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Comparison

  • Robert L. Goldstone
  • Sam Day
  • Ji Y. Son
Chapter
Part of the On Thinking book series (ONTHINKING)

Abstract

The process of comparison plays a critical role in problem solving, ­judgment, decision making, categorization, and cognition, broadly construed. In turn, determination of similarities and differences plays a critical role for comparison. In this chapter, we describe important classes of formal models of similarity and comparison: geometric, featural, alignment-based, and transformational. We also consider the question of whether similarity is too flexible to provide a stable ground for cognition, and conversely, whether it is insufficiently flexible to account for the sophistication of cognition. Both similarity assessments and comparison are argued to provide valuable general-purpose cognitive strategies.

Keywords

Feature Match Kolmogorov Complexity Similarity Judgment Contrast Model Conjunctive Feature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Author Notes

This research was funded by National Science Foundation REESE grant DRL-0910218. Correspondence concerning this chapter should be addressed to rgoldsto@indiana.edu or Robert Goldstone, Psychological and Brain Sciences Department, Indiana University, Bloomington, Indiana 47405. Further information about the laboratory can be found at http://cognitrn.psych.indiana.edu.

References

  1. Allen SW, Brooks LR (1991) Specializing the operation of an explicit rule. J Exp Psychol Gen 120:3-19Google Scholar
  2. Attneave F (1950) Dimensions of similarity. Am J Psychol 63:516-556PubMedGoogle Scholar
  3. Bassok M, Medin DL (1997) Birds of a feather flock together: similarity judgments with semantically rich stimuli. J Mem Lang 36:311-336Google Scholar
  4. Bernstein LE, Demorest ME, Eberhardt SP (1994) A computational approach to analyzing sentential speech perception: Phoneme-to-phoneme stimulus/response alignment. J Acoust Soc Am 95:3617-3622PubMedGoogle Scholar
  5. Bransford JD, Schwartz DL (1999) Rethinking transfer: a simple proposal with multiple implications. Rev Res Educ 24:61-100Google Scholar
  6. Burgess C, Lund K (2000) The dynamics of meaning in memory. In: Diettrich E, Markman AB (eds) Cognitive dynamics: conceptual change in humans and machines. Lawrence Erlbaum, Mahwah, NJ, pp 117-156Google Scholar
  7. Bush RR, Mosteller F (1951) A model for stimulus generalization and discrimination. Psychol Rev 58:413-423PubMedGoogle Scholar
  8. Carroll JD, Wish M (1974) Models and methods for three-way multidimensional scaling. In Krantz DH, Atkinson RC, Luce RD, Suppes P (eds) Contemporary developments in mathematical psychology, vol 2. Freeman, San Francisco, pp 57-105Google Scholar
  9. Collins AM, Quillian MR (1969) Retrieval time from semantic memory. J Verbal Learn Verbal Behav 8:240-247Google Scholar
  10. Doumas LAA, Hummel JE (2005) Approaches to modeling human mental representation: what works, what doesn’t, and why. In Holyoak KJ, Morrison RG (eds) The Cambridge handbook of thinking and reasoning. Cambridge University Press, Cambridge, England, pp 73-91Google Scholar
  11. Eisler H, Ekman G (1959) A mechanism of subjective similarity. Acta Psychol 16:1-10Google Scholar
  12. Falkenhainer B, Forbus KD, Gentner D (1989) The structure-mapping engine: Algorithm and examples. Artif Intell 41:1-63Google Scholar
  13. Frisch SA, Broe MB, Pierrehumbert JB (1995) The role of similarity in phonology: Explaining OCP-Place. In Elenius K, Branderud P (eds) Proceedings of the, 13th International Conference of the Phonetic Sciences, Stockholm, vol 3, pp 544-547Google Scholar
  14. Garner WR (1974) The processing of information and structure. Wiley, New YorkGoogle Scholar
  15. Gati I, Tversky A (1984) Weighting common and distinctive features in perceptual and conceptual judgments. Cogn Psychol 16:341-370PubMedGoogle Scholar
  16. Gentner D (1983) Structure-mapping: a theoretical framework for analogy. Cogn Sci 7:155-170Google Scholar
  17. Gentner D, Namy L (1999) Comparison in the development of categories. Cogn Dev 14:487-513Google Scholar
  18. Gentner D, Rattermann MJ (1991) Language and the career of similarity. In: Gelman SA, Byrnes JP (eds) Perspectives on language and thought interrelations in development. Cambridge University Press, Cambridge, EnglandGoogle Scholar
