  In recent years, large high-dimensional data sets have become commonplace in
a wide range of applications in science and commerce. Techniques for dimension
reduction are of primary concern in statistical analysis. Projection methods
play an important role. We investigate the use of projection algorithms that
exploit properties of the alpha-stable distributions. We show that l_{alpha}
distances and quasi-distances can be recovered from random projections with
full statistical efficiency by L-estimation. The computational requirements of
our algorithm are modest; after a once-and-for-all calculation to determine an
array of length k, the algorithm runs in O(k) time for each distance, where k
is the reduced dimension of the projection.
