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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.
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]
The most accepted solution to this problem is the elbow method. It consists of running k-means clustering to the data set with a range of values, calculating the sum of squared errors for each, and plotting them in a line chart. If the chart looks like an arm, the best value of k will be on the "elbow". [2]
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 ...
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.
Similar to other clustering evaluation metrics such as Silhouette score, the CH index can be used to find the optimal number of clusters k in algorithms like k-means, where the value of k is not known a priori. This can be done by following these steps: Perform clustering for different values of k. Compute the CH index for each clustering result.
Several of these models correspond to well-known heuristic clustering methods. For example, k-means clustering is equivalent to estimation of the EII clustering model using the classification EM algorithm. [8] The Bayesian information criterion (BIC) can be used to choose the best clustering model as well as the number of clusters. It can also ...
K-means clustering is an algorithm for grouping genes or samples based on pattern into K groups. Grouping is done by minimizing the sum of the squares of distances between the data and the corresponding cluster centroid. Thus the purpose of K-means clustering is to classify data based on similar expression. [20]