Metric and Euclidean properties of dissimilarity coefficients

Gower, J. C.; Legendre, Pierre

doi:10.1007/bf01896809

Cited by 806 publications

(542 citation statements)

References 23 publications

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“…Many different disciplines require the ability to quantify the degree of similarity (or conversely, the distance or dissimilarity) between two objects, each characterised by some number of attributes or descriptors, and there is thus a very extensive literature describing similarity coefficients that can be used for this purpose (see, e.g., [56][57][58]). Although many of these are designed for use with continuous, real-valued data they can often be expressed in a form that makes them suitable for determining the similarities between pairs of binary records, such as 2D fingerprints [20].…”

Section: Comparison Of Similarity Coefficientsmentioning

confidence: 99%

Similarity-based virtual screening using 2D fingerprints

Willett

2006

Drug Discovery Today

783

673

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Teaser This paper discusses the use of binary-encoded fragment substructures to scan databases to find molecules that are structurally similar to a bioactive query compound.Abstract This paper summarises recent work at the University of Sheffield on virtual screening methods that use 2D fingerprint measures of structural similarity. A detailed comparison of a large number of similarity coefficients demonstrates that the well-known Tanimoto coefficient remains the method of choice for the computation of fingerprintbased similarity, despite possessing some inherent biases related to the sizes of the molecules that are being sought. Group fusion involves combining the results of similarity searches based on multiple reference structures and a single similarity measure. We demonstrate the effectiveness of this approach to screening, and also describe an approximate form of group fusion, turbo similarity searching, that can be used when just a single reference structure is available.

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Section: Comparison Of Similarity Coefficientsmentioning

confidence: 99%

Similarity-based virtual screening using 2D fingerprints

Willett

2006

Drug Discovery Today

783

673

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“…For example, in decision making, preference modeling and social choice theory, one can argue that reciprocal relations like choice probabilities and preference judgments should satisfy certain transitivity properties, if they represent rational human decisions made after well-reasoned comparisons on objects [26,27,28]. For symmetric relations as well, transitivity plays an important role [29,30], when modeling similarity relations, metrics, kernels, etc.…”

Section: Relationships With Fuzzy Set Theorymentioning

confidence: 99%

“…Ranking representability as defined above cannot represent relations that originate from an underlying metric or similarity measure. For such relations, one needs another connection with its roots in Euclidean metric spaces [29].…”

Section: Relationships With Fuzzy Set Theorymentioning

confidence: 99%

Learning Valued Relations from Data

Waegeman

Pahikkala

Airola

et al. 2011

Advances in Intelligent and Soft Computing

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Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated quite intensively in the machine learning community. To this end, current approaches typically consider datasets containing crisp relations, so that standard classification methods can be adopted. However, relations between objects like similarities and preferences are in many real-world applications often expressed in a graded manner. A general kernel-based framework for learning relations from data is introduced here. It extends existing approaches because both crisp and valued relations are considered, and it unifies existing approaches because different types of valued relations can be modeled, including symmetric and reciprocal relations. This framework establishes in this way important links between recent developments in fuzzy set theory and machine learning. Its usefulness is demonstrated on a case study in document retrieval.

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“…As noted above, the Székely-Rizzo method requires the use of a distance, and we have hence used the ten distance coefficients listed below, taken from the extensive review of metric coefficients presented by Gower and Legendre [25]. Assume that a molecule X i is represented by a pelement vector, with the element X ik containing the frequency of occurrence of the k-th fragment in X i (and similarly for another molecule Xj).…”

Section: Distance Coefficientsmentioning

confidence: 99%

“…A potential problem with many of these coefficients is that both X ik and X jk are frequently zero: this corresponds to a substructural fragment that is absent from both of the molecules that are being compared and results in the denominator in the expression for the coefficient having a value of zero. In each such case, we have ignored the k-th fragment and reduced the value of p by one, as recommended by Gower and Legendre [25].…”

Section: Distance Coefficientsmentioning

confidence: 99%

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

Varin

Bureau

Mueller

et al. 2009

Journal of Molecular Graphics and Modelling

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Ward's method is extensively used for clustering chemical structures represented by 2D fingerprints. This paper compares Ward clusterings of 14 datasets (containing between 278 and 4332 molecules) with those obtained using the Székely-Rizzo clustering method, a generalization of Ward's method. The clusters resulting from these two methods were evaluated by the extent to which the various classifications were able to group active molecules together, using a novel criterion of clustering effectiveness. Analysis of a total of 1400 classifications (Ward and Székely-Rizzo clustering methods, fourteen different datasets, five different fingerprints and ten different distance coefficients) demonstrated the general superiority of the Székely-Rizzo method. The distance coefficient first described by Soergel performed extremely well in these experiments, and this was also the case when it was used in simulated virtual screening experiments.

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Metric and Euclidean properties of dissimilarity coefficients

Abstract: Choice of coefficient, Dissimilarity, Distance, Euclidean property, Metric property, Similarity,

Cited by 806 publications

References 23 publications

Similarity-based virtual screening using 2D fingerprints

Similarity-based virtual screening using 2D fingerprints

Learning Valued Relations from Data

Clustering files of chemical structures using the Székely–Rizzo generalization of Ward's method

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