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The accuracy of regression based on hyperspectral data is degraded by a restricted number of labeled data and the curse of dimensionality inherent in the high-dimensional feature space. In this paper, we propose two types of semi-supervised manifold learning methods for regression by a combination of supervised learning based on a small number of labeled data and unsupervised learning based on abundant...
We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The resulting points on the Grassmannian have representations as orthonormal matrices and as such do not reside in Euclidean space in the usual sense. There are a variety...
This paper introduces a new method for dimensionality reduction via regression (DRR). The method generalizes Principal Component Analysis (PCA) in such a way that reduces the variance of the PCA scores. In order to do so, DRR relies on a deflationary process in which a non-linear regression reduces the redundancy between the PC scores. Unlike other nonlinear dimensionality reduction methods, DRR is...
In this paper, we will show that the Hapke model, a well known radiative transfer scattering model for intimate mixtures, when considered as a nonlinear function of endmember grain sizes, abundances, illumination and viewing angles, can be represented geometrically as a low dimensional manifold with a gentle curvature. In this scenario, we can represent the data cloud of a scene composed by several...
Manifold learning techniques have been demonstrated to be successful in representing spectral signatures in hyperspectral images, which consist of spectral features with very subtle differences and often spatially induced disjoint classes whose neighborhood relations are difficult to capture using traditional graph based embedding techniques. Robust parameter estimation is a challenge in traditional...
Classification of hyperspectral remote sensing images is affected by two main problems: high dimensionality of the acquired signatures and scarce availability of labeled samples. Learning a low dimensional manifold and active learning represent two approaches that have been investigated in the literature to mitigate these effects. However they are usually applied independently from each other. In...
Hyperspectral image data are traditionally analyzed using statistical models. However, as the spatial and spectral resolutions of the images improve as a result of advances in sensor technology, the data no longer maintain a Gaussian distribution; this is due to increased material diversity in the scene, i.e., clutter. This causes many statistical assumptions about the data — and subsequently, the...
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