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Function Description

Returns the result (in a single array) of applying a k-means clustering analysis, as per Press et al. (2007).


In k-means clustering, we have n m-dimensional datapoints (where n = NumberOfSeries, m = NumberOfDataPointsPerSeries) and we ascribe them to clusters depending on how near they are (in a spherical Euclidean sense) to potential cluster centres. We need to specify the number of clusters (NumberOfClusters) and some initial starting means (i.e. centres) for each cluster. The algorithm then uses a variant of the EM algorithm to find which datapoints belong to which clusters and where the cluster centres need to be to minimise the sum of the distance that the datapoints are away from their cluster centres.


InputData is a 2d array of size NumberOfSeries x NumberOfDataPointsPerSeries and StartMeans is a 2d array of size NumberOfClusters x NumberOfSeries.


The output is an array with 3 + NumberOfClusters x NumberOfSeries + NumberOfDataPointsPerSeries as follows:


First 3 values = NumberOfSeries, NumberOfDataPointsPerSeries and NumberOfMixtureComponents


Following NumberOfClusters x NumberOfSeries values = locations of means (centres) of each cluster


Following NumberOfDataPointsPerSeries values = cluster to which datapoint has been assigned (counting from 0).


The probability that a datapoint selected randomly is in a particular cluster can be found if needed by counting the proportion of the datapoints assigned to different clusters.


See also Gaussian mixture modelling (which can be thought of as akin to a generalisation of k-means clustering) and example data series for Gaussian mixture modelling and k-means clustering.


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