Feasibility of EdgeFeatureGraphCRF to be used for higher order CRFs

[Amrith Krishna]

Hi,

I am planning to build a model based on the EdgeFeatureGraphCRF. The task is reduced to search for a maximal clique from an arbitraty graph.

From my understanding of EdgeFeatureGraphCRF, it is  a second order model i.e., when predicting for the ouptut node, its edge features with all its neighbourts are considered. But the interactions shared between the neighbours (Feature vector betweeen two neighbours) are not considered.

Is my understanding correct here?

Can this be extended to higher order connections in the class? I plan to use the QPBO with alpha extension as the inference. I assume the said inference approach would support inference for higher order CRFs.

ANy help or discussion in this direction would be helpful and is highly appreciated.

Amrith Krishna,
PhD (pursuing), Computer Science,
IIT Kharagpur

[JL Meunier]

Hi,

Maybe it's question of terminology, but my understanding differs:

- in the EdgeFeatureGraphCRF model, the potential of a labeling (i.e. associating one label to each node of the graph) is the sum of the node's and edge's potentials

- the unary potential of each node depends on the node's features and node's label

- the pairwise potential of each edge depends on the edge's features and on the label the 2 nodes linked by the edge

So the features of each edge connecting two nodes are considered.

What do you mean by "higher order connections in the class"?

JL

[Amrith Krishna]

Hi,

Thanks for the response. Your discussion with Andreas on an older post was helpful for my understanding.

What I wanted to ask was the following. If a node has multiple neighbours, it will have multiple edges and hence multiple edge vectors to take into consideration. I assume all the edge vectors are taken into consideration, as represented by the pairwise potential. But does the edge vectors between the neighbours of a node is also taken into consideration. I think the default implemenetaion, do not take this into consideration. If so, how can the current class imlementation be extended.


My terminology was primarily taken from the follwoing paper by Hiroshi Ishikawa, Section 2 - Transformation of General Binary MRF Minimization to the First-Order Case.

[JL Meunier]

Hi,

Would this be equivalent to considering an hyper-edge, i.e. an edge that links more than 2 nodes?

In this case, I think the extension is doable with AD3 by binarizing the graph. That would be nice.

JL

Le mardi 6 février 2018 14:51:46 UTC+1, Amrith Krishna a écrit :

Hi,