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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.
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 by the standard k-means algorithm.
Lloyd's algorithm starts by an initial placement of some number k of point sites in the input domain. In mesh-smoothing applications, these would be the vertices of the mesh to be smoothed; in other applications they may be placed at random or by intersecting a uniform triangular mesh of the appropriate size with the input domain.
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. The criterion ...
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 points ...
Of course, k-means algorithm is used synonymously with Lloyd's algorithm by many. "The most prominent and widely used clustering algorithm is Lloyd's algorithms sometimes also referred to as the k-means algorithm." (From Frahling, G. and Sohler, C. 2006. A fast k-means implementation using coresets.
A problem set, sometimes shortened as pset, [1] is a teaching tool used by many universities. Most courses in physics , math , engineering , chemistry , and computer science will give problem sets on a regular basis. [ 2 ]
In graph theory, the metric k-center problem or vertex k-center problem is a classical combinatorial optimization problem studied in theoretical computer science that is NP-hard. Given n cities with specified distances, one wants to build k warehouses in different cities and minimize the maximum distance of a city to a warehouse.
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