Data clustering groups data points into components so that similar points are within the same component. Data clustering is commonly used for data exploration and is sometimes used as a preprocessing step for later analysis [1]. In this paper, the multivariate beta mixture model (MBMM), a new probabilistic model for soft clustering, is proposed. As the MBMM is a mixture model, it shares many properties with the Gaussian mixture model (GMM), including its soft cluster assignment and parametric modeling. In addition, the MBMM allows the generation of new (synthetic) instances based on a generative process. Because the beta distribution is highly flexible (e.g., unimodal, bimodal, straight line, or exponentially increasing or decreasing), MBMM can fit data with versatile shapes.

This paper is concerned with rank aggregation, which aims to combine multiple input rankings to get a better ranking. A popular approach to rank aggregation is based on probabilistic models on permutations, e.g., the Luce model and the Mallows model. However, these models have their limitations in either poor expressiveness or high computational complexity. To avoid these limitations, in this paper, we propose a new model, which is defined with a coset-permutation distance, and models the generation of a permutation as a stagewise process. We refer to the new model as coset-permutation distance based stagewise (CPS) model.

This paper is concerned with rank aggregation, which aims to combine multiple input rankings to get a better ranking. A popular approach to rank aggregation is based on probabilistic models on permutations, e.g., the Luce model and the Mallows model. However, these models have their limitations in either poor expressiveness or high computational complexity. To avoid these limitations, in this paper, we propose a new model, which is defined with a coset-permutation distance, and models the generation of a permutation as a stagewise process. We refer to the new model as coset-permutation distance based stagewise (CPS) model.