Perform an entropy weighted subspace k-means.
ewkm(x, centers, lambda=1, maxiter=100, delta=0.00001, maxrestart=10)numeric matrix of observations and variables.
target number of clusters or the initial centers for clustering.
parameter for variable weight distribution.
maximum number of iterations.
maximum change allowed between iterations for convergence.
maximum number of restarts. Default is 10 so that we stand a good chance of getting a full set of clusters. Normally, any empty clusters that result are removed from the result, and so we may obtain fewer than k clusters if we don't allow restarts (i.e., maxrestart=0). If < 0 then there is no limit on the number of restarts and we are much more likely to get a full set of k clusters.
Returns an object of class "kmeans" and "ewkm", compatible with other functions that work with kmeans objects, such as the 'print' method. The object is a list with the following components in addition to the components of the kmeans object:
weights: A matrix of weights recording the relative importance of each variable for each cluster.
iterations: This reports on the number of iterations before termination. Check this to see whether the maxiters was reached. If so then the algroithm may not be converging,and thus the resulting clustering may not be particularly good.
restarts: The number of times the clustering restarted because of a disappearing cluster resulting from one or more k-means having no observations associated with it. An number here greater than 0 indicates that the algorithm is not converging on a clustering for the given k. It is recommended that k be reduced.
total.iterations: The total number of iterations over all restarts.
The entopy weighted k-means clustering algorithm is a subspace clusterer ideal for high dimensional data. Along with each cluster we also obtain variable weights that provide a relative measure of the importance of each variable to that cluster.
The algorithm is based on the k-means approach to clustering. An initial set of k means are identified as the starting centroids. Observartions are clustered to the nearest centroid according to a distance measure. This defines the initial clustrering. New centroids are then identified based on these clusters.
Weights are then calculated for each variable within each cluster, based on the current clustering. The weights are a measure of the relative importance of each variable with regard to the membership of the observations to that cluster. These weights are then incorporated into the distance function, typically reducing the distance for the more important variables.
New centroids are then calculated, and using the weighted distance measure each observation is once again clustered to its nearest centroid.
The process continues until convergence (using a measure of dispersion and stopping when the change becomes less than delta) or until a specified number of iterations has been reached (maxiter).
Large lambda (e,g, > 3) lead to a relatively even distribution of weights across the variables. Small lambda (e.g., < 1) lead to a more uneven distribution of weights, giving more discrimintation between features. Recommended values are between 1 and 3.
Always check the number of iterations, the number of restarts, and the total number of iterations as they give a good indication of whether the algorithm converged.
As with any distance based algorithm, be sure to rescale your numeric
data so that large values do not bias the clustering. A quick
rescaling method to use is scale.
Liping Jing, Michael K. Ng and Joshua Zhexue Huang (2007). An Entropy Weighting k-Means Algorithm for Subspace Clustering of High-Dimensional Sparse Data. IEEE Transactions on Knowledge and Data Engineering, 19(8), 1026--1041.
# NOT RUN {
myewkm <- ewkm(iris[1:4], 3, lambda=0.5, maxiter=100)
plot(iris[1:4], col=myewkm$cluster)
# For comparative testing
mykm <- kmeans(iris[1:4], 3)
plot(iris[1:4], col=mykm$cluster)
# }
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