Many of the algorithms designed to cluster large data sets compute representations of the data which are based on a single vector, without a unique representation of the original data items. We present an extension of Principal Direction Divisive Partitioning which creates a least-squares approximation of the data based on a small number of vectors. We show that the extension can save significant amounts of memory and cluster the data as well as the original method. We also show that in some cases using more than one vector to approximate each data item results in superior quality clusterings.
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