  Datasets in high-dimension do not typically form clusters in their original
space; the issue is worse when the number of points in the dataset is small. We
propose a low-computation method to find statistically significant clustering
structures in a small dataset. The method proceeds by projecting the data on a
random line and seeking binary clusterings in the resulting one-dimensional
data. Non-linear separations are obtained by extending the feature space using
monomials of higher degrees in the original features. The statistical validity
of the clustering structures obtained is tested in the projected
one-dimensional space, thus bypassing the challenge of statistical validation
in high-dimension. Projecting on a random line is an extreme dimension
reduction technique that has previously been used successfully as part of a
hierarchical clustering method for high-dimensional data. Our experiments show
that with this simplified framework, statistically significant clustering
structures can be found with as few as 100-200 points, depending on the
dataset. The different structures uncovered are found to persist as more points
are added to the dataset.
