  Graph embedding techniques are useful to characterize spectral signature
relations for hyperspectral images. However, such images consists of disjoint
classes due to spatial details that are often ignored by existing graph
computing tools. Robust parameter estimation is a challenge for kernel
functions that compute such graphs. Finding a corresponding high quality
coordinate system to map signature relations remains an open research question.
We answer positively on these challenges by first proposing a kernel function
of spatial and spectral information in computing neighborhood graphs. Secondly,
the study exploits the force field interpretation from mechanics and devise a
unifying nonlinear graph embedding framework. The generalized framework leads
to novel unsupervised multidimensional artificial field embedding techniques
that rely on the simple additive assumption of pair-dependent attraction and
repulsion functions. The formulations capture long range and short range
distance related effects often associated with living organisms and help to
establish algorithmic properties that mimic mutual behavior for the purpose of
dimensionality reduction. The main benefits from the proposed models includes
the ability to preserve the local topology of data and produce quality
visualizations i.e. maintaining disjoint meaningful neighborhoods. As part of
evaluation, visualization, gradient field trajectories, and semisupervised
classification experiments are conducted for image scenes acquired by multiple
sensors at various spatial resolutions over different types of objects. The
results demonstrate the superiority of the proposed embedding framework over
various widely used methods.
