Gustavo Camps-Valls

Kernel-based methods for hyperspectral image classification

This paper presents the framework of kernel-based methods in the context of hyperspectral image classification, illustrating from a general viewpoint the main characteristics of different kernel-based approaches and analyzing their properties in the hyperspectral domain. In particular, we assess performance of regularized radial basis function neural networks (Reg-RBFNN), standard support vector machines (SVMs), kernel Fisher discriminant (KFD) analysis, and regularized AdaBoost (Reg-AB). The novelty of this work consists in: 1) introducing Reg-RBFNN and Reg-AB for hyperspectral image classification; 2) comparing kernel-based methods by taking into account the peculiarities of hyperspectral images; and 3) clarifying their theoretical relationships. To these purposes, we focus on the accuracy of methods when working in noisy environments, high input dimension, and limited training sets. In addition, some other important issues are discussed, such as the sparsity of the solutions, the computational burden, and the capability of the methods to provide outputs that can be directly interpreted as probabilities.

Composite kernels for hyperspectral image classification

This letter presents a framework of composite kernel machines for enhanced classification of hyperspectral images. This novel method exploits the properties of Mercers kernels to construct a family of composite kernels that easily combine spatial and spectral information. This framework of composite kernels demonstrates: 1) enhanced classification accuracy as compared to traditional approaches that take into account the spectral information only: 2) flexibility to balance between the spatial and spectral information in the classifier; and 3) computational efficiency. In addition, the proposed family of kernel classifiers opens a wide field for future developments in which spatial and spectral information can be easily integrated.

Hyperspectral Remote Sensing Data Analysis and Future Challenges

Hyperspectral remote sensing technology has advanced significantly in the past two decades. Current sensors onboard airborne and spaceborne platforms cover large areas of the Earth surface with unprecedented spectral, spatial, and temporal resolutions. These characteristics enable a myriad of applications requiring fine identification of materials or estimation of physical parameters. Very often, these applications rely on sophisticated and complex data analysis methods. The sources of difficulties are, namely, the high dimensionality and size of the hyperspectral data, the spectral mixing (linear and nonlinear), and the degradation mechanisms associated to the measurement process such as noise and atmospheric effects. This paper presents a tutorial/overview cross section of some relevant hyperspectral data analysis methods and algorithms, organized in six main topics: data fusion, unmixing, classification, target detection, physical parameter retrieval, and fast computing. In all topics, we describe the state-of-the-art, provide illustrative examples, and point to future challenges and research directions.

Semi-Supervised Graph-Based Hyperspectral Image Classification

This paper presents a semi-supervised graph-based method for the classification of hyperspectral images. The method is designed to handle the special characteristics of hyperspectral images, namely, high-input dimension of pixels, low number of labeled samples, and spatial variability of the spectral signature. To alleviate these problems, the method incorporates three ingredients, respectively. First, being a kernel-based method, it combats the curse of dimensionality efficiently. Second, following a semi-supervised approach, it exploits the wealth of unlabeled samples in the image, and naturally gives relative importance to the labeled ones through a graph-based methodology. Finally, it incorporates contextual information through a full family of composite kernels. Noting that the graph method relies on inverting a huge kernel matrix formed by both labeled and unlabeled samples, we originally introduce the Nystro umlm method in the formulation to speed up the classification process. The presented semi-supervised-graph-based method is compared to state-of-the-art support vector machines in the classification of hyperspectral data. The proposed method produces better classification maps, which capture the intrinsic structure collectively revealed by labeled and unlabeled points. Good and stable accuracy is produced in ill-posed classification problems (high dimensional spaces and low number of labeled samples). In addition, the introduction of the composite-kernel framework drastically improves results, and the new fast formulation ranks almost linearly in the computational cost, rather than cubic as in the original method, thus allowing the use of this method in remote-sensing applications.

Global and time-resolved monitoring of crop photosynthesis with chlorophyll fluorescence.

