Ranking data, which result from m raters ranking n items, are difficult to visualize due to their discrete algebraic structure, and the computational difficulties associated with them when n is large. This problem becomes worse when raters provide tied rankings or not all items are ranked. We develop an approach for the visualization of ranking data for large n which is intuitive, easy to use, and computationally efficient. The approach overcomes the structural and computational difficulties by utilizing a natural measure of dissimilarity for raters, and projecting the raters into a low dimensional vector space where they are viewed. The visualization techniques are demonstrated using voting data, jokes, and movie preferences.

Summary.  Recommendation systems are emerging as an important business application with significant economic impact. Currently popular systems include Amazon's book recommendations, Netflix's movie recommendations and Pandora's music recommendations. We address the problem of estimating probabilities associated with recommendation system data by using non‐parametric kernel smoothing. In our estimation we interpret missing items as randomly censored observations of preference relations and obtain efficient computation schemes by using combinatorial properties of generating functions. We demonstrate our approach with several case‐studies involving real world movie recommendation data. The results are comparable with state of the art techniques while also providing probabilistic preference estimates outside the scope of traditional recommender systems.

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