  High dimensional data can contain multiple scales of variance. Analysis tools
that preferentially operate at one scale can be ineffective at capturing all
the information present in this cross-scale complexity. We propose a multiscale
joint characterization approach designed to exploit synergies between global
and local approaches to dimensionality reduction. We illustrate this approach
using Principal Components Analysis (PCA) to characterize global variance
structure and t-stochastic neighbor embedding (t-sne) to characterize local
variance structure. Using both synthetic images and real-world imaging
spectroscopy data, we show that joint characterization is capable of detecting
and isolating signals which are not evident from either PCA or t-sne alone.
Broadly, t-sne is effective at rendering a randomly oriented low-dimensional
map of local clusters, and PCA renders this map interpretable by providing
global, physically meaningful structure. This approach is illustrated using
imaging spectroscopy data, and may prove particularly useful for other
geospatial data given robust local variance structure due to spatial
autocorrelation and physical interpretability of global variance structure due
to spectral properties of Earth surface materials. However, the fundamental
premise could easily be extended to other high dimensional datasets, including
image time series and non-image data.
