CrossBridge: Finding Analogies Using Dimensionality Reduction

We present CrossBridge, a practical algorithm for retrieving analogies in large, sparse semantic networks. Other algorithms adopt a generate-and-test approach, retrieving candidate analogies by superficial similarity of concepts, then testing them for the particular relations involved in the analogy. CrossBridge adopts a global approach. It organizes the entire knowledge space at once, as a matrix of small concept-and-relation subgraph patterns versus actual occurrences of subgraphs from the knowledge base. It uses the familiar mathematics of dimensionality reduction to reorganize this space along dimensions representing approximate semantic similarity of these subgraphs. Analogies can then be retrieved by simple nearest-neighbor comparison. CrossBridge also takes into account not only knowledge directly related to the source and target domains, but also a large background Commonsense knowledge base. Commonsense influences the mapping between domains, preserving important relations while ignoring others. This property allows CrossBridge to find more intuitive and extensible analogies. We compare our approach with an implementation of structure mapping and show that our algorithm consistently finds analogies in cases where structure mapping fails. We also present some discovered analogies.