We propose an EM-based framework for learning Plackett-Luce model and its mixtures from partial orders. The core of our framework is the efficient sampling of linear extensions of partial orders under Plackett-Luce model. We propose two Markov Chain Monte Carlo (MCMC) samplers: Gibbs sampler and the generalized repeated insertion method tuned by MCMC (GRIM-MCMC), and prove the efficiency of GRIM-MCMC for a large class of preferences.Experiments on synthetic data show that the algorithm with Gibbs sampler outperforms that with GRIM-MCMC. Experiments on real-world data show that the likelihood of test dataset increases when (i) partial orders provide more information; or (ii) the number of components in mixtures of PlackettLuce model increases.
We proposed a texture mapping technique that comprises mesh partitioning, mesh parameterization and packing, texture transferring, and texture correction and optimization for generating a high-quality texture map of a three-dimensional (3D) model for applications in e-commerce presentations. The main problems in texture mapping are that the texture resolution is generally worse than in the original images and considerable photo inconsistency exists at the transition of different image sources. To improve the texture resolution, we employed an oriented boundary box method for placing mesh islands on the parametric (UV) map. We also provided a texture size that can keep the texture resolution of the 3D textured model similar to that of the object images. To improve the photo inconsistency problem, we employed a method to detect and overcome the missing color that might exist on a texture map. We also proposed a blending process to minimize the transition error caused by different image sources. Thus, a high-quality 3D textured model can be obtained by applying this series of processes for presentations in e-commerce.
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