Making Comparisons: Similarity, Analogy, and Translating Between Conceptual Systems

Making Comparisons


In exploring links between ‚Äúhigh-level‚ÄĚ cognition (such as categorization, decision making, problem solving) and perception, we have become interested in the nature of perceptual similarity.¬†¬†The question of ‚Äúwhat makes two things similar‚ÄĚ is of fundamental importance to cognitive psychology.¬†¬†William James calls similarity ‚Äúthe very keel and backbone of our cognition.‚Ä̬†¬†On the other hand, many researchers (Murphy, Rips, Keil, Carey, Gelman, Markman, and Atrans among others) have argued that high-level cognition is often not related to simple perceptual similarity.¬†¬†Our research suggests that perceptual similarity is highly related to general cognition.¬†¬†Perceptual similarity is quite sophisticated, and vestiges of perceptual similarity can be found in higher-level cognition.

One of the reasons why similarity is able to provide the underpinnings for many cognitive processes is that perception itself is sophisticated and flexible.  Our empirical research and computational modeling efforts have indicated that when people evaluate similarity they carry out a process not unlike analogical reasoning (e.g., in research by Gentner, Hofstadter, Hummel, and Holyoak).  Namely, the parts from one compared object are placed in alignment or correspondence with the parts from the other object, and these correspondences mutually affect each other.  The discovery that alignment, rather than sheer overlap between properties, determines similarity is important because virtually all traditional models of similarity have no way to account for this influence, and because it allies perceptual similarity judgments with conceptual comparisons such as metaphors, similes, and analogies.  We have developed a neural network model (SIAM) of similarity judgments that shows how large-scale, well-structured visual interpretations can emerge even though very simple processing units only communicate with each other locally and without supervision (Goldstone, 1994-b, 1994-d, 1996. 1998; Goldstone & Medin, 1994-a, 1994-b). The model is unique in predicting that assessments of similarity should dynamically vary across time (Goldstone & Medin, 1994-a, 1994-b; Spencer-Smith & Goldstone, 1997).

A second reason why similarity is smart enough to be useful in explaining cognition is that it is adaptive and context-sensitive (Goldstone, 1995-b, Goldstone, Medin, & Halberstadt, 1997; Medin & Goldstone, 1995; Medin, Goldstone, & Gentner, 1991, 1993; Medin, Goldstone, & Markman, 1995).¬†This context sensitivity leads to violations of the assumptions of many traditional models of similarity. The context effects in similarity are important because they provide persuasive evidence that similarity is¬†constructed¬†for particular purposes and circumstances rather than memorized.¬†¬†Objects do not have fixed similarities that people simply uncover; it would be more accurate (though less grammatical) to say that ‚Äúpeople similaritize objects.‚ÄĚ

Perceptual similarity may be a useful notion in understanding high-level cognition because it is sophisticated, but the converse also appears to be true.¬†Similarity is useful because ‚Äúhigh-level‚ÄĚ cognition is not always very high-level.¬†¬†In many cases, perceptual similarity intrudes on categorization and decision making even when it is inappropriate or irrelevant (Goldstone, 1994; Goldstone & Barsalou, 1998).¬†¬†Other work in our laboratory has explored links between similarity and categorization (Kroska & Goldstone, 1996),¬†¬†decision making (Medin, Goldstone, & Markman, 1995), and judgment (Levin, Halberstadt, & Goldstone, 1996).¬†¬†Taken in total, this research argues that similarity plays a role even in highly symbolic processes because it is flexible enough to provide the groundwork for many cognitive processes, yet constrained enough to provide non-circular explanations for these cognitive processes.

Translating Between Conceptual Systems

As an outgrowth of our work on comparing structured representations, we have become interested in translating between conceptual systems.¬†¬†For example, how can we determine that John and Mary both have a concept of, say,¬†Horse? John and Mary may not have exactly the same knowledge of horses, but it is important to be able to place their horse concepts into correspondence with one another, if only so that we can say things like, ‚ÄúMary‚Äôs concept of horse is much more sophisticated than John‚Äôs.‚ÄĚ

There have been two major approaches in cognitive science to conceptual meaning that could potentially provide a solution to finding translations between conceptual systems. According to an ‚Äúexternal grounding‚ÄĚ account, concepts‚Äô meanings depend on their connection to the external world (this account is more thoroughly defined in the next section) .¬†¬†By this account, the concept Horse means what it does because our perceptual apparatus can identify features that characterize horses.¬†¬†According to what we call a ‚ÄúConceptual web‚ÄĚ account, concepts‚Äô meanings depend on their connections to each other.¬†¬†By this account, Horse‚Äôs meaning depends on Gallop, Domesticated, and Quadruped, and in turn, these concepts depend on other concepts, including Horse.

