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k-means clustering is a popular algorithm used for partitioning data into k clusters, where each cluster is represented by its centroid. However, the pure k -means algorithm is not very flexible, and as such is of limited use (except for when vector quantization as above is actually the desired use case).
Variations of k-means often include such optimizations as choosing the best of multiple runs, but also restricting the centroids to members of the data set (k-medoids), choosing medians (k-medians clustering), choosing the initial centers less randomly (k-means++) or allowing a fuzzy cluster assignment (fuzzy c-means). Most k-means-type ...
The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]
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.
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.
The Jump Flooding Algorithm can generate approximate Voronoi diagrams in constant time and is suited for use on commodity graphics hardware. [42] [43] Lloyd's algorithm and its generalization via the Linde–Buzo–Gray algorithm (aka k-means clustering) use the construction of Voronoi diagrams as a subroutine. These methods alternate between ...
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 ...
In applied mathematics, k-SVD is a dictionary learning algorithm for creating a dictionary for sparse representations, via a singular value decomposition approach. k-SVD is a generalization of the k-means clustering method, and it works by iteratively alternating between sparse coding the input data based on the current dictionary, and updating the atoms in the dictionary to better fit the data.