Features of Similarity
TL;DR: The metric and dimensional assumptions that underlie the geometric representation of similarity are questioned on both theoretical and empirical grounds and a set of qualitative assumptions are shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features.
Abstract: The metric and dimensional assumptions that underlie the geometric representation of similarity are questioned on both theoretical and empirical grounds. A new set-theoretical approach to similarity is developed in which objects are represented as collections of features, and similarity is described as a feature-matching process. Specifically, a set of qualitative assumptions is shown to imply the contrast model, which expresses the similarity between objects as a linear combination of the measures of their common and distinctive features. Several predictions of the contrast model are tested in studies of similarity with both semantic and perceptual stimuli. The model is used to uncover, analyze, and explain a variety of empirical phenomena such as the role of common and distinctive features, the relations between judgments of similarity and difference, the presence of asymmetric similarities, and the effects of context on judgments of similarity. The contrast model generalizes standard representations of similarity data in terms of clusters and trees. It is also used to analyze the relations of prototypicality and family resemblance
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TL;DR: A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LSA), is presented and used to successfully simulate such learning and several other psycholinguistic phenomena.
Abstract: How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LSA), is presented and used to successfully simulate such learning and several other psycholinguistic phenomena. By inducing global knowledge indirectly from local co-occurrence data in a large body of representative text, LSA acquired knowledge about the full vocabulary of English at a comparable rate to schoolchildren. LSA uses no prior linguistic or perceptual similarity knowledge; it is based solely on a general mathematical learning method that achieves powerful inductive effects by extracting the right number of dimensions (e.g., 300) to represent objects and contexts. Relations to other theories, phenomena, and problems are sketched.
6,014 citations
Cites background or methods from "Features of Similarity"
...This would bring LSA's similarity computations close to those proposed by Tversky (1977), allowing asymmetric judgments, for example, while preserving its dimension-matching inductive properties....
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...Similarity is either taken as primitive (e.g. Posner & Keele, 1968; Rosch, 1978 ) or as dependent on shared component features (e.g. Smith & Medin, 1981; Tversky, 1977; Tversky & Gati, 1978)....
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..., Posner & Keele, 1968; Rosch, 1978) or as dependent on shared component features (e.g.. Smith & Medin, 1981; Tversky, 1977; Tversky & Gati, 1978)....
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TL;DR: Recognition-by-components (RBC) provides a principled account of the heretofore undecided relation between the classic principles of perceptual organization and pattern recognition.
Abstract: The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory, recognition-by-components (RBC), is that a modest set of generalized-cone components, called geons (N £ 36), can be derived from contrasts of five readily detectable properties of edges in a two-dimensiona l image: curvature, collinearity, symmetry, parallelism, and cotermination. The detection of these properties is generally invariant over viewing position an$ image quality and consequently allows robust object perception when the image is projected from a novel viewpoint or is degraded. RBC thus provides a principled account of the heretofore undecided relation between the classic principles of perceptual organization and pattern recognition: The constraints toward regularization (Pragnanz) characterize not the complete object but the object's components. Representational power derives from an allowance of free combinations of the geons. A Principle of Componential Recovery can account for the major phenomena of object recognition: If an arrangement of two or three geons can be recovered from the input, objects can be quickly recognized even when they are occluded, novel, rotated in depth, or extensively degraded. The results from experiments on the perception of briefly presented pictures by human observers provide empirical support for the theory. Any single object can project an infinity of image configurations to the retina. The orientation of the object to the viewer can vary continuously, each giving rise to a different two-dimensional projection. The object can be occluded by other objects or texture fields, as when viewed behind foliage. The object need not be presented as a full-colored textured image but instead can be a simplified line drawing. Moreover, the object can even be missing some of its parts or be a novel exemplar of its particular category. But it is only with rare exceptions that an image fails to be rapidly and readily classified, either as an instance of a familiar object category or as an instance that cannot be so classified (itself a form of classification).
5,464 citations
Cites background from "Features of Similarity"
...A similarity measure reflecting common and distinctive components (Tversky, 1977) may be adequate for describing the similarity among a pair of objects or between a given instance and its stored or expected representation, whatever their basicor subordinate-level designation....
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TL;DR: In this paper, the interpretation rules of OS implicit rules for mapping knowledge about a base domain into a torget domain are defined by the existence of higher-order relations, which depend only on syntactic properties of the knowledge representation, and not on specific content of the domoins.
4,667 citations
Cites background from "Features of Similarity"
...In Tversky's (1977) contrast model, the similarity between A and В is greater the greater size of the intersection (А П В) of their feature sets and the less the size of the two...
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...'According to Tversky (1977), the negative effects of the two complement sets are not equal: for example, if we are asked "How similar is A to B", the set (B - A)—features of B not shared by A—counts much more than the set (A - B)....
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TL;DR: This paper investigates the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval, and compares the retrieval performance of the EMD with that of other distances.
