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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).
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.
For example, k-means clustering naturally optimizes object distances, and a distance-based internal criterion will likely overrate the resulting clustering. Therefore, the internal evaluation measures are best suited to get some insight into situations where one algorithm performs better than another, but this shall not imply that one algorithm ...
Another set of methods for determining the number of clusters are information criteria, such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), or the deviance information criterion (DIC) — if it is possible to make a likelihood function for the clustering model. For example: The k-means model is "almost" a ...
This image is part of an example of the K-means algorithm. This is the first step, where the points and centroids are randomly placed. ... K-means clustering; Global ...
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.
Another method that modifies the k-means algorithm for automatically choosing the optimal number of clusters is the G-means algorithm. It was developed from the hypothesis that a subset of the data follows a Gaussian distribution. Thus, k is increased until each k-means center's data is Gaussian. This algorithm only requires the standard ...
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 ...