Simultaneous Clustering and Ranking from Pairwise Comparisons

When people make decisions with a number of ideas, designs, or other kinds of objects, one attempt is probably to organize them into several groups of objects and to prioritize them according to some preference. The grouping task is referred to as clustering and the prioritizing task is called as ranking. These tasks are often outsourced with the help of human judgments in the form of pairwise comparisons. Two objects are compared on whether they are similar in the clustering problem, while the object of higher priority is determined in the ranking problem. Our research question in this paper is whether the pairwise comparisons for clustering also help ranking (and vice versa). Instead of solving the two tasks separately, we propose a unified formulation to bridge the two types of pairwise comparisons. Our formulation simultaneously estimates the object embeddings and the preference criterion vector. The experiments using real datasets support our hypothesis; our approach can generate better neighbor and preference estimation results than the approaches that only focus on a single type of pairwise comparisons.

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