Tversky similarity

Asymmetry in a similarity measure is the result of asymmetrical weighing of a dissimilarity component - multiplication is commutative by definition, difference is not. By weighing a and h, one obtains asymmetric similarity measures, including the Tversky similarity measure c j aa 4- fih + c), where a and fi are user-defined constants. The Tversky measure can be regarded as a generalization of the Tanimoto and Dice similarity measures like them, it does not consider the absence matches d. A particular case is c(a + c), which measures the number of common features relative to all the features present in A, and gives zero weight to h. 

Bradshaw J 1997. Introduction to Tversky Similarity Measure. At http //www.daylight.com meetings / mu g97 / Bradshaw / MUG97 / tv tversky.html. 

Tuz Golu (lake), 5 784 Tversky similarity, 6 8 T vessicant agent, 5 816 physical properties, 5 817t Twaron fiber, 13 373 Tween surfactants, 24 150 12-membered ring macrolides, 15 272, 275t 2,6-TDI, reaction with a polyether triol, 25 459. See also Toluene diisocyanate (TDI)... 

Fig. 4. (A) The other asymmetric Tversky similarity index, S VC, has a value of 0.69. Exchanging the roles of the query and target molecules (Q<=>T) gives (B), which shows that smaller target molecules are more likely to be retrieved from a large query structure using the asymmetric Tversky similarity index than the Tanimoto similarity index.

Bradshaw, J. (1997) Introduction to the Tversky Similarity Measure. Presented at... 

A weighted version of the Jaccard-Tanimoto association measure is the Tversky similarity coefficient, given as [Tversky, 1977]... 

There are other coefficients like the Dice coefficient. Cosine coefficient, simple matching coefficient, and Tversky similarity coefficient. 

TABLE 15.5 Parameter Values That Convert the Tversky Similarity Function, Equation 15.5.1, into the Other Well-Known Set-Based Similarity Functions Listed in Table 153... 

Wang and Bajorath [97] have carried out an extensive study based on their earlier work [96]. Both studies used the Tversky similarity function given in Equation 15.5.2, to assess how molecular complexity ( size ) and bit density influence the results of similarity searches based on molecular fingerprints. Generally, but not always, molecular complexity and bit density are closely related, that is, more complex molecules tend to have greater bit densities than less complex molecules. A key element of their study is the construction of bit-density invariant similarity functions that account for the distribution of both 1-bits and 0-bits. The functions are based on weighted combinations of terms of the form given in Equation 15.5.2 or 15.5.3... 

The Tversky similarity function S J i,j a,p) is written in a form reminiscent of conditional probabilities to explicitly indicate that the similarity function is conditioned on the value of the parameters a and j8. 

Senger S. Using Tversky similarity searches for core hopping Finding the needles in the haystack. J Chem Inf Model 2009 49 1514-1524. 

A generalisation of the similarity formulae for binary data can be derived, based on the work of Tversky [Tversky 1977 Bradshaw 1997]. This takes the form ... 

The pragmatic beauty of the chemical fingerprint is that the more common features of two molecules that there are, the more common bits are set. The mathematic approach used to translate the fingerprint comparison data into a measure of similarity tunes the molecular comparison [5]. The Tanimoto similarity index works well when a relatively sparse fingerprint is used and when the molecules to be compared are broadly comparable in size and complexity [5]. If the nature of the molecules or the comparison desired is not adequately met by the Tanimoto index, multiple other indices are available to the researcher. For example, the Daylight software offers the user over ten similarity metrics, and the Pipeline Pilot as distributed offers at least three. Some of these metrics (e.g., Tversky, Cosine) offer better behavior if the query molecule is significantly smaller than the molecule compared to it. 

A similarity index called subsimilaritywhich is short for substructure similarity, has been developed by developed by Hagadone (37). In form it is identical to one of the family of asymmetric similarity indices developed by Tversky (6) that is discussed in Subheading 2.2.2.,... 

Most similarity measures for binary-valued feature vectors in use today are symmetric Tversky (6), however, has defined an infinite family of asymmetric measures... 

