There has been much recent interest in developing fair clustering algorithms that seek to do justice to the representation of groups defined along sensitive attributes such as race and sex. Within the centroid clustering paradigm, these algorithms are seen to generate clusterings where different groups are disadvantaged within different clusters with respect to their representativity, i.e., distance to centroid. In view of this deficiency, we propose a novel notion of cluster-level centroid fairness that targets the representativity unfairness borne by groups within each cluster, along with a metric to quantify the same. Towards operationalising this notion, we draw on ideas from political philosophy aligned with consideration for the worst-off group to develop Fair-Centroid; a new clustering method that focusses on enhancing the representativity of the worst-off group within each cluster. Our method uses an iterative optimisation paradigm wherein an initial cluster assignment is refined by reassigning objects to clusters such that the worst-off group in each cluster is benefitted. We compare our notion with a related fairness notion and show through extensive empirical evaluations on real-world datasets that our method significantly enhances cluster-level centroid fairness at low impact on cluster coherence.

Regular expressions are an important building block of rule-based information extraction systems. Regexes can encode rules to recognize instances of simple entities which can then feed into the identification of more complex cross-entity relationships. Manually crafting a regex that recognizes all possible instances of an entity is difficult since an entity can manifest in a variety of different forms. Thus, the problem of automatically generalizing manually crafted seed regexes to improve the recall of IE systems has attracted research attention. In this paper, we propose a bootstrapped approach to improve the recall for extraction of regex-formatted entities, with the only source of supervision being the seed regex. Our approach starts from a manually authored high precision seed regex for the entity of interest, and uses the matches of the seed regex and the context around these matches to identify more instances of the entity. These are then used to identify a set of diverse, high recall regexes that are representative of this entity. Through an empirical evaluation over multiple real world document corpora, we illustrate the effectiveness of our approach.