Uncertainty in Artificial Intelligence
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Clique Matrices for Statistical Graph Decomposition and Parameterising Restricted Positive Definite Matrices
David Barber
Abstract:
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.
Keywords:
Pages: 26-33
PS Link:
PDF Link: /papers/08/p26-barber.pdf
BibTex:
@INPROCEEDINGS{Barber08,
AUTHOR = "David Barber ",
TITLE = "Clique Matrices for Statistical Graph Decomposition and Parameterising Restricted Positive Definite Matrices",
BOOKTITLE = "Proceedings of the Twenty-Fourth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-08)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2008",
PAGES = "26--33"
}


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