So similarity between two q/a pairs 50,-, 533-, is represented with wij E 32””, i.e., edge weights , and is measured as:

As total entailment scores get closer, the larger their edge weights would be.

Thus, we modify edge weights in (1) as follows:

Our idea of summarization is to create representative vertices of data points that are very close to each other in terms of edge weights .

We identify the edge weights wfj between each node in the boundary Bf via (1), thus the boundary is connected.

If any testing vector has an edge between a labeled vector, then with the usage of the local density constraints, the edge weights will not not only be affected by that labeled node, but also how dense that node is within that part of the graph.

Formally, it is a function d :C><C a [Rh where C is the set of terms in T. An ontology metric d on a taxonomy T with edge weights w

for any term pair (ox,cy)EC is the sum of all edge weights along the shortest path between the pair:

In the training data, an ontology metric d(c,,,cy) for a term pair (obey) is generated by assuming every edge weight as 1 and summing up all the edge weights along the shortest path from C, to Cy.