Dimension Reduction of Optical Remote Sensing Images via Minimum Change Rate Deviation Method

This paper introduces a new dimension reduction (DR) method, called
minimum change rate deviation
(MCRD), which is applicable to the DR of remote sensing images. As the main shortcoming of the well-known
principal component analysis
(PCA) method is that it does not consider the spatial relation among image points, our proposed approach takes into account the spatial relation among neighboring image pixels while preserving all useful properties of PCA. These include uncorrelatedness property in resulted components and the decrease of error with the increasing of the number of selected components. Our proposed method can be considered as a generalization of PCA and, under certain conditions, reduces to it. The proposed MCRD method employs linear spatial operators to consider the spatiality of images. The superiority of MCRD over conventional PCA is demonstrated both mathematically and experimentally. It is shown that MCRD, with an acceptable speed, outperforms PCA in retaining the required information for classification purposes. Moreover, as the
locally linear embedding
(LLE) method also employs the spatial relations in its DR process, the performances of MCRD and LLE are compared, and the superiority of the proposed method in both classification accuracy and computational cost is shown.