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In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.
Ward's minimum variance method can be defined and implemented recursively by a Lance–Williams algorithm. The Lance–Williams algorithms are an infinite family of agglomerative hierarchical clustering algorithms which are represented by a recursive formula for updating cluster distances at each step (each time a pair of clusters is merged).
Given a set of n objects, centroid-based algorithms create k partitions based on a dissimilarity function, such that k≤n. A major problem in applying this type of algorithm is determining the appropriate number of clusters for unlabeled data. Therefore, most research in clustering analysis has been focused on the automation of the process.
In statistics, a location parameter of a probability distribution is a scalar- or vector-valued parameter, which determines the "location" or shift of the distribution.In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent ways:
Objects are detected out to a pre-determined maximum detection distance w. Not all objects within w will be detected, but a fundamental assumption is that all objects at zero distance (i.e., on the line itself) are detected. Overall detection probability is thus expected to be 1 on the line, and to decrease with increasing distance from the line.
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.
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.
Objects B and C have the same reachability distance (k=3), while D is not a k nearest neighbor. This distance is used to define what is called reachability distance: reachability-distance k (A,B)=max{k-distance(B), d(A,B)} In words, the reachability distance of an object A from B is the true distance of the two objects, but at least the k ...