Data description in subspaces

We investigate how the boundary of a data set can be obtained in case of (very) low sample sizes. This boundary can be used to detect if new objects resemble the data set and therefore make the subsequent classification more confident. When a large number of training objects is available it is possible to directly estimate the density. After thresholding the probability density a boundary around the data is obtained. However, in the case of very low sample sizes, extrapolations have to be performed. In this paper we propose a simple method based on nearest neighbor distances which is capable of finding data boundaries in these low sample sizes. It appears to be especially useful when the data is distributed in subspaces