Significance Global food and biofuel production and their vulnerability in a changing climate are of paramount societal importance. However, current global model predictions of crop photosynthesis are highly uncertain. Here we demonstrate that new space-based observations of chlorophyll fluorescence, an emission intrinsically linked to plant biochemistry, enable an accurate, global, and time-resolved measurement of crop photosynthesis, which is not possible from any other remote vegetation measurement. Our results show that chlorophyll fluorescence data can be used as a unique benchmark to improve our global models, thus providing more reliable projections of agricultural productivity and climate impact on crop yields. The enormous increase of the observational capabilities for fluorescence in the very near future strengthens the relevance of this study. Photosynthesis is the process by which plants harvest sunlight to produce sugars from carbon dioxide and water. It is the primary source of energy for all life on Earth; hence it is important to understand how this process responds to climate change and human impact. However, model-based estimates of gross primary production (GPP, output from photosynthesis) are highly uncertain, in particular over heavily managed agricultural areas. Recent advances in spectroscopy enable the space-based monitoring of sun-induced chlorophyll fluorescence (SIF) from terrestrial plants. Here we demonstrate that spaceborne SIF retrievals provide a direct measure of the GPP of cropland and grassland ecosystems. Such a strong link with crop photosynthesis is not evident for traditional remotely sensed vegetation indices, nor for more complex carbon cycle models. We use SIF observations to provide a global perspective on agricultural productivity. Our SIF-based crop GPP estimates are 50–75% higher than results from state-of-the-art carbon cycle models over, for example, the US Corn Belt and the Indo-Gangetic Plain, implying that current models severely underestimate the role of management. Our results indicate that SIF data can help us improve our global models for more accurate projections of agricultural productivity and climate impact on crop yields. Extension of our approach to other ecosystems, along with increased observational capabilities for SIF in the near future, holds the prospect of reducing uncertainties in the modeling of the current and future carbon cycle.

Advances in Hyperspectral Image Classification: Earth Monitoring with Statistical Learning Methods

The technological evolution of optical sensors over the last few decades has provided remote sensing analysts with rich spatial, spectral, and temporal information. In particular, the increase in spectral resolution of hyperspectral images (HSIs) and infrared sounders opens the doors to new application domains and poses new methodological challenges in data analysis. HSIs allow the characterization of objects of interest (e.g., land-cover classes) with unprecedented accuracy, and keeps inventories up to date. Improvements in spectral resolution have called for advances in signal processing and exploitation algorithms. This article focuses on the challenging problem of hyperspectral image classification, which has recently gained in popularity and attracted the interest of other scientific disciplines such as machine learning, image processing, and computer vision. In the remote sensing community, the term classification is used to denote the process that assigns single pixels to a set of classes, while the term segmentation is used for methods aggregating pixels into objects and then assigned to a class.

