  Applying dimensionality reduction (DR) to large, high-dimensional data sets
can be challenging when distinguishing the underlying high-dimensional data
clusters in a 2D projection for exploratory analysis. We address this problem
by first sharpening the clusters in the original high-dimensional data prior to
the DR step using Local Gradient Clustering (LGC). We then project the
sharpened data from the high-dimensional space to 2D by a user-selected DR
method. The sharpening step aids this method to preserve cluster separation in
the resulting 2D projection. With our method, end-users can label each distinct
cluster to further analyze an otherwise unlabeled data set. Our
`High-Dimensional Sharpened DR' (HD-SDR) method, tested on both synthetic and
real-world data sets, is favorable to DR methods with poor cluster separation
and yields a better visual cluster separation than these DR methods with no
sharpening. Our method achieves good quality (measured by quality metrics) and
scales computationally well with large high-dimensional data. To illustrate its
concrete applications, we further apply HD-SDR on a recent astronomical
catalog.
