Spatial-Spectral Multiple Manifold Discriminant Analysis for Dimensionality Reduction of Hyperspectral Imagery

Abstract

Hyperspectral images (HSI) possess abundant spectral bands and rich spatial information, which can be utilized to discriminate different types of land cover. However, the high dimensional characteristics of spatial-spectral information commonly cause the Hughes phenomena. Traditional feature learning methods can reduce the dimensionality of HSI data and preserve the useful intrinsic information but they ignore the multi-manifold structure in hyperspectral image. In this paper, a novel dimensionality reduction (DR) method called spatial-spectral multiple manifold discriminant analysis (SSMMDA) was proposed for HSI classification. At first, several subsets are obtained from HSI data according to the prior label information. Then, a spectral-domain intramanifold graph is constructed for each submanifold to preserve the local neighborhood structure, a spatial-domain intramanifold scatter matrix and a spatial-domain intermanifold scatter matrix are constructed for each sub-manifold to characterize the within-manifold compactness and the between-manifold separability, respectively. Finally, a spatial-spectral combined objective function is designed for each submanifold to obtain an optimal projection and the discriminative features on different submanifolds are fused to improve the classification performance of HSI data. SSMMDA can explore spatial-spectral combined information and reveal the intrinsic multi-manifold structure in HSI. Experiments on three public HSI data sets demonstrate that the proposed SSMMDA method can achieve better classification accuracies in comparison with many state-of-the-art methods.

An outlook: machine learning in hyperspectral image classification and dimensionality reduction techniques

“…78 Many graph learning algorithms and variants have been presented to discover the fundamental geometric structure of high-dimensional data based on this concept. 79 For example, Spatial-Spectral Multiple Manifold Discriminant Analysis (SSMMDA) 80 and Isometric Feature Mapping (ISOMAP). 81 For delivering extremely non-linear manifolds, ISOMAP strives to preserve geodesic distances of all similarity pairs, and it approximates the geodesic distance between two points by measuring the shortest path between these points.…”

Improved Active Deep Learning for Semi-Supervised Classification of Hyperspectral Image

“…One of the challenges for the high-dimensional characteristics of hyperspectral remote sensing data is that HSI classification has to face the so-called Hughes phenomenon [31]. A new semi-supervised framework has been proposed to cope with high-dimensional and large-scale data, which combined the randomness with anchor graphs [32].…”

“…A previous study [31] applied the Local Anchor Embedding algorithm to retrieve anchor points, and the data-anchor mapping problem can be formulated by Equation (10):…”

A Two-Staged Feature Extraction Method Based on Total Variation for Hyperspectral Images

“…What's more, manifold learning methods [18] have been continuously developed, and some advanced methods include GPU parallel implementation of isometric mapping [19], which can greatly accelerate the speed of data transformation. Spatialspectral multiple manifold discriminant analysis (SSMMDA) [20] can explore spatialspectral combined information and reveal the intrinsic multi-manifold structure in HSIs. In [21], a novel local constrained collaborative representation model was designed; it can characterize the collaborative relationship between sample pairs and explore the intrinsic geometric structure in HSI.…”