## Toward a unified theory of similarity and recognition (1988)

Venue: | Psychological Review |

Citations: | 83 - 6 self |

### BibTeX

@ARTICLE{Ashby88towarda,

author = {E Gregory Ashby and Nancy A. Perrin},

title = {Toward a unified theory of similarity and recognition},

journal = {Psychological Review},

year = {1988},

volume = {95},

pages = {124--150}

}

### Years of Citing Articles

### OpenURL

### Abstract

A new theory of similarity, rooted in the detection and recognition literatures, is developed. The general recognition theory assumes that the perceptual effect of a stimulus is random but that on any single trial it can be represented as a point in a multidimensional space. Similarity is a function of the overlap of perceptual distributions. It is shown that the general recognition theory contains Euclidean distance models of similarity as a special case but that unlike them, it is not constrained by any distance axioms. Three experiments are reported that test the empirical validity of the theory. In these experiments the general recognition theory accounts for similarity data as well as the cur-rently popular similarity theories do, and it accounts for identification data as well as the long-standing "champion " identification model does. The concept of similarity is of fundamental importance in psychology. Not only is there a vast literature concerned directly with the interpretation of subjective similarity judgments (e.g., as in multidimensional scaling) but the concept also plays a cru-cial but less direct role in the modeling of many psychophysical tasks. This is particularly true in the case of pattern and form recognition. It is frequently assumed that the greater the simi-larity between a pair of stimuli, the more likely one will be con-fused with the other in a recognition task (e.g., Luce, 1963; Shepard, 1964; Tversky & Gati, 1982). Yet despite the poten-tially close relationship between the two, there have been only a few attempts at developing theories that unify the similarity and recognition literatures. Most attempts to link the two have used a distance-based similarity measure to predict the confusions in recognition ex-

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Citation Context ...e of pattern and form recognition. It is frequently assumed that the greater the similarity between a pair of stimuli, the more likely one will be confused with the other in a recognition task (e.g., =-=Luce, 1963-=-; Shepard, 1964; Tversky & Gati, 1982). Yet despite the potentially close relationship between the two, there have been only a few attempts at developing theories that unify the similarity and recogni... |

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Citation Context ...GGR stands for general Gaussian recognition. MDS = multidimensional scaling. Values with a subscript a are significant at a = .05. Values with a subscript b are significant at a = .01. metrics (e.g., =-=Attneave, 1950-=-; Garner, 1974; Shepard, 1964; Torgerson, 1958; Tversky & Gati, 1982; for an exception, see Nosofsky, 1987). Ashby and Townsend (1986) presented independent evidence that the stimulus components used ... |

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Citation Context ...the similarity and recognition literatures. Most attempts to link the two have used a distance-based similarity measure to predict the confusions in recognition experiments (Appelman & Mayzner, 1982; =-=Getty, Swets, & Swets, 1980-=-; Getty, Swets, Swets, & Green, 1979; Nakatani, 1972; Nosofsky, 1984, 1985b, 1986; Shepard, 1957, 1958b). It is now widely suspected, however, that standard distance-based similarity measures do not p... |

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Citation Context ...ing ~ in Equation 11 with exp(-d~), where d~.is the distance between the perceptual representations of stimuli Si and Sj. The resulting model, which has come to be known as the MDSchoice model (e.g., =-=Nosofsky, 1985-=-a, 1985b, 1986) predicts that m ~i exp(-dl) (12) P(RjlSi) = ~ ~m exp(-dim) " m Many different versions of this model can be formulated. Among the simplest and most obvious is one based on simples128 E... |

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Citation Context ...oping theories that unify the similarity and recognition literatures. Most attempts to link the two have used a distance-based similarity measure to predict the confusions in recognition experiments (=-=Appelman & Mayzner, 1982-=-; Getty, Swets, & Swets, 1980; Getty, Swets, Swets, & Green, 1979; Nakatani, 1972; Nosofsky, 1984, 1985b, 1986; Shepard, 1957, 1958b). It is now widely suspected, however, that standard distance-based... |

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2 |
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2 |
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Citation Context ... the two have used a distance-based similarity measure to predict the confusions in recognition experiments (Appelman & Mayzner, 1982; Getty, Swets, & Swets, 1980; Getty, Swets, Swets, & Green, 1979; =-=Nakatani, 1972-=-; Nosofsky, 1984, 1985b, 1986; Shepard, 1957, 1958b). It is now widely suspected, however, that standard distance-based similarity measures do not provide an adequate account of perceived similarity (... |

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1 |
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1 |
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Citation Context ...al space to be metric. An alternative approach, proposed by Micko and yielding similar results, represents stimuli as vectors in a multidimensional space (Micko, 1970; Micko & Fischer, 1970; see also =-=Eisler, 1960-=-; Ekman, 1963; Ekman & Lindman, 1961). Throughout this article, we will carefully distinguish between MDS as a theory of perceived similarity and MDS as a datareduction technique. As a method of analy... |

1 |
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Citation Context ...confusions. The model that has been most successful in predicting a wide variety of confusion matrices over the last 20 years is the biasedchoice model (Luce, 1963; Shepard, 1957; but see also, e.g., =-=Holbrook, 1975-=-; Luce, 1977; Townsend, 1971; Townsend & Ashby, 1982). In the biased-choice model, P(RjlSi) is a function of the similarity of stimulus Si to stimulus Sj, denoted ~, and of the bias toward response Rj... |

1 |
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Citation Context ...tructurally, the general recognition theory closely resembles Nakatani's (1972) confusion-choice model and the probabilistic MDS models described earlier (Ennis & Mullen, 1986; Luce & Galanter, 1963; =-=MacKay & Zinnes, 1981-=-; Mullen & Ennis, 1987; Suppes & Zinnes, 1963; Zinnes & MacKay, 1983). In all cases a multidimensional probabilistic stimulus representation is postulated. However, only the general recognition theory... |

1 |
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Citation Context ...n but do not necessarily require the perceptual space to be metric. An alternative approach, proposed by Micko and yielding similar results, represents stimuli as vectors in a multidimensional space (=-=Micko, 1970-=-; Micko & Fischer, 1970; see also Eisler, 1960; Ekman, 1963; Ekman & Lindman, 1961). Throughout this article, we will carefully distinguish between MDS as a theory of perceived similarity and MDS as a... |

1 |
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(Show Context)
Citation Context ...necessarily require the perceptual space to be metric. An alternative approach, proposed by Micko and yielding similar results, represents stimuli as vectors in a multidimensional space (Micko, 1970; =-=Micko & Fischer, 1970-=-; see also Eisler, 1960; Ekman, 1963; Ekman & Lindman, 1961). Throughout this article, we will carefully distinguish between MDS as a theory of perceived similarity and MDS as a datareduction techniqu... |