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Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some specific sense defined by the analyst) to each other than to those in other groups (clusters).
In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted. For example, if the numerical data 3.4, 5.1, 2.6, 7.3 are observed, the ranks of these data items would be 2, 3, 1 and 4 respectively.
Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near ...
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
A ranking is a relationship between a set of items, often recorded in a list, such that, for any two items, the first is either "ranked higher than", "ranked lower than", or "ranked equal to" the second. [1] In mathematics, this is known as a weak order or total preorder of objects.
Much of the model-based clustering software is in the form of a publicly and freely available R package. Many of these are listed in the CRAN Task View on Cluster Analysis and Finite Mixture Models. [34] The most used such package is mclust, [35] [36] which is used to cluster continuous data and has been downloaded over 8 million times. [37]
Order statistics have a lot of applications in areas as reliability theory, financial mathematics, survival analysis, epidemiology, sports, quality control, actuarial risk, etc. There is an extensive literature devoted to studies on applications of order statistics in these fields.
In statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between different values is significant.