|
[L, C, D] = FKMEANS(X, k) partitions the vectors in the n-by-p matrix Xinto k (or, rarely, fewer) clusters by applying the well known batchK-means algorithm. Rows of X correspond to points, columns correspond tovariables. The output k-by-p matrix C contains the cluster centroids. Then-element output column vector L contains the cluster label of eachpoint. The k-element output column vector D contains the residual clusterdistortions as measured by total squared distance of cluster members fromthe centroid.FKMEANS(X, C0) where C0 is a k-by-p matrix uses the rows of C0 as theinitial centroids instead of choosing them randomly from X.FKMEANS(X, k, options) allows optional parameter name/value pairs tobe specified. Parameters are: 'weight' - n-by-1 weight vector used to adjust centroid and distortion calculations. Weights should be positive. 'careful' - binary option that determines whether "careful seeding" as recommended by Arthur and Vassilvitskii is used when choosing initial centroids. This option should be used with care because numerical experiments suggest it may be counter-productive when the data is noisy.NOTES(1) The careful seeding procedure chooses the first centroid at randomfrom X, and each successive centroid from the remaining points accordingto the categorical distribution with selection probabilities proportionalto the point's minimum squared Euclidean distance from the already chosencentroids. This tends to spread the points out more evenly, and, if thedata is made of k well separated clusters, is likely to choose an initialcentroid from each cluster. This can speed convergence and reduce thelikelihood of getting a bad solution [1]. However, in experiments where5% uniformly distributed noise data was added to such naturally clustereddata the results were frequently worse then when centroids were chosen atrandom.(2) If, as is possible, a cluster is empty at the end of an iteration,then there may be fewer than k clusters returned. In practice this seemsto happen very rarely.(3) Unlike the Mathworks KMEANS this implementation does not perform afinal, slow, phase of incremental K-means ('onlinephase') that guaranteesconvergence to a local minimum.References[1] "k-means++: The Advantages of Careful Seeding", by David Arthur andSergei Vassilvitskii, SODA 2007.
|
Windows Software
Albina Merfyn - I find this to be really easy to use. I can...
