Using Diffusion Geometric Coordinates for Hyperspectral Imagery Representation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Modeling hyperspectral imagery via nonlinear manifold learning approaches can successfully capture the intrinsic geometries of the underlying complex high-dimensional data, which gives the state-of-the-art hyperspectral imagery representation. In this letter, we demonstrate that diffusion geometric coordinates can also represent hyperspectral imagery in a concise way and reveal much more significant structures than traditional linear methods. This diffusion framework tries to form a diffusion operator on the investigated hyperspectral imagery which simulates Markov random walk on the constructed affinity graph. The diffusion geometric coordinates derived from diffusion maps of the hyperspectral data incorporate the intrinsic geometries well where much more details about species-level spatial distributions are revealed in our experiments which show better classification results than principle component analysis (PCA). For <formula formulatype="inline"><tex Notation="TeX">10⁵</tex></formula>– <formula formulatype="inline"><tex Notation="TeX">10⁶</tex></formula> or even larger imagery, by exploiting the backbone approach, the computation complexity and memory requirement of the full-scene computation and representation are tractable, which shows the potential significant usefulness in the hyperspectral remote sensing field. </para>