Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 450-463.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a specific cluster of documents with something in common. Figure 2. Distinctive local patterns are still difficult to detect (User profiles not included) 5.2 The Role of Reference Points Our magnetic field metaphor is based on the notion of reference points. The notion of reference points [17] suggests that some particularly salient or distinctive points, conceptually or visually, play the role of a reference context to which other points are seen in relation to. Geometric properties such as symmetry, perpendicularity and parallelism can make a pattern distinctive and special. People ....

Krumhansl, C. L. (1978). "Concerning the applicability of geometric models to similar data: The interrelationship between similarity and spatial density." Psychological Review, 85(5), 445-463.

....years of extensive researches, how to help users to find their desired images accurately and quickly is still an open problem. In the early years of content based image retrieval (CBIR) most researchers devote their efforts to f mding the best visual features or the best similarity measure [10][11][14] 16] 17] 32] However, because of the complexity and subjectivity of the visual content, no single feature can discriminate all images, neither can single similarity measure meet every user s need. On the other hand, according to recent user study results [22] what average users really want ....

.... et al. have shown that the similarity model in human vision is a complex nonlinear model[10] Furthermore, Kmmhansl has proposed a distance density model of similarity, in which similarity is assumed to be a fimction of both the feature difference and the feature density of the feature space[11]. However, because we know little about the density distribution of the feature space and the property of the similarity model due to limited number of training samples, accurate similarity measures are usually difficult to achieve in reality. Fortunately, we can adopt a divide and conquer ....

Krumhansl, CL., (1978) Concerning the applicability of geometric models to similarity data: the interrelationship between similarity and spatial density, Psychological Review, vol. 85, pp. 445-464.

....consider cognitive properties of similarity. In this sense, studies have shown that the perceived similarity from a class to its superclass is greater than the perceived similarity from the superclass to the class, and that the superclass is commonly used as base 1 of the similarity evaluation [44, 49]. There have given different explanations for the asymmetric evaluations of similarity. Asymmetry can be explained by 1 The first term of a comparison is referred to as the target and the second term as the base. Determining Semantic Similarity Among Entity Classes from Different Ontologies M. ....

....Semantic Similarity Among Entity Classes from Different Ontologies M. Andrea Rodrguez and Max J. Egenhofer IEEE Transactions on Knowledge and Data Engineering the relative size and salience of distinctive features sets [20] by potential stimulus biases, such as density and prototypicality [44, 50], by a natural reference point or landmark for members of a category [49] and by the direction of maximum informativiness [51] Common to all these explanations is the different role that the target and base positions play in a similarity evaluation. The most salient term, the item with larger ....

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Krumhansl, C., Concerning the Applicability of Geometric Models to Similarity Data: The Interrelationship Between Similarity and Spatial Density. Psychological Review, 1978. 85(5): p. 445-4 63.

....users queries express only an approximation of what users want to retrieve, which is likely an inexact match to any stored data. This paper explores the use and effect of context over a model of semantic similarity among entity classes, the matching distance model [7] Like feature based models [1, 8, 9], the matching distance model defines a similarity function in terms of common and different features of entities (i.e. descriptors and attributes) The matching distance model, however, defines asymmetric evaluations of semantic similarity that are a product of the weighted contribution of the ....

....entity classes as nouns, which are organized into sets of synonyms. Thus, this model allows not only the definition of synonyms, but also the identification of polysemous words. Context becomes important for similarity assessment, because it affects the determination of the relevant features [1, 8, 9]. Although a feature based approach is sensible to the way people assess similarity, it may be argued that the extent to which a concept possesses or is associated with a feature may be a matter of a degree. Consequently, a specific feature can be more important to the meaning of an entity class ....

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Krumhansl, C., 1978, Concerning the Applicability of Geometric Models to Similarity Data: The Interrelationship Between Similarity and Spatial Density. Psychological Review 85(5): 445-463.

.... first requirement for a distance function is that d(S A , SA ) d(S B , SB ) 2) for all stimuli (constancy of self similarity) This hypothesis can be tested using the judged similarity, since it implies #(S A , SA ) #(S B , SB ) The constancy of self similarity has been refuted by Krumhansl [19]. A second axiom of the distance model is minimality: d(S A , SB ) # d(S A , SA ) 3) again, this hypothesis is open to experimental investigation since, due to the monotonicity of the relation between d and #, it implies #(S A , SB ) # #(S A , SA ) Tversky [39] argued that this assumption ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445-- 463., 1978.

