Manifold-Learning-Based Feature Extraction for Classification of Hyperspectral Data: A Review of Advances in Manifold Learning

Advances in hyperspectral sensing provide new capability for characterizing spectral signatures in a wide range of physical and biological systems, while inspiring new methods for extracting information from these data. HSI data often lie on sparse, nonlinear manifolds whose geometric and topological structures can be exploited via manifold-learning techniques. In this article, we focused on demonstrating the opportunities provided by manifold learning for classification of remotely sensed data. However, limitations and opportunities remain both for research and applications. Although these methods have been demonstrated to mitigate the impact of physical effects that affect electromagnetic energy traversing the atmosphere and reflecting from a target, nonlinearities are not always exhibited in the data, particularly at lower spatial resolutions, so users should always evaluate the inherent nonlinearity in the data. Manifold learning is data driven, and as such, results are strongly dependent on the characteristics of the data, and one method will not consistently provide the best results. Nonlinear manifold-learning methods require parameter tuning, although experimental results are typically stable over a range of values, and have higher computational overhead than linear methods, which is particularly relevant for large-scale remote sensing data sets. Opportunities for advancing manifold learning also exist for analysis of hyperspectral and multisource remotely sensed data. Manifolds are assumed to be inherently smooth, an assumption that some data sets may violate, and data often contain classes whose spectra are distinctly different, resulting in multiple manifolds or submanifolds that cannot be readily integrated with a single manifold representation. Developing appropriate characterizations that exploit the unique characteristics of these submanifolds for a particular data set is an open research problem for which hierarchical manifold structures appear to have merit. To date, most work in manifold learning has focused on feature extraction from single images, assuming stationarity across the scene. Research is also needed in joint exploitation of global and local embedding methods in dynamic, multitemporal environments and integration with semisupervised and active learning.