Data clustering based on family resemblance

In this paper, a novel framework for data clustering is presented based on Wittgenstein´s family resemblance. Family resemblance emphasizes that things in the same concept are connected by an overlapping sets of features, but not necessarily a common set of features. In other words, any two things in the same concept may not be similar to each other but must have a similarity connected path between them, in which any two directly linked things are highly similar to each other. Therefore, if a cluster is meaningful in perception, a cluster should represent a concept. Such an assumption leads to a new description of cluster: data pairs in the same cluster are not necessary highly similar to each other but must have such a path that any two neighboring data (called neighboring data pair) have relative high similarity in this path. Such property is called similarity connectivity. Based on this new definition of cluster, we present a novel clustering method based on similarity connectivity. Its basic steps can be expressed as follows: Given a similarity matrix of a data set, firstly find a threshold to partition the similarity values to two parts: high similarity (1: similar) and low similarity (0: dissimilar), then form an adjacency matrix and output the clustering result by searching for connected components in this adjacency matrix. This new framework is applied to image segmentation and the results are very encouraging.