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Lee distance in analyzing and modeling rank data

ще изнесе Николай И. Николов, главен асистент в секция ИОВС на ИМИ.

Резюме: Distances on permutations are commonly used in rank data analysis and are an efficient tool for constructing probability models for rankings. In this talk, we consider some probabilistic applications of the Lee distance, which was originally developed as a generalization of the Hamming distance for error correction coding in modulation. In particular, we study the “K-means” clustering procedure based on Lee distance and approximate the normalizing constant needed for assessing the number of clusters. Furthermore, several asymptotic properties of the random variable induced by the Lee distance are derived and applied to distance-based models for rank data. By making use of the optimal property of the Mallows model in terms of the Kullback-Leibler divergence, a generalization based on the Cressie-Read power divergence is proposed.