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k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid ), serving as a prototype of the cluster. This results in a partitioning of the data space ...
k -means++. k. -means++. In data mining, k-means++ [1] [2] is an algorithm for choosing the initial values (or "seeds") for the k -means clustering algorithm. It was proposed in 2007 by David Arthur and Sergei Vassilvitskii, as an approximation algorithm for the NP-hard k -means problem—a way of avoiding the sometimes poor clusterings found ...
k. -medoids. The k-medoids problem is a clustering problem similar to k -means. The name was coined by Leonard Kaufman and Peter J. Rousseeuw with their PAM (Partitioning Around Medoids) algorithm. [1] Both the k -means and k -medoids algorithms are partitional (breaking the dataset up into groups) and attempt to minimize the distance between ...
Fuzzy clustering (also referred to as soft clustering or soft k-means) is a form of clustering in which each data point can belong to more than one cluster.. Clustering or cluster analysis involves assigning data points to clusters such that items in the same cluster are as similar as possible, while items belonging to different clusters are as dissimilar as possible.
This relates directly to the k-median problem which is the problem of finding k centers such that the clusters formed by them are the most compact with respect to the 2-norm. Formally, given a set of data points x , the k centers c i are to be chosen so as to minimize the sum of the distances from each x to the nearest c i .
Machine learningand data mining. In data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories:
STREAM is an algorithm for clustering data streams described by Guha, Mishra, Motwani and O'Callaghan [3] which achieves a constant factor approximation for the k-Median problem in a single pass and using small space. Theorem — STREAM can solve the k -Median problem on a data stream in a single pass, with time O ( n1+e) and space θ ( nε) up ...
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