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Similarity metrics within a point of view

Aerts, Sven, Kitto, Kirsty, & Sitbon, Laurianne (2011) Similarity metrics within a point of view. In Quantum Interaction 2011, 26-29 June 2011, Robert Gordon University, Aberdeen.

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Abstract

In vector space based approaches to natural language processing, similarity is commonly measured by taking the angle between two vectors representing words or documents in a semantic space. This is natural from a mathematical point of view, as the angle between unit vectors is, up to constant scaling, the only unitarily invariant metric on the unit sphere. However, similarity judgement tasks reveal that human subjects fail to produce data which satisfies the symmetry and triangle inequality requirements for a metric space. A possible conclusion, reached in particular by Tversky et al., is that some of the most basic assumptions of geometric models are unwarranted in the case of psychological similarity, a result which would impose strong limits on the validity and applicability vector space based (and hence also quantum inspired) approaches to the modelling of cognitive processes. This paper proposes a resolution to this fundamental criticism of of the applicability of vector space models of cognition. We argue that pairs of words imply a context which in turn induces a point of view, allowing a subject to estimate semantic similarity. Context is here introduced as a point of view vector (POVV) and the expected similarity is derived as a measure over the POVV's. Different pairs of words will invoke different contexts and different POVV's. Hence the triangle inequality ceases to be a valid constraint on the angles. We test the proposal on a few triples of words and outline further research.

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ID Code: 41864
Item Type: Conference Paper
Keywords: Similarity, Semantic Space, Triangle Inequality, Metric, Context
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Natural Language Processing (080107)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Simulation and Modelling (080110)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > LIBRARY AND INFORMATION STUDIES (080700) > Information Retrieval and Web Search (080704)
Australian and New Zealand Standard Research Classification > PSYCHOLOGY AND COGNITIVE SCIENCES (170000) > COGNITIVE SCIENCE (170200) > Linguistic Processes (incl. Speech Production and Comprehension) (170204)
Divisions: Past > Schools > Computer Science
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Information Systems
Copyright Owner: Copyright 2011 Please consult the authors.
Deposited On: 03 Jun 2011 16:21
Last Modified: 15 Jun 2012 19:59

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