Protecting Individual Interests across Clusters: Spectral Clustering with Guarantees

• URL: http://arxiv.org/abs/2105.03714v1
• Date: Sat, 8 May 2021 15:03:25 GMT
• Title: Protecting Individual Interests across Clusters: Spectral Clustering with Guarantees
• Authors: Shubham Gupta and Ambedkar Dukkipati
• Abstract summary: We propose an individual fairness criterion for clustering a graph $mathcalG$ that requires each cluster to contain an adequate number of members connected to the individual. We devise a spectral clustering algorithm to find fair clusters under a given representation graph.
• Score: 20.350342151402963
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Studies related to fairness in machine learning have recently gained traction due to its ever-expanding role in high-stakes decision making. For example, it may be desirable to ensure that all clusters discovered by an algorithm have high gender diversity. Previously, these problems have been studied under a setting where sensitive attributes, with respect to which fairness conditions impose diversity across clusters, are assumed to be observable; hence, protected groups are readily available. Most often, this may not be true, and diversity or individual interests can manifest as an intrinsic or latent feature of a social network. For example, depending on latent sensitive attributes, individuals interact with each other and represent each other's interests, resulting in a network, which we refer to as a representation graph. Motivated by this, we propose an individual fairness criterion for clustering a graph $\mathcal{G}$ that requires each cluster to contain an adequate number of members connected to the individual under a representation graph $\mathcal{R}$. We devise a spectral clustering algorithm to find fair clusters under a given representation graph. We further propose a variant of the stochastic block model and establish our algorithm's weak consistency under this model. Finally, we present experimental results to corroborate our theoretical findings.

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