Dissimilarity measurement

To construct dissimilarity measures, one uses mismatches Here a + b is the Hamming (Manhattan, taxi-cab, city-block) distance, and a + h) is the Euclidean distance. 

In view of the conflict between the reliability and the cost of adding more hardware, it is sensible to attempt to use the dissimilar measured values together to cross check each other, rather than replicating each hardware individually. This is the concept of analytical i.e. functional) redundancy which uses redundant analytical (or functional) relationships between various measured variables of the monitored process e.g., inputs/outputs, out-puts/outputs and inputs/inputs). Figure 3 illustrates the hardware and analytical redundancy concepts. 

Subheading 2.5. provides a very brief discussion of molecular dissimilarity measures that are basically the complement of their corresponding molecular similarity measures. This section also presents reasons as to why similarity is preferred over dissimilarity, except in studies of diversity, as a measure of molecular resemblance. 

Adamson, G. W. and Bush, J. A. (1975) A comparison of the performance of some similarity and dissimilarity measures in the automatic classification of chemical structures../. Chem. Inf Comput. Sci. 15, 55-58. 

Fig. 3. Coverage of chemistry space by four overlapping sublibraries. (A) Different diversity libraries cover similar chemistry space but show little overlap. This shows three libraries chosen using different dissimilarity measures to act as different representations of the available chemistry space. The compounds from these libraries are presented in this representation by first calculating the intermolecular similarity of each of the compounds to all of the other compounds using fingerprint descriptors and the Tanimoto similarity index. Principal component analysis was then conducted on the similarity matrix to reduce it to a series of principal components that allow the chemistry space to be presented in three dimensions.

Mezey, P. G. (1997) A proof of the metric properties of the symmetric scalingnesting dissimilarity measure and related symmetry deficiency measures. Int. J. Quantum Chem. 63, 105-109. 

Dissimilarity-based classifiers. Dissimilarity-based classifiers (DBCs) use a dissimilarity measure Md to transform the input data into a dissimilarity space, where each trained class represents a separate dimension. Any dissimilarity measure with the following properties can be used ... 

This chapter is concerned with some of the background theory for molecular diversity analysis and includes a discussion of diversity indices, intermolecular similarity and dissimilarity measures. The extent to which the different approaches to diversity analysis have been validated and compared is reviewed. Algorithms for the selection of diverse sets of compounds are covered in detail elsewhere in this book and are mentioned only briefly here. However, consideration is given to whether these algorithms should be applied in reactant or product space. 

Lajiness, M. An evaluation ofthe performance of dissimilarity measures. In QSAR Rational Approaches to the Design of Bioactive Compounds, Eds Silipo, C. and Vittoria, A., 1991, Elsevier Science Publishers, Amsterdam, pp. 201-204. 

SHAPE SIMILARITY MEASURES AND DISSIMILARITY MEASURES IN THE STUDY OF HOST-GUEST INTERACTIONS... 

For applications of the scaled fuzzy Hausdorff-type metric f p(A,B) for assessing the similarity of molecules, the f p(A,B) distance can be used as a dissimilarity measure. 

VII. PROOF OF THE METRIC PROPERTIES OF THE SYMMETRIC SCALING-NESTING DISSIMILARITY MEASURE... 

By applying the SNSM similarity measure to mirror images, the quantity is a measure of achirality, whereas the dissimilarity measure d A,A ), denoted as Xs J A), is a measure of chirality, where the interrelation (137) between Xs,J A) and implies that this measure can take values from the unit interval. The measure Xs A), first proposed as an example of dissimilarity measures of the second kind, is zero for achiral objects and takes positive values for all chiral objects. Objects perceived as having prominent chirality tend to have large Xs A) values. The SNSM measures have also been applied to more general molecular shape problems. More recently, Klein showed that by a logarithmic transformation of the scaling factors s g, a metric can be constructed to provide a proper distance-like measure of dissimilarity of shapes. 

It can also be shown, however, that the SNSM dissimilarity measure, defined as d = I -s g, is a proper metric itself and there is no need for logarithmic transformations. We use the acronym SNDSM for this scaling-nesting dissimilarity metric d,. A, B). A proof of the metric properties of SNDSM dJ,A, B) is given subsequently. 

In terms of FSNSM fs g, the fuzzy scaling-nesting dissimilarity measure dfJ,A,B) is defined as... 

This measure df (A,B) of fuzzy dissimilarity is in fact a metric for fuzzy shapes. With the provision that volume of ordinary sets is replaced with the mass of fuzzy sets, all the steps in the proof of the metric properties of the ordinary SNDSM measure, described in Section VII, can be repeated for FSNDSM df A,B) in identical form, proving that the fuzzy set version FSNDSM of the SNDSM measure is, indeed, a metric. The fuzzy scaling-nesting dissimilarity measure FSDNSM dfJ A, B) provides a useful definition for distance between fuzzy sets, interpreted as a metric expressing dissimilarity in a formal space of fuzzy shapes, such as electronic densities of molecules. 

TTie dissimilarity of A and Af i p p provides a symmetry deficiency measure analogous to the ZPA continuous symmetry measure of discrete point sets. As a dissimilarity measure, both the SNDSM metric and the Hausdorff metric, or any other dissimilarity measure suitable for continua, are applicable. 

These symmetry deficiency measures and others employing different general dissimilarity measures exploit the advantages of the elegance of... 

Fuzzy dissimilarity measures, such as the fuzzy FSNDSM metric fs(/l, B), and any one of the fuzzy Hausdorff-type dissimilarity metrics, for example, f(A,B), can be applied to the pair of set A and the folded-unfolded set Aff p p. These fuzzy dissimilarity measures generate fuzzy symmetry deficiency measures analogous to the ZPA continuous symmetry measure of discrete point sets. 

It has been demonstrated that an automatic segmentation of molecular surfaces into distinct domains can be performed with a dissimilarity measure for linguistic variables which have the form... 

If the two molecules A and B turn out to be dissimilar by a given (P,W)-shape similarity criterion [i.e., if they do not fulfill the equivalence relation A (P,W) B], then the differences between their numerical shape descriptors can serve as a dissimilarity measure. That is, for a (P,W)-dissimilar molecule pair A and B, the (P,W)-similarity concept allows one to quantify how different their topological invariants are. A simple and straightforward approach is based on a simple vector comparison of the lists of Betti numbers of the shape group technique, or on the numerical comparison of shape matrices. 

Similarity and distance (or dissimilarity) measures provide the means for converting the attributes of the objects into a relevant numerical score. 

Equations (1) and (2) represent the most general form of the optimal clustering problem. The objective is to find the clustering c that minimizes an internal clustering criterion J. J typically employs a similarity/dissimilarity measure to judge the quality of any c. The set C defines c s data structure, including all the feasible clusterings of the set Q of all objects to be clustered. 

Luque Ruiz, L, Urbano-Cuadrado, M. and Gomez-Nieto, M.A. (2007) Data fusion of similarity and dissimilarity measurements using Wiener-based indices for the prediction of the NPY Y5 receptor antagonist capacity of benzoxazinones. J. Chem. Inf Model., 47, 2235-2241. 

Fig. 7. Dendrogram of propolis samples using average linkage with Bray-Curtis dissimilarity measure. Data calculations were based on the absorbance values for the UV-visible spectral window of 200 iim to 700 t m of propolis samples produced in Santa Catarina State - southern Brazil, autumn-2010.

A typical dissimilarity measure is the so-called Hamming distance based on the exclusive OR (cf. Figure 7.7) calculated as follows ... 

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