  19. Gentner D, Toupin C (1986) Systematicity and surface similarity in the development of analogy. Cogn Sci 10(3):277-300Google Scholar
  20. Gentner D, Loewenstein J, Thompson L (2003) Learning and transfer: a general role for analogical encoding. J Educ Psychol 95:393-408Google Scholar
  21. Gick ML, Holyoak KJ (1983) Schema induction and analogical transfer. Cogn Psychol 15:1-38Google Scholar
  22. Gluck MA (1991) Stimulus generalization and representation in adaptive network models of category learning. Psychol Sci 2:50-55Google Scholar
  23. Goldstone RL (1994a) Similarity, interactive activation, and mapping. J Exp Psychol Learn Mem Cogn 20:3-28Google Scholar
  24. Goldstone RL (1994b) The role of similarity in categorization: Providing a groundwork. Cognition 52:125-157PubMedGoogle Scholar
  25. Goldstone RL (1996) Alignment-based nonmonotonicities in similarity. J Exp Psychol Learn Mem Cogn 22:988-1001PubMedGoogle Scholar
  26. Goldstone RL, Medin DL (1994) The time course of comparison. J Exp Psychol Learn Mem Cogn 20:29-50Google Scholar
  27. Goldstone RL, Medin DL, Gentner D (1991) Relations, attributes, and the non-independence of features in similarity judgments. Cogn Psychol 23:222-264PubMedGoogle Scholar
  28. Goldstone RL, Medin DL, Halberstadt J (1997) Similarity in context. Mem Cogn 25:237-255Google Scholar
  29. Griffiths TL, Steyvers M, Tenenbaum JBT (2007) Topics in semantic representation. Psychol Rev 114(2):211-244PubMedGoogle Scholar
  30. Hahn U (2003) Similarity. In: Nadel L (ed) Encyclopedia of cognitive science. Macmillan, LondonGoogle Scholar
  31. Hahn U, Bailey RM (2005) What makes words sound similar? Cognition 97:227-267PubMedGoogle Scholar
  32. Hahn U, Chater N (1998) Understanding similarity: a joint project for psychology, case-based reasoning and law. Artif Intell Rev 12:393-427Google Scholar
  33. Hahn U, Chater N, Richardson LB (2003) Similarity as transformation. Cognition 87:1-32PubMedGoogle Scholar
  34. Hayes-Roth B, Hayes-Roth F (1977) Concept learning and the recognition and classification of exemplars. J Verbal Learn Verbal Behav 16:321-338Google Scholar
  35. Hintzman DL (1986) Schema abstraction in a multiple-trace memory model. Psychol Rev 93:411-428Google Scholar
  36. Hofstadter D (1997) Fluid concepts and creative analogies: computer models of the fundamental mechanisms of thought. Basic Books, New YorkGoogle Scholar
  37. Holyoak KJ (2005) Analogy. In: Holyoak KJ, Morrison RG (eds) The Cambridge Handbook of Thinking and Reasoning. Cambridge University Press, Cambridge, UKGoogle Scholar
  38. Holyoak KJ, Hummel JE (2000) The proper treatment of symbols in a connectionist architecture. In: Dietrich E, Markman A (eds) Cognitive dynamics: conceptual change in humans and machines. Erlbaum, Hillsdale, NJGoogle Scholar
  39. Holyoak KJ, Koh K (1987) Surface and structural similarity in analogical transfer. Mem Cogn 15:332-340Google Scholar
  40. Holyoak KJ, Thagard P (1989) Analogical mapping by constraint satisfaction. Cogn Sci 13:295-355Google Scholar
  41. Holyoak KJ, Thagard P (1995) Mental leaps: analogy in creative thought. MIT, Cambridge, MAGoogle Scholar
  42. Horgan DD, Millis K, Neimeyer RA (1989) Cognitive reorganization and the development of chesss expertise. Int J Pers Construct Psychol 2:15-36Google Scholar
  43. Hubel DH, Wiesel TN (1968). Receptive fields and functional architecture of monkey striate cortex. J Physiol 195:215-243PubMedGoogle Scholar
  44. Huber J, Payne JW, Puto C (1982) Adding asymmetrically dominated alternatives: violations of regularity and the similarity hypothesis. J Consum Res 9:90-98Google Scholar
  45. Hummel JE (2000) Where view-based theories break down: the role of structure in shape perception and object recognition. In: Dietrich E, Markman A (eds) Cognitive dynamics: conceptual change in humans and machines. Erlbaum, Hillsdale, NJGoogle Scholar
  46. Hummel JE (2001) Complementary solutions to the binding problem in vision: implications for shape perception and object recognition. Vis Cogn 8:489-517Google Scholar
  47. Hummel JE, Biederman I (1992) Dynamic binding in a neural network for shape recognition. Psychol Rev 99:480-517PubMedGoogle Scholar
