  We present a new technique for visualizing high-dimensional data called
cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality
reduction methods: preserving both local and global structures of the original
sample in a single 2-dimensional visualization. Its algorithm combines the
well-known multidimensional scaling (MDS) tool with the $k$-medoids data
clustering technique, and enables hierarchical embedding, sparsification and
estimation of 2-dimensional coordinates for additional points. While cl-MDS is
a generally applicable tool, we also include specific recipes for atomic
structure applications. We apply this method to non-linear data of increasing
complexity where different layers of locality are relevant, showing a clear
improvement in their retrieval and visualization quality.
