From Context to Distance

Abstract

Clustering data described by categorical attributes is a challenging task in data mining applications. Unlike numerical attributes, it is difficult to define a distance between pairs of values of a categorical attribute, since the values are not ordered. In this article, we propose a framework to learn a context-based distance for categorical attributes. The key intuition of this work is that the distance between two values of a categorical attribute A i can be determined by the way in which the values of the other attributes A j are distributed in the dataset objects: if they are similarly distributed in the groups of objects in correspondence of the distinct values of A i a low value of distance is obtained. We propose also a solution to the critical point of the choice of the attributes A j . We validate our approach by embedding our distance learning framework in a hierarchical clustering algorithm. We applied it on various real world and synthetic datasets, both low and high-dimensional. Experimental results show that our method is competitive with respect to the state of the art of categorical data clustering approaches. We also show that our approach is scalable and has a low impact on the overall computational time of a clustering task.