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One of the most commonly used similarity measures is the Euclidean distance, which is used in many clustering techniques including K-means clustering and Hierarchical clustering. The Euclidean distance is a measure of the straight-line distance between two points in a high-dimensional space.
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.
It is defined as the ratio between the minimal inter-cluster distance to maximal intra-cluster distance. For each cluster partition, the Dunn index can be calculated by the following formula: [40] = < (,) ′ (), where d(i,j) represents the distance between clusters i and j, and d '(k) measures the intra-cluster distance of cluster k.
The Jaccard distance, which measures dissimilarity between ... an n × n matrix for clustering and ... similarity between the two baskets as measured by the Jaccard ...
Complete-linkage or furthest-neighbor clustering is a form of agglomerative clustering that defines the dissimilarity between clusters to be the maximum distance between any two points from the two clusters. Similarly, average-distance clustering uses the average pairwise distance as the dissimilarity. Like Ward's distance, these two forms of ...
Hierarchical clustering has the distinct advantage that any valid measure of distance can be used. In fact, the observations themselves are not required: all that is used is a matrix of distances . On the other hand, except for the special case of single-linkage distance, none of the algorithms (except exhaustive search in O ( 2 n ...
The definition of 'shortest distance' is what differentiates between the different agglomerative clustering methods. In complete-linkage clustering, the link between two clusters contains all element pairs, and the distance between clusters equals the distance between those two elements (one in each cluster) that are farthest away from each ...
For example, given a weighted graph = (,) where the edge weight indicates whether two nodes are similar (positive edge weight) or different (negative edge weight), the task is to find a clustering that either maximizes agreements (sum of positive edge weights within a cluster plus the absolute value of the sum of negative edge weights between ...