Continuously indexed Potts models on unoriented graphs
Landrieu Loic, Guillaume Obozinski
This paper introduces an extension to undirected
graphical models of the classical continuous time
Markov chains. This model can be used to solve
a transductive or unsupervised multi-class classi-
fication problem at each point of a network de-
fined as a set of nodes connected by segments of
different lengths. The classification is performed
not only at the nodes, but at every point of the
edge connecting two nodes. This is achieved by
constructing a Potts process indexed by the con-
tinuum of points forming the edges of the graph.
We propose a homogeneous parameterization
which satisfies Kolmogorov consistency, and
show that classical inference and learning algo-
rithms can be applied.
We then apply our model to a problem from geo-
matics, namely that of labelling city blocks auto-
matically with a simple typology of classes (e.g.
collective housing) from simple properties of the
shape and sizes of buildings of the blocks. Our
experiments shows that our model outperform
standard MRFs and a discriminative model like
PDF Link: /papers/14/p459-loic.pdf
AUTHOR = "Landrieu Loic
and Guillaume Obozinski",
TITLE = "Continuously indexed Potts models on unoriented graphs",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "459--468"