Dimensionality reduction via regression on hyperspectral infrared sounding data
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 easy to apply, it has out-of-sample extension, it is invertible, and the learned transformation is volume-preserving. These properties make the method useful for a wide range of applications, especially in very high dimensional data in general, and for hyperspectral image processing in particular. We illustrate the performance of the algorithm in reducing the dimensionality of IASI hyperspectral image sounding data. We compare DRR with related and invertible methods such as linear PCA and Principal Polynomial Analysis (PPA) in terms of reconstruction error, and expressive power of the extracted features to estimate atmospheric variables.