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Network embedding aims to automatically learn the node representations in networks. The basic idea of network embedding is to first construct a network to describe the neighborhood context for each node, and then learn the node representations by designing an objective function to preserve certain properties of the constructed context network. The vast majority of the existing methods, explicitly or implicitly, follow a pointwise design principle. That is, the objective can be decomposed into the summation of the certain goodness function over each individual edge of the context network. In this paper, we propose to go beyond such pointwise approaches, and introduce the ranking-oriented design principle for network embedding. The key idea is to decompose the overall objective function into the summation of a goodness function over a set of edges to collectively preserve their relative rankings on the context network. We instantiate the ranking-oriented design principle by two new network embedding algorithms, including a pairwise network embedding method PaWine which optimizes the relative weights of edge pairs, and a listwise method LiWine which optimizes the relative weights of edge lists. Both proposed algorithms bear a linear time complexity, making themselves scalable to large networks. We conduct extensive experimental evaluations on five real datasets with a variety of downstream learning tasks, which demonstrate that the proposed approaches consistently outperform the existing methods. 

Multivariate spatial point process models can describe heterotopic data over space. However, highly multivariate intensities are computationally challenging due to the curse of dimensionality. To bridge this gap, we introduce a declustering based hidden variable model that leads to an efficient inference procedure via a variational autoencoder (VAE). We also prove that this model is a generalization of the VAE-based model for collaborative filtering. This leads to an interesting application of spatial point process models to recommender systems. Experimental results show the method’s utility on both synthetic data and real-world data sets.