We have developed a computer algorithm that translates between conceptual systems (Feng, Goldstone, & Menkov, in press; Goldstone & Rogosky, 2002; Goldstone, Feng, & Rogosky, in press).  The initial goal of this computational work is to show how translating across systems is possible using only within-system relations, as is predicted by a conceptual web account.  However, the additional goal is to show how the synthesis of external and internal information can dramatically improve translation.  This work suggests that the external grounding and conceptual web accounts should not be viewed as competitors, but rather, that these two sources of information strengthen one another. We have recently been developing applications of the ABSURDIST algorithm to object recognition, large corpora translation, analogical reasoning, and statistical scaling.

Our Software for Making Comparisons

  • Ancient Macintosh software¬†by Rob Goldstone for collecting similarity judgment data by having subjects move visual stimuli on the screen so that their spatial proximity reflects their subjective similarity.
  • Rob Goldstone‚Äôs truly ancient Macintosh software for¬†SIAM¬†simulations.¬†¬†There is no help functionality at all.¬†¬†It is also hard-wired to compare two two-object scenes with four features per objects.¬†¬†So, to run a comparison with 3 matches-in-place and 2 matches-out-of-place (read¬†this¬†for an explanation of these terms), you might specify Object 1 of Scene 1 to be: 1 1 1 1, Object 2 of Scene 1 to be: 2 2 2 2, Object 1 of Scene 2 to be: 1 1 1 2, and Object 2 of Scene 2 to be: 2 2 2 1.¬†¬†Here is thesource code¬†for SIAM, but it is written for Macintosh Pascal so its usefulness is highly questionable. The best way to see SIAM in action comes to us from¬†¬†Peter Wiemer-Hastings¬†who has¬†updated SIAM and put it on-line

Our Selected Papers Relevant to Making Comparisons

Visit our paper repository for abstracts.  Clicking on the paper below will download a PDF version of the paper, but the repository has additional formats.

Goldstone, R. L., Feng, Y., & Rogosky, B. (in press).  In D. Pecher & R. Zwaan (Eds.)  Grounding cognition: The role of perception and action in memory, language, and thinking.  Cambridge: Cambridge University Press.

Feng, Y., Goldstone, R. L., & Menkov, V (in press).  ABSURDIST II: A Graph Matching Algorithm and its Application to Conceptual System Translation.  FLAIRS 2004.

Goldstone, R. L, & Son, J. (in press).  Similarity.  In K. Holyoak & R. Morrison (Eds.).  Cambridge Handbook of Thinking and Reasoning. Cambridge: Cambridge University Press.

Goldstone, R. L., & Rogosky, B. J. (2002). Using relations within conceptual systems to translate across conceptual systems, Cognition, 84, 295-320.

Here is a brief description and commentary on ABSURDIST:
Dietrich, E. (2003).  An ABSURDIST model vindicates a venerable theory.  Trends in Cognitive Science, 7, 57-59.

Goldstone, R. L., & Rogosky, B. J. (2002). The role of roles in translating across conceptual systems, Proceedings of the Twenty-fourth Annual Conference of the Cognitive Science Society.  Hillsdale, New Jersey: Lawrence Erlbaum Associates.  (pp. 369-374).

Goldstone, R. L. (1999). Similarity. in R.A. Wilson & F. C. Keil (eds.) MIT encylopedia of the cognitive sciences.(pp. 763-765).Cambridge, MA: MIT Press.
View This Paper (HTML)

Goldstone, R. L. (1998). Hanging Together: A connectionist model of similarity. In J. Grainger & A. M. Jacobs (Eds.)  Localist Connectionist Approaches to Human Cognition.  (pp. 283 Р325).  Mahwah, NJ: Lawrence Erlbaum Associates.

Goldstone, R. L., Medin, D. L., & Halberstadt, J. (1997) Similarity in Context.. Memory & Cognition, 25, 237-255

Spencer-Smith, J., & Goldstone, R. L. (1997).  The dynamics of similarity.  Bulletin of the Japanese Cognitive Science Society, 4, 38-56.

