Compute association strength over semantic networks in a dimensionality-reduced form.

This code is used for doing cool things with ConceptNet. It's probably useful for other things too.

The high-level idea is:

• You have a relatively unstructured semantic network, with undirected edges
• You want to find out how strongly connected two nodes of the network are (based on how many paths get you from node 1 to node 2, vs. how complex those paths are)
• One way to do that is to apply spreading activation from node 1, and see how much of it reaches node 2, except that's terribly inefficient
• Dimensionality reduction applies:
  • You could represent this semantic network as a sparse matrix A of which nodes are connected to which other nodes
  • You can represent a reasonable approximation to this semantic network as a smaller dense matrix U and a diagonal Σ, where U · Σ · U^T ~= A
  • (This is an application of SVD)
• You can now simulate spreading activation with a really straightforward operation on Σ.
• That's what assoc-space does.