Dalton Lunga

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.

Spherical Stochastic Neighbor Embedding of Hyperspectral Data

In hyperspectral imagery, low-dimensional representations are sought in order to explain well the nonlinear characteristics that are hidden in high-dimensional spectral channels. While many algorithms have been proposed for dimension reduction and manifold learning in Euclidean spaces, very few attempts have focused on non-Euclidean spaces. Here, we propose a novel approach that embeds hyperspectral data, transformed into bilateral probability similarities, onto a nonlinear unit norm coordinate system. By seeking a unit l2-norm nonlinear manifold, we encode similarity representations onto a space in which important regularities in data are easily captured. In its general application, the technique addresses problems related to dimension reduction and visualization of hyperspectral images. Unlike methods such as multidimensional scaling and spherical embeddings, which are based on the notion of pairwise distance computations, our approach is based on a stochastic objective function of spherical coordinates. This allows the use of an Exit probability distribution to discover the nonlinear characteristics that are inherent in hyperspectral data. In addition, the method directly learns the probability distribution over neighboring pixel maps while computing for the optimal embedding coordinates. As part of evaluation, classification experiments were conducted on the manifold spaces for hyperspectral data acquired by multiple sensors at various spatial resolutions over different types of land cover. Various visualization and classification comparisons to five existing techniques demonstrated the strength of the proposed approach while its algorithmic nature is guaranteed to converge to meaningful factors underlying the data.

Multidimensional Artificial Field Embedding With Spatial Sensitivity

Multidimensional embedding is a technique useful for characterizing spectral signature relations in hyperspectral images. However, such images consist of disjoint similar spectral classes that are spatially sensitive, thus presenting challenges to existing graph embedding tools. Robust parameter estimation is often difficult when the image pixels contain several hundreds of bands. In addition, finding a corresponding high-quality lower dimensional coordinate system to map signature relations remains an open research question. We answer positively on these challenges by first proposing a combined kernel function of spatial and spectral information in computing neighborhood graphs. We further adapt a force field intuition from mechanics to develop a unifying nonlinear graph embedding framework. The generalized framework leads to novel unsupervised multidimensional artificial field embedding techniques that rely on the simple additive assumption of pair-dependent attraction and repulsion functions. The formulations capture long-range- and short-range-distance-related effects often associated with living organisms and help to establish algorithmic properties that mimic mutual behavior for the purpose of dimensionality reduction. In its application, the framework reveals strong relations to existing embedding techniques, and also highlights sources of weaknesses in such techniques. As part of evaluation, visualization, gradient field trajectories, and semisupervised classification experiments are conducted for image scenes acquired by multiple sensors at various spatial resolutions over different types of objects. The results demonstrate the superiority of the proposed embedding framework over various widely used methods.

Dynamic hyperspectral embedding with a spatial sensitive graph

Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools. Robust parameter estimation is a challenge for kernel functions that compute such graphs. Finding a corresponding high quality coordinate system to map signature relations remains an open research question. We answer positively on these challenges by proposing a kernel function of spatial and spectral information in computing neighborhood graphs. Furthermore, a multidimensional artificial field graph embedding technique that relies on simple additive assumptions of pair-dependent attraction and repulsion functions is proposed. High quality visualizations and improved classification performance demonstrate the benefits of the approach.

Unsupervised classification of hyperspectral images on spherical manifolds

Traditional statistical models for remote sensing data have mainly focused on the magnitude of feature vectors. To perform clustering with directional properties of feature vectors, other valid models need to be developed. Here we first describe the transformation of hyperspectral images onto a unit hyperspherical manifold using the recently proposed spherical local embedding approach. Spherical local embedding is a method that computes high-dimensional local neighborhood preserving coordinates of data on constant curvature manifolds. We then propose a novel von Mises-Fisher (vMF) distribution based approach for unsupervised classification of hyperspectral images on the established spherical manifold. A vMF distribution is a natural model for multivariate data on a unit hypersphere. Parameters for the model are estimated using the Expectation-Maximization procedure. A set of experimental results on modeling hyperspectral images as vMF mixture distributions demonstrate the advantages.

Kent mixture model for classification of remote sensing data on spherical manifolds

Modern remote sensing imaging sensor technology provides detailed spectral and spatial information that enables precise analysis of land cover usage. From a research point of view, traditional widely used statistical models are often limited in the sense that they do not incorporate some of the useful directional information contained in the feature vectors, and hence alternative modeling methods are required. In this paper, use of cosine angle information and its embedding onto a spherical manifold is investigated. The transformation of remote sensing images onto a unit spherical manifold is achieved by using the recently proposed spherical embedding approach. Spherical embedding is a method that computes high-dimensional local neighborhood preserving coordinates of data on constant curvature manifolds. We further develop a novel Kent mixture model for unsupervised classification of embedded cosine pixel coordinates. A Kent distribution is one of the natural models for multivariate data on a spherical surface. Parameters for the model are estimated using the Expectation-Maximization procedure. The mixture model is applied to two different Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data that were acquired from the Tippecanoe County in Indiana. The results obtained present insights on cosine pixel coordinates and also serve as a motivation for further development of new models to analyze remote sensing images in spherical manifolds.

Spherical nearest neighbor classification: application to hyperspectral data

The problem of feature transformation arises in many fields of information processing including machine learning, data compression, computer vision and geoscientific applications. In this paper, we investigate the transformation of hyperspectral data to a coordinate system that preserves geodesic distances on a constant curvature space. The transformation is performed using the recently proposed spherical embedding method. Based on the properties of hyperspherical surfaces and their relationship with local tangent spaces we propose three spherical nearest neighbor metrics for classification. As part of experimental validation, results on modeling multi-class multispectral data using the proposed spherical geodesic nearest neighbor, the spherical mahalanobis nearest neighbor and the spherical discriminant adaptive nearest neighbor rules are presented. The results indicate that the proposed metrics yields better classification accuracies especially for difficult tasks in spaces with complex irregular class boundaries. This promising outcome serves as a motivation for further development of new models to analyze hyperspectral images in spherical manifolds.