Concept Lattice Reduction by Matrix Decomposition

Abstract

The large volume of data from the large-scale computing platforms for high-fidelity design and simulations and instrumentation for gathering scientific, as well as, business data, and the huge information in the web, can be problematic if we want to compute all concepts from huge incidence matrix. High complexity of formal concept analysis algorithms and lattice construction algorithms are the main problems today. If we want to compute all concepts from huge incidence matrix, complexity plays a great role. In some cases, we do not need to compute all concepts, but only some of them. This thesis proposed minimizing incidence matrix using matrix decompositions (Singular Value Decomposition SVD and non-negative matrix factorization NMF). Modified matrix has lower dimensions and acts as input for some known algorithms for lattice construction. In this work, I would like to describe methods for matrix decompositions and describe their influence on the concept lattice. v