The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc) in each cluster is similar to the proportion of the entire data. Various fair clustering algorithms have been proposed, which modify standard K-means clustering to satisfy a given fairness constraint. A critical limitation of several existing fair clustering algorithms is that the number of parameters to be learned is proportional to the sample size because the cluster assignment of each datum should be optimized simultaneously with the cluster center, and thus scaling up the algorithms is difficult. In this paper, we propose a new fair clustering algorithm based on finite mixture model called Fair Model-based Clustering (FMC). A main advantage of FMC is that the number of learnable parameters is independent to the sample size and thus can be scaled up easily. In particular, a mini-batch learning is possible to obtain clusters that are approximately fair. Moreover, FMC can be applied to non-metric data (e.g., categorical data) as long as the likelihood is well-defined. Theoretical and empirical justifications of the superiority of the proposed algorithm are provided.

Haze removal, which is also referred to as image dehazing, has been extensively used to improve the visibility in images captured under inclement weather. In particular, the dark channel prior (DCP)-based single image dehazing has received the greatest amount of interest due to its superior performance. However, since the DCP is based on the characteristics of natural outdoor images, its reliability tends to decrease especially when an image contains man-made textures. In this paper, we present a DCP-based single image dehazing method that is robust when text or text-like patterns are present in the image. The proposed method first estimates the text likelihood from a hazy image using the stroke width transform (SWT) and uses the estimated likelihood to correct the DCP. The experimental results show that the proposed algorithm outperforms the conventional DCP-based dehazing methods.