creators_name: Vigo, Ronaldo creators_id: vigo@ohio.edu type: journalp datestamp: 2012-11-09 17:47:35 lastmod: 2012-11-09 17:47:35 metadata_visibility: show title: Towards a Law of Invariance in Human Concept Learning ispublished: pub subjects: appl-cog-psy subjects: cog-psy subjects: comp-sci-art-intel subjects: comp-sci-complex-theory subjects: comp-sci-mach-learn subjects: percep-cog-psy subjects: phil-logic subjects: psy-phys full_text_status: public keywords: Concepts; concept learning; categorization; law of invariance; mathematical model; pattern perception; ideotype. abstract: Invariance principles underlie many key theories in modern science. They provide the explanatory and predictive framework necessary for the rigorous study of natural phenomena ranging from the structure of crystals, to magnetism, to relativistic mechanics. Vigo (2008, 2009)introduced a new general notion and principle of invariance from which two parameter-free (ratio and exponential) models were derived to account for human conceptual behavior. Here we introduce a new parameterized exponential “law” based on the same invariance principle. The law accurately predicts the subjective degree of difficulty that humans experience when learning different types of concepts. In addition, it precisely fits the data from a large-scale experiment which examined a total of 84 category structures across 10 category families (R-Squared =.97, p < .0001; r= .98, p < .0001). Moreover, it overcomes seven key challenges that had, hitherto, been grave obstacles for theories of concept learning. date: 2011-07 date_type: published publication: Proceedings of the 33rd Annual Meeting of the Cognitive Science Society publisher: Cognitive Science Society pagerange: 2580-2585 refereed: TRUE referencetext: Bourne, L. E. (1966). Human conceptual behavior. Boston: Allyn and Bacon. Estes, W. K. (1994). Classification and Cognition. Oxford Psychology Series, 22, Oxford University Press, Oxford. Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature, 407, 630-633. Garner, W. R. (1970). Good patterns have few alternatives. American Scientist, 58, 34-42. Garner, W. R. (1974). The processing of information and structure. New York: Wiley. Gibson, J. J. (1966). The senses considered as perceptual systems. Boston: Houghton Mifflin. Haygood, R. C., & Bourne, L. E., Jr. (1965). Attribute-andrule learning aspects of conceptual behavior. Psychological Review, 72, 175-195. Kruschke, J. K. (1992). ALCOVE: An exemplar-based connectionist model of category learning. Psychological Review, 99, 22-44. Love, B. C., and Medin, D. L. (1998). SUSTAIN: A model of human category learning. Proceedings of the Fifteenth National Conference on Artificial Intelligence, 15, 671-676. Murphy, G. L. (2002). The big book of concepts. MIT Press. Nosofsky, R. M. (1984). Choice, similarity, and the context theory of classification. Journal of Experimental Psychology: Learning, Memory, and Cognition, 10(1), 104-114. Nosofsky, R. M. (1991). Typicality in logically defined categories: Exemplar-similarity versus rule instantiation. Memory and Cognition, 19(2), 131-150. Shepard, R. N., Hovland, C. L., & Jenkins, H. M. (1961). Learning and memorization of classifications. Psychological Monographs: General and Applied, 75(13), 1-42. Vigo, R. (2006). A note on the complexity of Boolean concepts. Journal of Mathematical Psychology, 50(5), 1-10. Vigo, R. (2009). Categorical invariance and structural complexity in human concept learning. Journal of Mathematical Psychology, Vol. 53, 203-221. Vigo, R. (2011). Towards a General Law of Human Conceptual Behavior (under review, contact the author for a copy) citation: Vigo, Professor Ronaldo (2011) Towards a Law of Invariance in Human Concept Learning. [Journal (Paginated)] document_url: http://cogprints.org/7960/7/Vigo%20%282011a%29.pdf