Kernel methods for remote sensing data analysis

About the editors. List of authors. Preface. Acknowledgments. List of symbols. List of abbreviations. I Introduction. 1 Machine learning techniques in remote sensing data analysis (Bjorn Waske, Mathieu Fauvel, Jon Atli Benediktsson and Jocelyn Chanussot). 1.1 Introduction. 1.2 Supervised classification: algorithms and applications. 1.3 Conclusion. Acknowledgments. References. 2 An introduction to kernel learning algorithms (Peter V. Gehler and Bernhard Scholkopf). 2.1 Introduction. 2.2 Kernels. 2.3 The representer theorem. 2.4 Learning with kernels. 2.5 Conclusion. References. II Supervised image classification. 3 The Support Vector Machine (SVM) algorithm for supervised classification of hyperspectral remote sensing data (J. Anthony Gualtieri). 3.1 Introduction. 3.2 Aspects of hyperspectral data and its acquisition. 3.3 Hyperspectral remote sensing and supervised classification. 3.4 Mathematical foundations of supervised classification. 3.5 From structural risk minimization to a support vector machine algorithm. 3.6 Benchmark hyperspectral data sets. 3.7 Results. 3.8 Using spatial coherence. 3.9 Why do SVMs perform better than other methods? 3.10 Conclusions. References. 4 On training and evaluation of SVM for remote sensing applications (Giles M. Foody). 4.1 Introduction. 4.2 Classification for thematic mapping. 4.3 Overview of classification by a SVM. 4.4 Training stage. 4.5 Testing stage. 4.6 Conclusion. Acknowledgments. References. 5 Kernel Fishers Discriminant with heterogeneous kernels (M. Murat Dundar and Glenn Fung). 5.1 Introduction. 5.2 Linear Fishers Discriminant. 5.3 Kernel Fisher Discriminant. 5.4 Kernel Fishers Discriminant with heterogeneous kernels. 5.5 Automatic kernel selection KFD algorithm. 5.6 Numerical results. 5.7 Conclusion. References. 6 Multi-temporal image classification with kernels (Jordi Munoz-Mari, Luis Gomez-Choa, Manel Martinez-Ramon, Jose Luis Rojo-Alvarez, Javier Calpe-Maravilla and Gustavo Camps-Valls). 6.1 Introduction. 6.2 Multi-temporal classification and change detection with kernels. 6.3 Contextual and multi-source data fusion with kernels. 6.4 Multi-temporal/-source urban monitoring. 6.5 Conclusions. Acknowledgments. References. 7 Target detection with kernels (Nasser M. Nasrabadi). 7.1 Introduction. 7.2 Kernel learning theory. 7.3 Linear subspace-based anomaly detectors and their kernel versions. 7.4 Results. 7.5 Conclusion. References. 8 One-class SVMs for hyperspectral anomaly detection (Amit Banerjee, Philippe Burlina and Chris Diehl). 8.1 Introduction. 8.2 Deriving the SVDD. 8.3 SVDD function optimization. 8.4 SVDD algorithms for hyperspectral anomaly detection. 8.5 Experimental results. 8.6 Conclusions. References. III Semi-supervised image classification. 9 A domain adaptation SVM and a circular validation strategy for land-cover maps updating (Mattia Marconcini and Lorenzo Bruzzone). 9.1 Introduction. 9.2 Literature survey. 9.3 Proposed domain adaptation SVM. 9.4 Proposed circular validation strategy. 9.5 Experimental results. 9.6 Discussions and conclusion. References. 10 Mean kernels for semi-supervised remote sensing image classification (Luis Gomez-Chova, Javier Calpe-Maravilla, Lorenzo Bruzzone and Gustavo Camps-Valls). 10.1 Introduction. 10.2 Semi-supervised classification with mean kernels. 10.3 Experimental results. 10.4 Conclusions. Acknowledgments. References. IV Function approximation and regression. 11 Kernel methods for unmixing hyperspectral imagery (Joshua Broadwater, Amit Banerjee and Philippe Burlina). 11.1 Introduction. 11.2 Mixing models. 11.3 Proposed kernel unmixing algorithm. 11.4 Experimental results of the kernel unmixing algorithm. 11.5 Development of physics-based kernels for unmixing. 11.6 Physics-based kernel results. 11.7 Summary. References. 12 Kernel-based quantitative remote sensing inversion (Yanfei Wang, Changchun Yang and Xiaowen Li). 12.1 Introduction. 12.2 Typical kernel-based remote sensing inverse problems. 12.3 Well-posedness and ill-posedness. 12.4 Regularization. 12.5 Optimization techniques. 12.6 Kernel-based BRDF model inversion. 12.7 Aerosol particle size distribution function retrieval. 12.8 Conclusion. Acknowledgments. References. 13 Land and sea surface temperature estimation by support vector regression (Gabriele Moser and Sebastiano B. Serpico). 13.1 Introduction. 13.2 Previous work. 13.3 Methodology. 13.4 Experimental results. 13.5 Conclusions. Acknowledgments. References. V Kernel-based feature extraction. 14 Kernel multivariate analysis in remote sensing feature extraction (Jeronimo Arenas-Garcia and Kaare Brandt Petersen). 14.1 Introduction. 14.2 Multivariate analysis methods. 14.3 Kernel multivariate analysis. 14.4 Sparse Kernel OPLS. 14.5 Experiments: pixel-based hyperspectral image classification. 14.6 Conclusions. Acknowledgments. References. 15 KPCA algorithm for hyperspectral target/anomaly detection (Yanfeng Gu). 15.1 Introduction. 15.2 Motivation. 15.3 Kernel-based feature extraction in hyperspectral images. 15.4 Kernel-based target detection in hyperspectral images. 15.5 Kernel-based anomaly detection in hyperspectral images. 15.6 Conclusions. Acknowledgments References. 16 Remote sensing data Classification with kernel nonparametric feature extractions (Bor-Chen Kuo, Jinn-Min Yang and Cheng-Hsuan Li). 16.1 Introduction. 16.2 Related feature extractions. 16.3 Kernel-based NWFE and FLFE. 16.4 Eigenvalue resolution with regularization. 16.5 Experiments. 16.6 Comments and conclusions. References. Index.

