Algorithm

Require: A collection of returned documents from a search query.

Ensure: A collection of semantic manifolds.

Step 1

Perform feature extractions using discriminative linear chain Conditional Random Field method to generate named entities.

Step 2

Construct a manifold from the set of named entities generated from the document collection.

Step 3

Classify the manifold into isomorphic (homogeneous) categories by using the Graph-based Tree-width Decomposition algorithm starting from a fixed dimension local manifold.

Require: is the vertex set of named entities that each ti is associated with its named categories equipped with a weighted probability.

Ensure: is the set of isomorphic semantic manifolds.

where.

Step 3.1

Let a semantic topic set:. Let G = (V, E) be the undirected connected graph generated from the returned documents.

Step 3.2

Given a tree-width d, find a semantic manifold Mj generated from single named entities for each semantic category zi initially in which |Mj| = d and the semantic mapping with a probability, and quantity

Step 3.3

Perform graph decompositions on G starting from Mj.