Abstract
Vector space based approaches to natural language processing are contrasted with human similarity judgements to show the manner in which human subjects fail to produce data which satisfies all requirements for a metric space. This result would constrains 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 problem, by arguing that pairs of words imply a context which in turn induces a point of view, so 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. We illustrate the proposal on a few triples of words and outline further research.
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References
Aerts, D., Gabora, L.: A theory of concepts and their combinations I: the structure of the sets of contexts and properties. Kybernetes 34, 151–175 (2005)
Aerts, D., Gabora, L.: A theory of concepts and their combinations II: A Hilbert space representation. Kybernetes 34, 192–221 (2005)
Aerts, D.: Quantum structure in cognition. Journal of Mathematical Psychology 53, 314–348 (2009)
Boyd-Graber, J., Fellbaum, C., Osherson, D., Schapire, R.: Adding dense, weighted connections to wordnet. In: Proceedings of the Third International WordNet Conference (2006)
Bruza, P.D., Kitto, K., Ramm, B., Sitbon, L.: The non-decomposability of concept combinations (2011) (under review)
Bruza, P.D., Kitto, K., Ramm, B., Sitbon, L., Blomberg, S., Song, D.: Quantum-like non-separability of concept combinations, emergent associates and abduction. Logic Journal of the IGPL (2010) (in press)
Bruza, P., Kitto, K., Nelson, D., McEvoy, C.: Is there something quantum-like about the human mental lexicon? Journal of Mathematical Psychology 53, 362–377 (2009)
Bullinaria, J.A., Levy, J.P.: Extracting semantic representations from word co-occurrence statistics: a computational study. Behavior Research Methods 39(3), 510–526 (2007)
Deerwester, S., Dumais, S., Furnas, G., Landauer, T., Harshman, R.: Indexing by latent semantic analysis. Journal of the American Society for Information Science 41(16), 391–407 (1990)
Firth, J.R.: Papers in Linguistics, pp. 1934–1951. Oxford University Press, London (1957)
Harris, Z.: Distributional structure. Word 10(23), 146–162 (1954)
Jones, M.N., Mewhort, D.J.K.: Representing word meaning and order information in a composite holographic lexicon. Psychological Review 114(1), 1–37 (2007)
Landauer, T., Dumais, S.T.: A solution to plato’s problem: the latent semantic analysis theory of acquisition, induction and representation of knowledge. Psychological Review 104(2), 211–240 (1997)
Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)
Nosofsky, R.M.: Attention, similarity, and the identification-categorization relationship. Journal of Experimental Psychology: General 115(1), 39–57 (1986)
Rosch, E.: Cognitive Representation of Semantic Categories. Journal of Experimental Psychology 104, 192–233
Rosch, E., Lloyd, B.B. (eds.): Cognition and categorization. Erlbaum, Hillsdale (1978)
Sahlgren, M.: An introduction to random indexing. In: Proceedings of Methods and Applications of Semantic Indexing Workshop at the 7th International Conference on Terminology and Knowledge Engineering, Copenhagen, Denmark (2005)
Sahlgren, M., Holst, A., Kanerva, P.: Permutations as a means to encode order in word space. In: Proceedings of the 30th Annual Meeting of the Cognitive Science Society (CogSci 2008), Washington, D.C., USA, July 23-26 (2008)
Salton, G., Wong, A., Yang, C.S.: A vector space model for automatic indexing. Communications of the ACM 18(11), 613–620 (1975)
Schütze, H.: Automatic word sense discrimination. Computational Linguistics 24(1), 97–123 (1998)
Smith, E.E., Osherson, D.N., Rips, L.J., Keane, M.: Combining prototypes: A selective modification model. Cognitive Science 12(4), 485–527 (1988)
Turney, P.T., Pantel, P.: From frequency to meaning: Vector space models of semantics. Journal of Artificial Intelligence Research 37, 141–188 (2010)
Tversky, A., Gati, I.: Similarity, separability, and the triangle inequality. Psychological Review 89(2), 123–154 (1982)
Tversky, A.: Features of similarity. Psychological Review 84(4), 327–352 (1977)
Veksler, V.D., Govostes, R.Z., Gray, W.D.: Defining the dimensions of the human semantic space. In: Sloutsky, V., Love, B., McRae, K. (eds.) 30th Annual Meeting of the Cognitive Science Society, pp. 1282–1287. Cognitive Science Society (2008)
Wooters, W.K.: The Acquisition of Information from Quantum Measurements. Ph.D. thesis, University of Texas at Austin (1980)
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Aerts, S., Kitto, K., Sitbon, L. (2011). Similarity Metrics within a Point of View. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds) Quantum Interaction. QI 2011. Lecture Notes in Computer Science, vol 7052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24971-6_3
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DOI: https://doi.org/10.1007/978-3-642-24971-6_3
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