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A distance between populations can be interpreted as measuring the distance between two probability distributions and hence they are essentially measures of distances between probability measures. Where statistical distance measures relate to the differences between random variables, these may have statistical dependence, [1] and hence these ...
In statistics, Gower's distance between two mixed-type objects is a similarity measure that can handle different types of data within the same dataset and is particularly useful in cluster analysis or other multivariate statistical techniques. Data can be binary, ordinal, or continuous variables.
An image distance measure compares the similarity of two images in various dimensions such as color, texture, shape, and others. For example, a distance of 0 signifies an exact match with the query, with respect to the dimensions that were considered. As one may intuitively gather, a value greater than 0 indicates various degrees of ...
The inter-cluster distance d(i,j) between two clusters may be any number of distance measures, such as the distance between the centroids of the clusters. Similarly, the intra-cluster distance d '(k) may be measured in a variety of ways, such as the maximal distance between any pair of elements in cluster k. Since internal criterion seek ...
The total variation distance (or half the norm) arises as the optimal transportation cost, when the cost function is (,) =, that is, ‖ ‖ = (,) = {(): =, =} = [], where the expectation is taken with respect to the probability measure on the space where (,) lives, and the infimum is taken over all such with marginals and , respectively.
Bhattacharyya, A. (1946). "On a Measure of Divergence between Two Multinomial Populations". Sankhyā: The Indian Journal of Statistics (1933-1960). 7 (4): 401–406. ISSN 0036-4452. JSTOR 25047882. Bhattacharyya, A. (1943). "On a measure of divergence between two statistical populations defined by their probability distributions". Bull ...
The normalized compression distance has been used to fully automatically reconstruct language and phylogenetic trees. [2] [3] It can also be used for new applications of general clustering and classification of natural data in arbitrary domains, [3] for clustering of heterogeneous data, [3] and for anomaly detection across domains. [5]
A common function in data mining is applying cluster analysis on a given set of data to group data based on how similar or more similar they are when compared to other groups. Distance matrices became heavily dependent and utilized in cluster analysis since similarity can be measured with a distance metric. Thus, distance matrix became the ...