统计图分解的团矩阵与约束正定矩阵的参数化
Clique Matrices for Statistical Graph Decomposition and Parameterising Restricted Positive Definite Matrices
摘要：
我们引入团矩阵作为无向图的另一种表示，是关联矩阵表示的推广。在这里，我们使用团矩阵将图分解为一组可能重叠的簇，定义为连通性良好的顶点子集。分解是基于一个统计描述，鼓励集群连接良好，数量很少。使用变分近似进行推断。团矩阵在零约束下的正定矩阵的参数化中也起着自然的作用。我们表明，集团矩阵可以参数化所有的正定矩阵限制根据可分解的图，并形成一个结构化的因子分析近似在不可分解的情况下。
英文摘要：
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a statistical description which encourages clusters to be well connected and few in number. Inference is carried out using a variational approximation. Clique matrices also play a natural role in parameterising positive de nite matrices under zero constraints on elements of the matrix. We show that clique matrices can parameterise all positive de nite matrices restricted according to a decomposable graph and form a structured Factor Analysis approximation in the non-decomposable case.
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