Abstract: We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval, we combine this idea with a representation scheme for distributions that is based on vector quantization. This combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.
4,593 citations
Proceedings Article•
24 Jul 1998
TL;DR: This work presents an informationtheoretic definition of similarity that is applicable as long as there is a probabilistic model and demonstrates how this definition can be used to measure the similarity in a number of different domains.
Abstract: Similarity is an important and widely used concept Previous definitions of similarity are tied to a particular application or a form of knowledge representation We present an informationtheoretic definition of similarity that is applicable as long as there is a probabilistic model We demonstrate how our definition can be used to measure the similarity in a number of different domains
4,336 citations
Cites methods from "Features of Similarity"
...We demonstrate how our definition can be used to measure the similarity in a number of different domains....
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References
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TL;DR: In this article, the authors show that the maximization of individual wealth is not an ordinary problem in variational calculus, because the individual does not control, and may even be ignorant of, some of the variables.
Abstract: THIS book is based on the theory that the economic man attempts to maximize his share of the world's goods and services in the same way that a participant in a game involving many players attempts to maximize his winnings. The authors point out that the maximization of individual wealth is not an ordinary problem in variational calculus, because the individual does not control, and may even be ignorant of, some of the variables. The general theory of social games, in their view, offers a simplified conceptual model of economic behaviour, and a study of that theory can do much to throw light on certain basic concepts of economics, for example, that of utility. Theory of Games and Economic Behavior By John Von Neumann Oskar Morgenstern. Pp. xviii + 625. (Princetown, N.J.: Princetown University Press; London: Sir Humphrey Milford, Oxford University Press, 1944.) 66s. 6d.
5,824 citations
"Features of Similarity" refers methods in this paper
...The nature of this result may be illuminated by an analogy to the classical theory of decision under risk (von Neumann & Morgenstern, 1947)....
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TL;DR: In this article, the authors explore the rules that determine intuitive predictions and judgments of confidence and contrast these rules to the normative principles of statistical prediction and show that people do not appear to follow the calculus of chance or the statistical theory of prediction.
Abstract: In this paper, we explore the rules that determine intuitive predictions and judgments of confidence and contrast these rules to the normative principles of statistical prediction. Two classes of prediction are discussed: category prediction and numerical prediction. In a categorical case, the prediction is given in nominal form, for example, the winner in an election, the diagnosis of a patient, or a person's future occupation. In a numerical case, the prediction is given in numerical form, for example, the future value of a particular stock or of a student's grade point average. In making predictions and judgments under uncertainty, people do not appear to follow the calculus of chance or the statistical theory of prediction. Instead, they rely on a limited number of heuristics which sometimes yield reasonable judgments and sometimes lead to severe and systematic errors (Kahneman & Tversky, 1972b, 3; Tversky & Kahneman, 1971, 2; 1973, 11). The present paper is concerned with the role of one of these heuristics – representativeness – in intuitive predictions. Given specific evidence (e.g., a personality sketch), the outcomes under consideration (e.g., occupations or levels of achievement) can be ordered by the degree to which they are representative of that evidence. The thesis of this paper is that people predict by representativeness, that is, they select or order outcomes by the degree to which the outcomes represent the essential features of the evidence.
5,484 citations
TL;DR: In this paper, the authors define basic objects as those categories which carry the most information, possess the highest category cue validity, and are the most differentiated from one another, and thus the most distinctive from each other.
5,074 citations
TL;DR: In this paper, the authors explored the hypothesis that the members of categories which are considered most prototypical are those with most attributes in common with other members of the category and least attributes with other categories and found that family resemblance offers an alternative to criterial features in defining categories.
5,002 citations
"Features of Similarity" refers methods or result in this paper
...Following Rosch and Mervis (1975), we instructed a second group of 40 subjects to list the characteristic features of each one of the vehicles....
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...The results of this study indicate that (i) it is possible to elicit from subjects detailed features of semantic stimuli such as vehicles (see Rosch & Mervis, 1975); (ii) the listed features can be used to predict similarity according to the contrast model with a reasonable degree of success; and…...
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TL;DR: A useful correspondence is developed between any hierarchical system of such clusters, and a particular type of distance measure, that gives rise to two methods of clustering that are computationally rapid and invariant under monotonic transformations of the data.
Abstract: Techniques for partitioning objects into optimally homogeneous groups on the basis of empirical measures of similarity among those objects have received increasing attention in several different fields. This paper develops a useful correspondence between any hierarchical system of such clusters, and a particular type of distance measure. The correspondence gives rise to two methods of clustering that are computationally rapid and invariant under monotonic transformations of the data. In an explicitly defined sense, one method forms clusters that are optimally “connected,” while the other forms clusters that are optimally “compact.”
4,560 citations
"Features of Similarity" refers methods in this paper
...Hence, the additive clustering model (Shepard & Arabie, Note 2), the additive similarity tree (Sattath & Tversky, in press), and the hierarchical clustering scheme (Johnson, 1967) are all special cases of the contrast model....
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