  48. Hummel JE, Holyoak KJ (1997) Distributed representations of structure: a theory of analogical access and mapping. Psychol Rev 104:427-466Google Scholar
  49. Hummel JE, Holyoak KJ (2003) A symbolic-connectionist theory of relational inference and generalization. Psychol Rev 110:220-263PubMedGoogle Scholar
  50. Imai S (1977) Pattern similarity and cognitive transformations. Acta Psychol 41:433-447Google Scholar
  51. Jakobson R, Fant G, Halle M (1963) Preliminaries to speech analysis : the distinctive features and their correlates. MIT, Cambridge, MAGoogle Scholar
  52. James W (1890/1950) The principles of psychology. Dover, New York (Original work published 1890)Google Scholar
  53. Katz JJ, Fodor J (1963) The structure of semantic theory. Language 39:170-210Google Scholar
  54. Kotovsky L, Gentner D (1996) Comparison and categorization in the development of relational similarity. Child Dev 67:2797-2822Google Scholar
  55. Landauer TK, Dumais ST (1997) A solution to Plato’s problem: the latent semantic analysis theory of the acquisition, induction, and representation of knowledge. Psychol Rev 104:211-240Google Scholar
  56. Larkey LB, Love BC (2003) CAB: connectionist analogy builder. Cogn Sci 27:781-794Google Scholar
  57. Lee MD (2002) A simple method for generating additive clustering models with limited complexity. Mach Learn 49:39-58Google Scholar
  58. Li M, Vitanyi P (1997) An introduction to Kolmogorov complexity and its applications, 2nd edn. Springer, New YorkGoogle Scholar
  59. Markman AB, Gentner D (1993a) Structural alignment during similarity comparisons. Cogn Psychol 25:431-467Google Scholar
  60. Markman AB, Gentner D (1993b) Splitting the differences: a structural alignment view of similarity. J Mem Lang 32:517-535Google Scholar
  61. Markman AB, Gentner D (1996) Commonalities and differences in similarity comparisons. Mem Cogn 24:235-249Google Scholar
  62. Markman AB, Gentner D (1997) The effects of alignability on memory. Psychol Sci 8:363-367Google Scholar
  63. Markman AB, Wisniewski EJ (1997) Similar and different: the differentiation of basic-level categories. J Exp Psychol Learn Mem Cogn 23:54-70Google Scholar
  64. Medin DL, Shaffer MM (1978) A context theory of classification learning. Psychol Rev 85:207-238Google Scholar
  65. Medin DL, Goldstone RL, Gentner D (1993) Respects for similarity. Psychol Rev 100:254-278Google Scholar
  66. Mitchell M (1993) Analogy-making as perception: a computer model. MIT, Cambridge, MAGoogle Scholar
  67. Murphy GL, Medin DL (1985) The role of theories in conceptual coherence. Psychol Rev 92:289-316PubMedGoogle Scholar
  68. Namy LL, Gentner D (2002) Making a silk purse out of two sow’s ears: Young children’s use of comparison in category learning. J Exp Psychol Gen 131:5-15PubMedGoogle Scholar
  69. Navarro DJ, Griffiths TL (2007) A nonparametric Bayesian method for inferring features from similarity judgments. Adv Neural Inform Process Syst 19:1033-1040Google Scholar
  70. Navarro DJ, Lee MD (2004) Common and distinctive features in stimulus representation: A modified version of the contrast model. Psychon Bull Rev 11(6):961-974PubMedGoogle Scholar
  71. Neisser U (1967) Cognitive psychology. Appleton-Century-Crofts, New YorkGoogle Scholar
  72. Nosofsky RM (1984) Choice, similarity, and the context theory of classification. J Exp Psychol Learn Mem Cogn 10:104-114PubMedGoogle Scholar
  73. Osherson D, Smith EE, Wilkie O, Lopez A, Shafir E (1990) Category-based induction. Psychol Rev 97:185-200Google Scholar
  74. Osterholm K, Woods DJ, Le Unes A (1985) Multidimensional scaling of Rorschach inkblots: Relationships with structured self-report. Pers Individ Dif 6:77-82Google Scholar
  75. Palmer SE (1975) Visual perception and world knowledge. In: Norman DA, Rumelhart DE (eds) Explorations in cognition. Freeman, San FranciscoGoogle Scholar
  76. Palmeri TJ (1997) Exemplar similarity and the development of automaticity. J Exp Psychol Learn Mem Cogn 23:324-354PubMedGoogle Scholar
  77. Polk TA, Behensky C, Gonzalez R, Smith EE (2002) Rating the similarity of simple perceptual stimuli: asymmetries induced by manipulating exposure frequency. Cognition 82:B75-B88PubMedGoogle Scholar
  78. Reed SK (1972) Pattern recognition and categorization. Cogn Psychol 3:382-407Google Scholar
  79. Rips LJ (1989) Similarity, typicality, and categorization. In: Vosniadu S, Ortony A (eds) Similarity, analogy, and thought. Cambridge University Press, Cambridge, pp 21-59Google Scholar
