Unsupervised learning is used to categorize multidimensional data into a number of meaningful classes on the basis of the similarity or correlation between individual samples. In neural-network implementation of various unsupervised algorithms such as principal component analysis, competitive learning or self-organizing map, sample vectors are normalized to equal lengths so that similarity could be easily and efficiently obtained by their dot products. In general, sample vectors span the whole multidimensional feature space and existing normalization methods distort the intrinsic patterns present in the sample set. In this work, a novel method of normalization by mapping the samples to a new space of one more dimension is proposed. The original distribution of the samples in the feature space is shown to be almost preserved in the transformed space. Simple rules are given to map from original space to the normalized space and vice versa.
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