Search results
Results from the WOW.Com Content Network
In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots ,x_{n}} in k -dimensional space ℝ k , the elements of their Euclidean distance matrix A are given by squares of distances between them.
The measure gives rise to an (,)-sized similarity matrix for a set of n points, where the entry (,) in the matrix can be simply the (reciprocal of the) Euclidean distance between and , or it can be a more complex measure of distance such as the Gaussian ‖ ‖ /. [5]
The first step is to determine which elements to merge in a cluster. Usually, we want to take the two closest elements, according to the chosen distance. Optionally, one can also construct a distance matrix at this stage, where the number in the i-th row j-th column is the distance between the i-th and j-th elements. Then, as clustering ...
The data to be analyzed is a collection of objects (colors, faces, stocks, . . .) on which a distance function is defined, ,:= distance between -th and -th objects. These distances are the entries of the dissimilarity matrix
Jaccard distance is commonly used to calculate an n × n matrix for clustering and multidimensional scaling of n sample sets. This distance is a metric on the collection of all finite sets. [8] [9] [10] There is also a version of the Jaccard distance for measures, including probability measures.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Also, = /, where is the squared Euclidean distance between the two objects (binary vectors) and n is the number of attributes. The SMC is very similar to the more popular Jaccard index . The main difference is that the SMC has the term M 00 {\displaystyle M_{00}} in its numerator and denominator, whereas the Jaccard index does not.