....p 2 ) d(p 2 , p 1 ) Triangle inequality: for all stimuli p 1 , p 2 , p 3 , it is d(p 1 , p 3 ) # d(p 1 , p 2 ) d(p 2 , p 3 ) This is also the common assumption in vision applications. On the other hand, there is convincing evidence that human similarity does not satisfy the metric axioms [7, 13]. Some relatively recent models in psychology make the assumption that, since so many metric axioms are violated, similarity assessment in human is not based on a distance function after all. One successful approach is based on set theoretic considerations. In a 1977 paper [13] Amos Tversky ....

....standard learning techniques to determine the metric of the space based on the statistics of the images in the database. Although the geometric formulation was derived from the Feature Contrast Model, there is no reason why we should limit to that. We can be guided by the following observation [7]: not all the similarity judgments follow the same law. Some judgments follow simple metric laws, and these are those associated with global, undecomposable properties of the images. In other words, similarity follows simpler metrics for the lowest frequencies of an image. This suggests to base ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

....the similarity criterion) of the whole database. It is obvious that similarity measurement is fundamental in perceptual databases. In particular, we look for a measure that replicate as well as possible human similarity assessment. The concept of perceptual similarity can be quite elusive (see [14, 20, 19, 1, 6, 23, 22]) and it is a good idea to spend a few words on it before we proceed further, since it will play a role in the definition of visual languages to interact with perceptual databases. A broad distinction can be made between pre attentive (or non interpretative) similarity and attentive (or ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978. 16

....other hand, bases similarity on the truth of a certain number of predicates. This is, to the best of our knowledge, the most successful similarity theory that makes no use of any geometrical construct. Apart from that, its predictions are quite similar to the quasi geometric model of Krumhansl [3]. In this section we show that a predicative distance, like Tversky s, can be seen as a quasi geometric model in a suitable Riemann manifold. In particular, the similarity will be given by the sum of two terms: a saliency term, depending only on the reference stimulus, and a distance term, ....

C. L. Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

....Triangle inequality: for all SA , SB , SC , it is d(SA , SC ) # d(SA , SB ) d(SB , SC ) This property cannot be tested experimentally. Even if d satisfies the triangle inequality, # might not, or vice versa. There is strong experimental evidence that selfsimilarity is not constant [5] that is, some things are more similar to themselves than others. Also, a number of researchers have proved experimentally that human similarity assessment is asymmetrical [9, 1] Monotonicity seems to hold, although in [9] it is argued that this might not always be the case. The triangular ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

....empirical evidence that this is not the case: experimental data reveal that human similarity assessment is not symmetric and that self similarity is neither constant nor (under special circumstances) minimal. This finding inspired a number 6 of mendaments to the raw distance model. Krumhansl [24],for instance, assumed that similarity is based on a pseudo distance function given by: d(S a , S b ) #(S a , S b ) #h(S a ) #h(S b ) 7) where # is a distance function, and h(S) is the density of stimuli around S. This model allows for violation of the distance axioms. For instance, ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

.... rst requirement for a distance function is that d(S A ; SA ) d(S B ; SB ) 2) for all stimuli (constancy of self similarity) This hypothesis can be tested using the judged similarity, since it implies (S A ; SA ) S B ; SB ) The constancy of self similarity has been refuted by Krumhansl [19]. A second axiom of the distance model is minimality: d(S A ; SB ) d(S A ; SA ) 3) again, this hypothesis is open to experimental investigation since, due to the monotonicity of the relation between d and , it implies (S A ; SB ) S A ; SA ) Tversky [39] argued that this assumption may ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445{ 463., 1978.

....change the degree of similarity. The fundamental assumption that is made for the measurement of similarity is that two points in a relatively dense region of a space would have a smaller similarity measure than two points of equal inter point distance but located in a less dense region of space [5]. This is the basis of our model of similarity too. There are many models for computing similarities between objects. Although we present here a function to measure the similarity of tuples in the context of their twins, we particularly do not commit to any such function. Instead, we describe some ....

Krumhansl, C. L.; "Concerning the Applicability of Geometric Models to Similarity Data: the Interrelationship Between Similarity and Spatial Density"; Psychological Review, 85; 1978; pp 445-463.

....Triangle inequality: for all SA , SB , SC , it is d(SA ; SC ) d(SA ; SB ) d(SB ; SC ) This property cannot be tested experimentally. Even if d satisfies the triangle inequality, ffi might not, or vice versa. There is strong experimental evidence that selfsimilarity is not constant [5] that is, some things are more similar to themselves than others. Also, a number of researchers have proved experimentally that human similarity assessment is asymmetrical [9, 1] Monotonicity seems to hold, although in [9] it is argued that this might not always be the case. The triangular ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

....empirical evidence that this is not the case: experimental data reveal that human similarity assessment is not symmetric and that self similarity is neither constant nor (under special circumstances) minimal. This finding inspired a number of aemendaments to the raw distance model. Krumhansl [24],for instance, assumed that similarity is based on a pseudo distance function given by: d(S a ; S b ) OE(S a ; S b ) ffh(S a ) fih(S b ) 7) where OE is a distance function, and h(S) is the density of stimuli around S. This model allows for violation of the distance axioms. For instance, ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445-- 463., 1978.

