Towards a Temporal Extension of Formal Concept Analysis

This article presents a method for analyzing the e volution of concepts represented by concept lattices in a time stamped d atabase, showing how the concepts that evolve with time induce a change in t he concept lattice. The purpose of this work is to extend formal concept an alysis to handle temporal properties and represent temporally evolving attrib utes. 1 Introduction Formal concept analysis (FCA) [2, 7, 14] is a mathe matical tool for analyzing data and formally representing conceptual knowledge. FCA helps forming conceptual structures from data. Such structures consist of un its, which are formal abstractions of concepts of human thought allowing meaningful and c omprehensible interpretation. FCA is a mathematical discipline whose features inc lude: − Visualizing inherent properties in data sets, − Interactively exploring attributes of objects and t heir corresponding contexts, and − Formally classifying systems based on relationships among objects and attributes through the concept of mathematical lattices. FCA automatically generates hierarchies called conc ept lattices that characterize the relationships among objects and their attributes. Concepts change and evolve with time. In fact, chan ge seems to be constant in a continuously changing world. In many domains such a s science, medicine, finance, population, and weather patterns, change is noticea ble from one time to another. The extension of concepts (set of objects) and their in tensions (set of related attributes) may change, affecting how the entities are related. As a consequence, the concept lattice characterizing the relationships among a se t of entities (objects and attributes) evolves over time. Temporal concept lattice metamor phosis is the change in the concept lattice over time. The rest of this section introduces some basic FCA definitions, terminology and states some assumptions. Section 2 presents tempora l lattices and the evolution of concept structures in these lattices. Section 3 ide ntifies the importance and applications of this work. In Section 4, the extens ion of FCA is developed and techniques for identifying temporal evolution patte rns are presented. Section 5 discusses the problem of inferring temporal propert ies.