There are many applications where similarity is categorical rather than binary. Consider, for example, a social network where two people have an edge between them if they are friends. But there are many categories of friends such as family, colleagues, schoolmates, neighbors etc. For a good clustering of such data, it is desirable to have mostly edges of similar type in a cluster. To capture this categorical similarity, Bonchi et al.  introduced chromatic correlation clustering, where each edge has a color associated with it, and as output one has to then also assign a color to each cluster.
Chromatic correlation clustering has applications from a variety of fields such as community detection in social network analysis, classifying proteins from protein-protein interaction networks in bioinformatics, and entity de-duplication in data-mining. Since finding the best clustering is NP-hard (already without colors), we focus on developing efficient algorithms that provide good approximate solutions.