(Translated into Japanese as: Spencer-Smith, J., & Goldstone, R. L. (2001).  The dynamics of similarity.  in A. Ohnishi and H. Suzuki (Eds.) Ruii kara mita kokoro (Similarity-based approach to mind).  Tokyo, Japan: Kyoritsu Shuppan.)

Goldstone, R. L. (1996). Isolated and Interrelated Concepts. Memory & Cognition, 24, 608-628

Goldstone, R. L. (1996). Alignment-based nonmonotonicities in similarity. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 988-1001.
View This Paper (HTML) [without figures]

Kroska, A., & Goldstone, R. L. (1996). Dissociations in the similarity and categorisation of emotions. Cognition and Emotion,10, 27-45.

Goldstone, R. L. (1995). Mainstream and avant-garde similarity. Psychologica Belgica, 35, 145-165.

Medin, D. L., & Goldstone, R. L. (1995). The predicates of similarity. In C. Cacciari (Ed.), Similarity in Language, Thought, and Perception. (pp. 83-110). Brussels: BREPOL.

Medin, D. L., Goldstone, R. L., & Markman, A. (1995). Comparison and choice: Relations between similarity processes and decision processes. Psychonomics Bulletin and Review, 2, 1-19.

Goldstone, R. L. (1994). The role of similarity in categorization: Providing a groundwork. Cognition, 52, 125-157.

Goldstone, R. L. (1994). Similarity, Interactive Activation, and Mapping. Journal of Experimental Psychology: Learning, Memory, and Cognition,20, 3- 28.

Goldstone, R. L. (1994). An efficient method for obtaining similarity data. Behavior Research Methods, Instruments, & Computers, 26, 381-386.

Download Macintosh application described in this paper

Goldstone, R. L., & Medin, D. L. (1994). The time course of comparison. Journal of Experimental Psychology: Learning, Memory, and Cognition,20, 29-50.

Goldstone, R.L., & Medin, D.L. (1994). Interactive activation, similarity, and mapping: An overview. in K. Holyoak and J. Barnden (Eds.) Advances in Connectionist and Neural Computation Theory, Vol. 2: Analogical Connections. (pp. 321-362). Ablex : New Jersey.

Medin, D.L., Goldstone, R.L., & Gentner, D. (1993). Respects for similarity. Psychological Review, 100, 254-278.

Goldstone, R. L. (1992). Locally-to-globally consistent processing in similarity. Proceedings of the Fourteenth Annual Conference of the Cognitive Science Society. (pp. 337-342). Hillsdale, New Jersey: Lawrence Erlbaum Associates.

Goldstone, R. L., Medin, D. L., & Gentner, D. (1991). Relational similarity and the nonindependence of features in similarity judgments. Cognitive Psychology, 23, 222-264.

Medin, D. L., Goldstone, R. L., & Gentner, D. (1990). Similarity involving attributes and relations: Judgments of similarity and difference are not inverses. Psychological Science, 1, 64-69.

Goldstone, R. L., Gentner, D., & Medin, D. L. (1989). Relations Relating Relations. Proceedings of the Eleventh Annual Conference of the Cognitive Science Society. (pp. 131-138). Hillsdale, New Jersey: Lawrence Erlbaum Associates.

Other Related Research on Making Comparisons

Brad Love has related work on similarity, comparison, and analogical reasoning.  See, in particular, his work with Levi Larkey on a Connectionist Analogy Builder, which has a somewhat similar aim as ABSURDIST

Dedre Gentner has developed computational models of analogical reasoning, together with Ken Forbus.

Ulrike Hahn has developed a transformational account of similarity along with Nick Chater.

Douglas Hofstadter has developed computational models of analogy, creativity, and representation building

Keith Holyoak has developed a connectionist model of analogical reasoning with Paul Thagard.

John Hummel has teamed up with Keith Holyoak to create the LISA model of analogical reasoning.

Michael Lee has many web resources for quantitative modeling of similarity data.

Boicho Kokinov has a model of analogical reasoning that strives to account for the context-sensitive nature of comparison

Art Markman is interested in the similarity, alignment, decision making, and all permutations of interactions among these.

Douglas Medin studies similarity in a cross-cultural context.


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