Manifold-learning-based feature extraction for classification of hyperspectral data: A review of advances in manifold learning

Interest in manifold learning for representing the topology of large, high-dimensional nonlinear data sets in lower, but still meaningful, dimensions for visualization and classification has grown rapidly over the past decade, particularly in the analysis of hyperspectral imagery. High spectral resolution and the typically continuous bands of hyperspectral image (HSI) data enable discrimination between spectrally similar targets of interest, provide capability to estimate within pixel abundances of constituents, and allow for the direct exploitation of absorption features in predictive models. Although hyperspectral data are typically modeled assuming that the data originate from linear stochastic processes, nonlinearities are often exhibited in the data due to the effects of multipath scattering, variations in sun-canopy-sensor geometry, nonhomogeneous composition of pixels, and attenuating properties of media [1]. Because of the dense spectral sampling of HSI data, the associated spectral information in many adjacent bands is highly correlated, resulting in a much lower intrinsic dimensional space spanned by the data (Figure 1). Increased availability of HSIs and greater access to advanced computing have motivated the development of specialized methods for the exploitation of the nonlinear characteristics of these data. In this context, feature selection and feature extraction approaches for dimensionality reduction have received significant attention. While both feature selection and extraction result in some loss of information relative to the original data, both have been demonstrated to be quite successful in the classification arena. Feature selection retains meaningful features for classification, but the algorithms are computationally intensive and often not robust in complex scenes. Alternatively, feature extraction approaches, which project the data to lower-dimensional intrinsic spaces, are typically more robust to variation in spectral signatures across scenes, and most are computationally superior to optimal feature selection, although the interpretation relative to the original spectral signatures is lost. Both feature selection and extraction are flexible relative to the choice of the back-end classifier. © 1991-2012 IEEE.