Dist Frequent Next Neighbours: A Distributed Galois Lattice Algorithm for Frequent Closed Itemsets Extraction

The general purpose of this paper is to propose a distributed version of frequent closed itemsets extraction in the context of big data. The goal is to have good performances of frequent closed itemsets extraction as frequent closed item-sets are bases for frequent itemsets. To achieve this goal, we have extended the Galois lattice technique (or concept lattice) in this context. Indeed, Galois lattices are an efficient alternative for extracting closed itemsets which are interesting approaches for generating frequent itemsets. Thus we proposed Dist Frequent Next Neighbour which is a distributed version of the Frequent Next Neighbour concept lattice construction algorithm, which considerably reduces the extraction time by parallelizing the computation of frequent concepts (closed itemsets).

Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach

Formal concept analysis (FCA) is a mathematical theory that is typically used as a knowledge representation method. The approach starts with an input binary relation specifying a set of objects and attributes, finds the natural groupings (formal concepts) described in the data, and then organizes the concepts in a partial order structure or concept (Galois) lattice. Unfortunately, the total number of concepts in this structure tends to grow exponentially as the size of the data increases. Therefore, there are numerous approaches for selecting a subset of concepts to provide full or partial coverage. In this paper, we rely on the battery of mathematical models offered by FCA to introduce a new greedy algorithm, called Concise, to compute minimal and meaningful subsets of concepts. Thanks to its theoretical properties, the Concise algorithm is shown to avoid the sluggishness of its competitors while offering the ability to mine both partial and full conceptual coverage of formal contexts. Furthermore, experiments on massive datasets also underscore the preservation of the quality of the mined formal concepts through interestingness measures agreed upon by the community.

Injective envelopes of transition systems and Ferrers languages

We consider reflexive and involutive transition systems over an ordered alphabet A equipped with an involution. We give a description of the injective envelope of any two-element set in terms of Galois lattice, from which we derive a test of its finiteness. Our description leads to the notion of Ferrers language.

A family of minimal and renormalizable rectangle exchange maps

A domain exchange map (DEM) is a dynamical system defined on a smooth Jordan domain which is a piecewise translation. We explain how to use cut-and-project sets to construct minimal DEMs. Specializing to the case in which the domain is a square and the cut-and-project set is associated to a Galois lattice, we construct an infinite family of DEMs in which each map is associated to a Pisot–Vijayaraghavan (PV) number. We develop a renormalization scheme for these DEMs. Certain DEMs in the family can be composed to create multistage, renormalizable DEMs.

An Optimized Associative Classifier for Incremental Data Based On Non-Trivial Data Insertion

Associative classification (AC) is an interesting approach in the domain of data mining which makes use of the association rules for building a classification system, which are easy for interpretation by the end user. The previous work [1] showed excellent performance in a static large data base but there existed a question of same performance when applied in an incremental data. Many of the Associative Classification methods have left the problem of data insertion and optimization unattended that results in serious performance degradation. To resolve this issue, we used new technique C-NTDI for building a classifier when there is an insertion of data that take place in a non-trivial fashion in the initial data that are used for updating the classification rules and thereafter to apply the PPCE technique for the generating of rules and further Proportion of Frequency occurrence count with BAT Algorithm (PFOCBA) is applied for optimizing the rules that are generated. The experiments were conducted on 6 different incremental data sets and we found that the proposed technique outperforms other methods such as ACIM, E-ACIM, Fast Update (FUP), Galois Lattice theory (GLT) and New Fast Update (NFUP) in terms of accuracy and time complexity.