  In this paper, we develop a local rank correlation measure which quantifies
the performance of dimension reduction methods. The local rank correlation is
easily interpretable, and robust against the extreme skewness of nearest
neighbor distributions in high dimensions. Some benchmark datasets are studied.
We find that the local rank correlation closely corresponds to our visual
interpretation of the quality of the output. In addition, we demonstrate that
the local rank correlation is useful in estimating the intrinsic dimensionality
of the original data, and in selecting a suitable value of tuning parameters
used in some algorithms.
