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CrossBridge: Finding Analogies Using Dimensionality Reduction
"... We present CROSSBRIDGE, a practical algorithm for retrieving analogies in large, sparse semantic networks. Other algorithms adopt a generateandtest approach, retrieving candidate analogies by superficial similarity of concepts, then testing them for the particular relations involved in the analogy ..."
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We present CROSSBRIDGE, a practical algorithm for retrieving analogies in large, sparse semantic networks. Other algorithms adopt a generateandtest 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 conceptandrelation 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 nearestneighbor 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.
Analogical proportions and the factorization of information in distributive lattices
"... Abstract. Analogical proportions are statements involving four entities, of the form ‘A is to B as C is to D’. They play an important role in analogical reasoning. Their formalization has received much attention from different researchers in the last decade, in particular in a propositional logic se ..."
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Abstract. Analogical proportions are statements involving four entities, of the form ‘A is to B as C is to D’. They play an important role in analogical reasoning. Their formalization has received much attention from different researchers in the last decade, in particular in a propositional logic setting. Analogical proportions have also been algebraically defined in terms of factorization, as a generalization of geometric numerical proportions (that equate ratios). In this paper, we define and study analogical proportions in the general setting of lattices, and more particularly of distributive lattices. The decomposition of analogical proportions in canonical proportions is discussed in details, as well as the resolution of analogical proportion equations, which plays a crucial role in reasoning. The case of Boolean lattices, which reflects the logical modeling, and the case corresponding to entities described in terms of gradual properties, are especially considered for illustration purposes.
Value Decomposition
, 2009
"... We present CrossBridge, an algorithm for finding analogies in large, sparse semantic networks. We treat analogies as comparisons between domains of knowledge. A domain is a small semantic network, i.e., a set of concepts and binary relations between concepts. We treat our knowledge base (the large s ..."
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We present CrossBridge, an algorithm for finding analogies in large, sparse semantic networks. We treat analogies as comparisons between domains of knowledge. A domain is a small semantic network, i.e., a set of concepts and binary relations between concepts. We treat our knowledge base (the large semantic network) as if it contained many domains of knowledge, then apply dimensionality reduction to find the most salient relation structures among the domains. Relation structures are systems of relations similar to the structures mapped between domains in structure mapping[6]. These structures are effectively nary relations formed by combining multiple pairwise relations. The most salient relation structures form the basis of domain space, a space containing all domains of knowledge from the large semantic network. The construction of domain space places analogous domains near each other in domain space. CrossBridge finds analogies using similarity information from domain space and a heuristic search process. We evaluate our method on ConceptNet[10], a large semantic network of common
Kernel Based Algorithms for Mining Huge
"... Further volumes of this series can be found on our homepage: springer.com Vol. 13. Nadia Nedjah, Ajith Abraham, Luiza de Macedo Mourelle (Eds.) ..."
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Further volumes of this series can be found on our homepage: springer.com Vol. 13. Nadia Nedjah, Ajith Abraham, Luiza de Macedo Mourelle (Eds.)
1st International Workshop on Similarity and Analogybased Methods in AI
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Author manuscript, published in "10th International Conference on Concept Lattices and Their Applications (CLA) (2013)" Analogical proportions and the factorization of
, 2013
"... information in distributive lattices ..."
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