A transformation for clustering noisy shape observations

In this paper we present a method of achievement dimensionality reduction on a set of data that is corrupted by Gaussian noise prior to observation. The noise is additive in the original space (domain) in which the pattern class is defined. In conjunction with the dimensionality reduction method, a pattern clustering technique is presented and employed in the range space. The p-dimensional observation is taken into a smaller -dimensional space by a linear transformation T. The transformation is derived using well-known variational calculus techniques after the optimumality criteria have been defined. It is shown that the dimensionality reduction technique has the properties of the discrete Wiener filter and therefore possesses well defined optimality properties in the mean square sense.