There are at least two kinds of similarity. Relational similarity is correspondence between relations, in contrast with attributional similarity, which is correspondence between attributes. When two words have a high degree of attributional similarity, we call them synonyms. When two pairs of words have a high degree of relational similarity, we say that their relations are analogous. For example, the word pair mason:stone is analogous to the pair carpenter:wood. This paper introduces Latent Relational Analysis (LRA), a method for measuring relational similarity. LRA has potential applications in many areas, including information extraction, word sense disambiguation, and information retrieval. Recently the Vector Space Model (VSM) of information retrieval has been adapted to measuring relational similarity, achieving a score of 47 on a collection of 374 college-level multiple-choice word analogy questions. In the VSM approach, the relation between a pair of words is characterized by a vector of frequencies of predefined patterns in a large corpus. LRA extends the VSM approach in three ways: (1) the patterns are derived automatically from the corpus, (2) the Singular Value Decomposition (SVD) is used to smooth the frequency data, and (3) automatically generated synonyms are used to explore variations of the word pairs. LRA achieves 56 on the 374 analogy questions, statistically equivalent to the average human score of 57 . On the related problem of classifying semantic relations, LRA achieves similar gains over the VSM.
french02 cites Structure Mapping Theory (SMT) @cite_43 and its implementation in the Structure Mapping Engine (SME) @cite_54 as the most influential work on modeling of analogy-making. The goal of computational modeling of analogy-making is to understand how people form complex, structured analogies. SME takes representations of a source domain and a target domain, and produces an analogical mapping between the source and target. The domains are given structured propositional representations, using predicate logic. These descriptions include attributes, relations, and higher-order relations (expressing relations between relations). The analogical mapping connects source domain relations to target domain relations.
@cite_43 @cite_54
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Many AI researchers and cognitive scientists have argued that analogy is the core of cognition. The most influential work on computational modeling of analogy-making is Structure Mapping Theory (SMT) and its implementation in the Structure Mapping Engine (SME). A limitation of SME is the requirement for complex hand-coded representations. We introduce the Latent Relation Mapping Engine (LRME), which combines ideas from SME and Latent Relational Analysis (LRA) in order to remove the requirement for hand-coded representations. LRME builds analogical mappings between lists of words, using a large corpus of raw text to automatically discover the semantic relations among the words. We evaluate LRME on a set of twenty analogical mapping problems, ten based on scientific analogies and ten based on common metaphors. LRME achieves human-level performance on the twenty problems. We compare LRME with a variety of alternative approaches and find that they are not able to reach the same level of performance. Thispaperdescribes thestructure-mapping engine(SME), a program for studying . analogical processing .SME has been built to explore Gentner's structure-mapping theory of analogy, and provides a "tool kit" for constructing matching algorithms consistent with this theory . Its flexibility enhances cognitive simulation studies by simplifying experimentation . Furthermore, SME is very efficient, making it a useful component in machine learning systems as well . We review the structure-mapping theory and describe the design of the engine . We analyze the complexity of the algorithm, and demonstrate that A theory of analogy must describe how the meaning of on analogy is derived from the meonings of its parts. In the structure-mapplng theory, the interpretation rules ore characterized OS implicit rules for mapping knowledge about a base domain into a torget domain. Two important features of the theory are (a) the rules depend only on syntactic properties of the knowledge representation, and not on the specific content of the domoins; ond (b) the theoretical fromework allows analogies to be distinguished o ond (b) The particular relations mapped ore determined by systemaficity. OS defined by the existence of higher-order relations. While classical approaches to unsupervised morphology acquisition often rely on metrics based on information theory for identifying morphemes, we describe a novel approach relying on the notion of formal analogy. A formal analogy is a relation between four forms, such as: reader is to doer as reading is to doing. Our assumption is that formal analogies identify pairs of morphologically related words. We first describe an approach which simply identifies all the formal analogies involving words in a lexicon. Despite its promising results, this approach is computationally too expensive. Therefore, we designed a more practical system which learns morphological structures using only a (small) subset of all formal analogies. We tested those two approaches on the five languages used in Morpho Challenge 2009.