Learning the manifold structure of remote sensing images is of paramount
relevance for modeling and understanding processes, as well as to encapsulate
the high dimensionality in a reduced set of informative features for subsequent
classification, regression, or unmixing. Manifold learning methods have shown
excellent performance to deal with hyperspectral image (HSI) analysis but,
unless specifically designed, they cannot provide an explicit embedding map
readily applicable to out-of-sample data. A common assumption to deal with the
problem is that the transformation between the high-dimensional input space and
the (typically low) latent space is linear. This is a particularly strong
assumption, especially when dealing with hyperspectral images due to the
well-known nonlinear nature of the data. To address this problem, a manifold
learning method based on High Dimensional Model Representation (HDMR) is
proposed, which enables to present a nonlinear embedding function to project
out-of-sample samples into the latent space. The proposed method is compared to
manifold learning methods along with its linear counterparts and achieves
promising performance in terms of classification accuracy of a representative
set of hyperspectral images.Comment: This is an accepted version of work to be published in the IEEE
Transactions on Geoscience and Remote Sensing. 11 page