Computing the Concept Lattice using Dendritical Neural Networks

Formal Concept Analysis (FCA) is a new and rich emerging discipline, and it provides e cient techniques and methods for e cient data analysis under the idea of attributes . The main tool used in this area is the Concept Lattice also named Galois Lattice or Maximal Rectangle Lattice. A naive way to generate the Concept Lattice is by enumeration of each cluster of attributes. Unfortunately the numbers of clusters under the inclusion attribute relation has an exponential upper bound. In this work, we present a novel algorithm, PIRA (PIRA is a Recursive Acronym), for computing Concept Lattices in an elegant way. This task is achieved through the relation between maximal height and width rectangles, and maximal anti-chains. Then, using a dendritical neural network is possible to identify the maximal anti-chains in the lattice structure by means of maximal height or width rectangles.