  Hyperspectral feature spaces are useful for many remote sensing applications
ranging from spectral mixture modeling to discrete thematic classification. In
such cases, characterization of the feature space dimensionality, geometry and
topology can provide guidance for effective model design. The objective of this
study is to compare and contrast two approaches for identifying feature space
basis vectors via dimensionality reduction. These approaches can be combined to
render a joint characterization that reveals spectral properties not apparent
using either approach alone. We use a diverse collection of AVIRIS-NG
reflectance spectra of the snow-firn-ice continuum to illustrate the utility of
joint characterization and identify physical properties inferred from the
spectra. Spectral feature spaces combining principal components (PCs) and
t-distributed Stochastic Neighbor Embeddings (t-SNEs) provide physically
interpretable dimensions representing the global (PC) structure of cryospheric
reflectance properties and local (t-SNE) manifold structures revealing
clustering not resolved in the global continuum. Joint characterization reveals
distinct continua for snow-firn gradients on different parts of the Greenland
Ice Sheet and multiple clusters of ice reflectance properties common to both
glacier and sea ice in different locations. Clustering revealed in t-SNE
feature spaces, and extended to the joint characterization, distinguishes
differences in spectral curvature specific to location within the snow
accumulation zone, and BRDF effects related to view geometry. The ability of
PC+t-SNE joint characterization to produce a physically interpretable spectral
feature spaces revealing global topology while preserving local manifold
structures suggests that this characterization might be extended to the much
higher dimensional hyperspectral feature space of all terrestrial land cover.
