Hyper-spectral Image Analysis with Partially-Latent Regression

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The analysis of hyper-spectral images is often needed to recover physical properties of planets. To address this inverse problem, the use of learning methods have been considered with the advantage that, once a relationship between physical parameters and spectra has been established through training, the learnt relationship can be used to estimate parameters from new images underpinned by the same physical model. Within this framework, we propose a partially-latent regression method which maps high-dimensional inputs (spectral images) onto low-dimensional responses (physical parameters). We introduce a novel regression method that combines a Gaussian mixture of locally-linear mappings with a partially-latent variable model. While the former makes high-dimensional regression tractable, the latter enables to deal with physical parameters that cannot be observed or, more generally, with data contaminated by experimental artifacts that cannot be explained with noise models. The method is illustrated on images collected from the Mars planet.