  80. Rips LJ, Shoben EJ, Smith EE (1973) Semantic distance and the verification of semantic relationships. Journal of Verbal Learning and Verbal Behavior, 12:1-20Google Scholar
  81. Ritov I, Gati I, Tversky A (1990) Differential weighting of common and distinctive components. J Exp Psychol Gen 119:30PubMedGoogle Scholar
  82. Ross BH (1989) Distinguishing types of superficial similarities: Different effects on the access and use of earlier problems. J Exp Psychol Learn Mem Cogn 15:456-468Google Scholar
  83. Schvaneveldt RW, Durso FT, Goldsmith TE, Breen TJ, Cooke NM, Tucker RG, DeMaio JC (1985) Measuring the structure of expertise. Int J Man-Mach Stud 23:699-728Google Scholar
  84. Shanon B (1988) On similarity of features. New Ideas Psychol 6:307-321Google Scholar
  85. Shepard RN (1962a) The analysis of proximities: multidimensional scaling with an unknown distance function. Part I. Psychometrika 27:125-140Google Scholar
  86. Shepard RN (1962b) The analysis of proximities: multidimensional scaling with an unknown distance function. Part II. Psychometrika 27:219-246Google Scholar
  87. Shepard RN (1972) Psychological representation of speech sounds. In: David EE Jr, Denes PB (eds) Human communication: a unified view. McGraw-Hill, New YorkGoogle Scholar
  88. Shepard RN (1982) Geometrical approximations to the structure of musical pitch. Psychol Rev 89:305-333PubMedGoogle Scholar
  89. Shepard RN (1987) Toward a universal law of generalization for psychological science. Science 237:1317-1323PubMedGoogle Scholar
  90. Shepard RN, Arabie P (1979) Additive clustering: representation of similarities as combinations of discrete overlapping properties. Psychol Rev 86:87-123Google Scholar
  91. Shiffrin RM, Steyvers M (1997) A model for recognition memory: REM: retrieving effectively from memory. Psychon Bull Rev 4(2):145-166Google Scholar
  92. Simon D, Holyoak KJ (2002) Structural dynamics of cognition: From consistency theories to constraint satisfaction. Pers Soc Psychol Rev 6:283-294Google Scholar
  93. Simonson I (1989) Choice based on reasons: the case of attraction and compromise effects. J Consum Res 16:158-174Google Scholar
  94. Sjoberg L (1972) A cognitive theory of similarity. Goteborg Psychol Rep 2(10)Google Scholar
  95. Sloman SA (1996) The empirical case for two systems of reasoning. Psychol Bull 119:3-22Google Scholar
  96. Smith EE, Sloman SA (1994) Similarity-versus rule-based categorization. Mem Cogn 22:377-386Google Scholar
  97. Smith EE, Shoben EJ, Rips LJ (1974) Structure and process in semantic memory: a featural model for semantic decisions. Psychol Rev 81:214-241Google Scholar
  98. Tenenbaum JB (1996) Learning the structure of similarity. In: Tesauro G, Touretzky DS, Leen TK (eds) Advances in neural information processing systems, 8. MIT, Cambridge, MA, pp 4-9Google Scholar
  99. Tenenbaum JB, De Silva V, Lanford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290:22-23Google Scholar
  100. Torgerson WS (1965) Multidimensionsal scaling of similarity. Psychometrika 30:379-393PubMedGoogle Scholar
  101. Treisman AM (1986) Features and objects in visual processing. Sci Am 255:106-115Google Scholar
  102. Tversky A (1977) Features of similarity. Psychol Rev 84:327-352Google Scholar
  103. Tversky A, Gati I (1982) Similarity, separability, and the triangle inequality. Psychol Rev 89:123-154PubMedGoogle Scholar
  104. Tversky A, Hutchinson JW (1986) Nearest neighbor analysis of psychological spaces. Psychol Rev 93:3-22Google Scholar
  105. Ullman S (1996) High-level vision: object recognition and visual cognition. MIT, LondonGoogle Scholar
  106. Wiener-Ehrlich WK, Bart WM, Millward R (1980) An analysis of generative representation systems. J Math Psychol 21(3):219-246Google Scholar
  107. Winston PH (1975) Learning structural descriptions from examples. In: Winston PH (ed) The psychology of computer vision. McGraw-Hill, New YorkGoogle Scholar
  108. Zhang S, Markman AB (1998) Overcoming the early entrant advantage: the role of alignable and nonalignable differences. J Market Res 35:413-426Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Psychological and Brain SciencesIndiana UniversityBloomingtonUSA

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