Support-based distance measurement between lattices

Abstract

Recently, there has been rapid growth in the volume of digital data from semi-structured and unstructured sources, such as web pages, images, videos, tweets, blog posts, and emails. The volume of data increases daily, making it difficult to access the data efficiently. To tackle the problems, we can represent the data in a summarised form using fuzzy formal concept lattices. In a situation where data is added dynamically, the concept lattices may evolve and the degree of change can be measured using a distance metric. In previous studies, we have successfully measured the change between two fuzzy lattices, based on pairing concepts in the two lattices and finding the cost of converting each concept to its counterpart. In this paper, we present a modification to the distance measurement, namely Support-based Distance Measurement. The aim of this method is to measure the change between lattices with disjoint sets of objects and identical attributes. The distance is found by considering the change in support (or relative cardinality) for each concept's extension. The method is illustrated by showing simple examples of its application to product review sites.