  Hyperspectral unmixing, the process of estimating a common set of spectral
bases and their corresponding composite percentages at each pixel, is an
important task for hyperspectral analysis, visualization and understanding.
From an unsupervised learning perspective, this problem is very
challenging---both the spectral bases and their composite percentages are
unknown, making the solution space too large. To reduce the solution space,
many approaches have been proposed by exploiting various priors. In practice,
these priors would easily lead to some unsuitable solution. This is because
they are achieved by applying an identical strength of constraints to all the
factors, which does not hold in practice. To overcome this limitation, we
propose a novel sparsity based method by learning a data-guided map to describe
the individual mixed level of each pixel. Through this data-guided map, the
$\ell_{p}(0<p<1)$ constraint is applied in an adaptive manner. Such
implementation not only meets the practical situation, but also guides the
spectral bases toward the pixels under highly sparse constraint. What's more,
an elegant optimization scheme as well as its convergence proof have been
provided in this paper. Extensive experiments on several datasets also
demonstrate that the data-guided map is feasible, and high quality unmixing
results could be obtained by our method.
