed sets.

Efficient algorithms for mining closed itemsets and their lattice structure

CHARM is an efficient algorithm for mining all frequent closed itemsets using a dual itemset-tidset search tree, using an efficient hybrid search that skips many levels, and uses a technique called diffsets to reduce the memory footprint of intermediate computations.

A Survey on Condensed Representations for Frequent Sets

The core concepts used in the recent works on condensed representation for frequent sets are surveyed, including exact representations while it is also possible to consider approximated ones, i.e., to trade computational complexity with a bounded approximation on the computed support values.

Discovering Frequent Closed Itemsets for Association Rules

This paper proposes a new algorithm, called A-Close, using a closure mechanism to find frequent closed itemsets, and shows that this approach is very valuable for dense and/or correlated data that represent an important part of existing databases.

ZART: A Multifunctional Itemset Mining Algorithm

Zart shows a number of additional features and performs the following, usually independent, tasks: identify frequent closed itemsets and associate generators to their closures, which makes Zart a complete algorithm for computing classes of itemsets including generators and closed itemset.

Symbolic Data Mining Methods with the Coron Platform. (Méthodes symboliques de fouille de données avec la plate-forme Coron)

This thesis has investigated two of the most important tasks of KDD today, namely itemset extraction and association rule generation and defined a new basis for association rules called Closed Rules.

Constraint-Based Mining and Inductive Databases, European Workshop on Inductive Databases and Constraint Based Mining, Hinterzarten, Germany, March 11-13, 2004, Revised Selected Papers

The Hows, Whys, and Whens of Constraints in Itemset and Rule Discovery.- A Relational Query Primitive for Constraint-Based Pattern Mining.- To See the Wood for the Trees: Mining Frequent Tree