图模型由点和线组成的用以描述系统的图形。图模型属于结构模型(见模型),可用于描述自然界和人类社会中的大量事物和事物之间的关系。在建模中采用图模型可利用图论作为工具。按图的性质进行分析为研究各种系统特别是复杂系统提供了一种有效的方法。构成图模型的图形不同于一般的几何图形。例如,它的每条边可以被赋以权,组成加权图。权可取一定数值,用以表示距离、流量、费用等。加权图可用于研究电网络、运输网络、通信网络以及运筹学中的一些重要课题。图模型广泛应用于自然科学、工程技术、社会经济和管理等方面。见动态结构图、信号流程图、计划协调技术、图解协调技术、风险协调技术、网络技术、网络理论。

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使用图模型解决问题时,面对实际环境中来源多样、形式复杂的数据,怎样将多种信息进行合理融合是一个值得关注的问题。本文将介绍两篇发表于KDD 2020的与图模型信息融合相关的工作。

第一篇工作为《HGMF: Heterogeneous Graph-based Fusion for Multimodal Data with Incompleteness》,该工作主要是基于异质图来解决多模态学习中在信息融合时会遇到的模态缺失问题。

第二篇工作为《Improving Conversational Recommender Systems via Knowledge Graph based Semantic Fusion》,该工作通过引入两个外部知识图谱丰富会话的语义信息,并通过互信息最大化弥补知识图谱间的语义鸿沟以提升会话推荐系统的表现。

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The characterisation of the spatial and temporal distribution of the root system in a cultivated field depends on the soil volume occupied by the root systems (the scatter), and the local intensity of the root colonisation in the field (the intensity). We introduce a multivariate generalised linear mixed model for simultaneously describing the scatter and the intensity using data obtained with minirhizotrons (i.e., tubes with observation windows, which are inserted in the soil, enabling to observe the roots directly). The models presented allow studying intricate spatial and temporal dependence patterns using a graphical model to represent the dependence structure of latent random components. The scatter is described by a binomial mixed model (presence of roots in observation windows). The number of roots crossing the reference lines in the observational windows of the minirhizotron is used to estimate the intensity through a specially defined Poisson mixed model. We explore the fact that it is possible to construct multivariate extensions of generalised linear mixed models that allow to simultaneously represent patterns of dependency of the scatter and the intensity along with time and space. We present an example where the intensity and scatter are simultaneously determined at three different time points. A positive association between the intensity and scatter at each time point was found, suggesting that the plants are not compensating a reduced occupation of the soil by increasing the number of roots per volume of soil. Using the general properties of graphical models, we identify a first-order Markovian dependence pattern between successively observed scatters and intensities. This lack of memory indicates that no long-lasting temporal causal effects are affecting the roots' development. The two dependence patterns described above cannot be detected with univariate models.

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The characterisation of the spatial and temporal distribution of the root system in a cultivated field depends on the soil volume occupied by the root systems (the scatter), and the local intensity of the root colonisation in the field (the intensity). We introduce a multivariate generalised linear mixed model for simultaneously describing the scatter and the intensity using data obtained with minirhizotrons (i.e., tubes with observation windows, which are inserted in the soil, enabling to observe the roots directly). The models presented allow studying intricate spatial and temporal dependence patterns using a graphical model to represent the dependence structure of latent random components. The scatter is described by a binomial mixed model (presence of roots in observation windows). The number of roots crossing the reference lines in the observational windows of the minirhizotron is used to estimate the intensity through a specially defined Poisson mixed model. We explore the fact that it is possible to construct multivariate extensions of generalised linear mixed models that allow to simultaneously represent patterns of dependency of the scatter and the intensity along with time and space. We present an example where the intensity and scatter are simultaneously determined at three different time points. A positive association between the intensity and scatter at each time point was found, suggesting that the plants are not compensating a reduced occupation of the soil by increasing the number of roots per volume of soil. Using the general properties of graphical models, we identify a first-order Markovian dependence pattern between successively observed scatters and intensities. This lack of memory indicates that no long-lasting temporal causal effects are affecting the roots' development. The two dependence patterns described above cannot be detected with univariate models.

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