....other hand, bases similarity on the truth of a certain number of predicates. This is, to the best of our knowledge, the most successful similarity theory that makes no use of any geometrical construct. Apart from that, its predictions are quite similar to the quasi geometric model of Krumhansl [5]. In this section we show that a predicative distance, like Tversky s, can be seen as a quasi geometric model in a suitable Riemann manifold. In particular, the similarity will be given by the sum of two terms: a saliency term, depending only on the reference stimulus, and a distance term, ....

.... Gamma j ) GammaP (j; M(j; ff; fi; 16) The first term, P , is the saliency term. The greater the saliency, the less we depart perceptually from a given reference stimulus for a given difference in the predicate truth. This term is analogous to the term h in Krumhansl theory [5]. The term M is what we are mostly interested in at the moment. This term represents a distance in the psychological space. The space will be in general nonlinear, and the first question we might ask ourselves is whether it is elliptic or hyperbolic. To determine this, we first note that M = 0 for ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

....the similarity criterion) of the whole database. It is obvious that similarity measurement is fundamental in perceptual databases. In particular, we look for a measure that replicate as well as possible human similarity assessment. The concept of perceptual similarity can be quite elusive (see [14, 20, 19, 1, 6, 23, 22]) and it is a good idea to spend a few words on it before we proceed further, since it will play a role in the definition of visual languages to interact with perceptual databases. A broad distinction can be made between pre attentive (or non interpretative) similarity and attentive (or ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

....The first requirement for a distance function is that d(A; A) d(B; B) 2) for all stimuli (constancy of self similarity. This hypothesis can be tested using the judged similarity, since it implies ffi(A; A) ffi(B; B) The constancy of self similarity has been refuted by Krumhansl [11]. A second axiom of the distance model is minimality: d(A; B) d(A; A) 3) again, this hypothesis is open to experimental investigation since, due to the monotonicity of the relation between d and ffi, it implies ffi(A; B) ffi(A; A) Tversky [25] argued that this assumption is violated in some ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

.... dictates of the task (Harnad, 1987; Goldstone, 1994) Furthermore, similarity need not remain restricted by the symmetry that it inherits from the underlying distance function; the metric space model can be considered a starting point for a more realistic definition, e.g. of the kind proposed in (Krumhansl, 1978). Indeed, as I shall argue in section 5, a distance based definition of similarity does not preclude one from modeling a considerable variety of similarity related phenomena in human perception. The possibility of a principled quantification both of the distal and of the proximal shape similarity ....

Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data: the interrelationship between similarity and spatial density. Psychological Review, 85:445--463.

....1 ; p 2 ) d(p 2 ; p 1 ) Triangle inequality: for all stimuli p 1 , p 2 , p 3 , it is d(p 1 ; p 3 ) d(p 1 ; p 2 ) d(p 2 ; p 3 ) This is also the common assumption in vision applications. On the other hand, there is convincing evidence that human similarity does not satisfy the metric axioms [7, 13]. Some relatively recent models in psychology make the assumption that, since so many metric axioms are violated, similarity assessment in human is not based on a distance function after all. One successful approach is based on set theoretic considerations. In a 1977 paper [13] Amos Tversky ....

....standard learning techniques to determine the metric of the space based on the statistics of the images in the database. Although the geometric formulation was derived from the Feature Contrast Model, there is no reason why we should limit to that. We can be guided by the following observation [7]: not all the similarity judgments follow the same law. Some judgments follow simple metric laws, and these are those associated with global, undecomposable properties of the images. In other words, similarity follows simpler metrics for the lowest frequencies of an image. This suggests to base ....

Carol L Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85:445--463., 1978.

No context found.

Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 450-463.

No context found.

Krumhansl, C., 1978, Concerning the Applicability of Geometric Models to Similarity Data: The Interrelationship Between Similarity and Spatial Density. Psychological Review 85(5): 445-463.

No context found.

Comput., 21:56--63. Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data: the interrelationship between similarity and spatial density. Psychological Review, 85:445--463.

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C.L. Krumhansl, Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density, Pschological Review, 85, 445-463 (1978).

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