The extreme forms, but not the intermediate forms, of asymmetric similarity defined by Tversky (6) given in Eqs. 2.26 and 2.27 can be transformed into two symmetric measures by taking the maximum and minimum of the set cardinalities in the denominators of the two equations. The forms of these equations are obtained in analogy to those developed by Petke (33) for vectors and field-based functions (see Subheadings 2.3. and 2.4. for further details) ... 

Vertical asymmetry Of all the possible orientations, then, graphic displays ordinarily only use the vertical and horizontal. What s more, they use these orientations differently. Vertical arrays take precedence over horizontal ones. Just as for the choice of dimensions, the precedence of the vertical is also rooted in perception (Clark, 1973 Cooper and Ross, 1975 Lakoff and Johnson, 1980 Franklin and Tversky, 1990). Gravity is correlated with vertical, and people are oriented vertically. The vertical axis of the world has a natural asymmetry, the ground and the sky, whereas the horizontal axis of the world does not. The dominance of the vertical over the horizontal is reflected in the dominance of columns over rows. Similarly, bar charts typically contain vertical columns (the exceptions seem to be aimed at conforming to accompanying text). 

Time is an abstract non-spatial construct, but humans often adapt spatial structures to convey temporal information (e.g., spatial metaphors, charts, and graphs see Tversky, this volume). Similarly, signers adapt signing space to express temporal information both at the lexical level and at the discourse level (see also Kita, this volume, for a discussion of how the gesture space of speakers is used to represent temporal information). 

Clark (1969, 1973) and others (Lakoff Johnson, 1980 see also Tversky, this volume) maintain that this asymmetry of linguistic structure is rooted in the asymmetries of perceptual space. The clearest form of this argument was given by Clark, who pointed out that the structure of our bodies and our movements in the world define three reference planes, two of which are asymmetrical. The only plane characterized by perceptual symmetry is the right-left plane. Two reference planes are asymmetrical the front-back plane, and the top-bottom (or head-feet) plane. Clark claimed that the front end of the front-back plane is positive because it is the direction of movement and the side toward which most of our perceptual receptors are oriented. Similarly, he reasoned that the top end of the top-bottom plane is positive because up-down is the canonical orientation of the body as well as the primary direction of observed movement (objects fall from up to down but never in the opposite direction). The asymmetric structure of perceptual space has since been confirmed... 

Structural similarity in children s reasoning with graphs The experiments described above and the patterns noted by Emmorey and Tversky (see chapters from each in this volume) lend support to the hypothesis that structural similarity constrains the mapping of simple relational structures—elements and the relations between elements—in conceptual and spatial schemas. Structural similarity also predicts, however, that similarity of more complex relational structures can influence mappings of conceptual and spatial schemas. Specifically, structural similarity claims that conceptual elements are mapped to spatial elements, conceptual relations are mapped to spatial relations, and higher-order conceptual relations are... 

Certainly it is the case that many representations are influenced by more than one form of similarity between concepts and spatial representations. Isotypes, for instance, are a form of bar graphs in which the bars are made of multiple icons of a commodity, such as barrels of oil (see Neurath, 1936, and Tversky, this volume). Within an isotype, the icons are a uniform size, and represent a uniform quantity. A bar composed of a large number of icons (relative to another bar) conveys more redundantly via at least two constraints. More oil barrows, for instance, communicate more oil via iconicity, and the greater vertical extent of the bar communicates more via the association between quantity and area. The interpretation of such a graphic could also be constrained by polarity, with the weighted continuum of big and small mapped to the continuum of more and less. 

Later, George Loewenstein and I generalized Tversky s idea to a larger variety of experiences.74 In addition to endowment and contrast effects that arise from one s own past experiences, we identified similar effects that arise from the anticipation of one s future experiences, from other people s experiences, and from merely imagined or counterfactual experiences. Because the term "endowment" does not fit these other contexts, we used "consumption effect" as the more general term. To some extent we also addressed the question of the net effect. We noted that in interpersonal comparisons there is a transition from a dominant consumption effect to a dominant contrast effect that occurs at the point of equality.75 We also noted the absence of a contrast effect when the future is expected to be worse than the present. In other cases, however, the net effect remains indeterminate. It is an open question, for instance, whether the consumption effect of daydreaming can offset the contrast effect.76 Also,... 

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