Kernel-Based Framework for Multitemporal and Multisource Remote Sensing Data Classification and Change Detection

The multitemporal classification of remote sensing images is a challenging problem, in which the efficient combination of different sources of information (e.g., temporal, contextual, or multisensor) can improve the results. In this paper, we present a general framework based on kernel methods for the integration of heterogeneous sources of information. Using the theoretical principles in this framework, three main contributions are presented. First, a novel family of kernel-based methods for multitemporal classification of remote sensing images is presented. The second contribution is the development of nonlinear kernel classifiers for the well-known difference and ratioing change detection methods by formulating them in an adequate high-dimensional feature space. Finally, the presented methodology allows the integration of contextual information and multisensor images with different levels of nonlinear sophistication. The binary support vector (SV) classifier and the one-class SV domain description classifier are evaluated by using both linear and nonlinear kernel functions. Good performance on synthetic and real multitemporal classification scenarios illustrates the generalization of the framework and the capabilities of the proposed algorithms.

Classification of Hyperspectral Images With Regularized Linear Discriminant Analysis

This paper analyzes the classification of hyperspectral remote sensing images with linear discriminant analysis (LDA) in the presence of a small ratio between the number of training samples and the number of spectral features. In these particular ill-posed problems, a reliable LDA requires one to introduce regularization for problem solving. Nonetheless, in such a challenging scenario, the resulting regularized LDA (RLDA) is highly sensitive to the tuning of the regularization parameter. In this context, we introduce in the remote sensing community an efficient version of the RLDA recently presented by Ye to cope with critical ill-posed problems. In addition, several LDA-based classifiers (i.e., penalized LDA, orthogonal LDA, and uncorrelated LDA) are compared theoretically and experimentally with the standard LDA and the RLDA. Method differences are highlighted through toy examples and are exhaustively tested on several ill-posed problems related to the classification of hyperspectral remote sensing images. Experimental results confirm the effectiveness of the presented RLDA technique and point out the main properties of other analyzed LDA techniques in critical ill-posed hyperspectral image classification problems.

Robust support vector method for hyperspectral data classification and knowledge discovery

We propose the use of support vector machines (SVMs) for automatic hyperspectral data classification and knowledge discovery. In the first stage of the study, we use SVMs for crop classification and analyze their performance in terms of efficiency and robustness, as compared to extensively used neural and fuzzy methods. Efficiency is assessed by evaluating accuracy and statistical differences in several scenes. Robustness is analyzed in terms of: (1) suitability to working conditions when a feature selection stage is not possible and (2) performance when different levels of Gaussian noise are introduced at their inputs. In the second stage of this work, we analyze the distribution of the support vectors (SVs) and perform sensitivity analysis on the best classifier in order to analyze the significance of the input spectral bands. For classification purposes, six hyperspectral images acquired with the 128-band HyMAP spectrometer during the DAISEX-1999 campaign are used. Six crop classes were labeled for each image. A reduced set of labeled samples is used to train the models, and the entire images are used to assess their performance. Several conclusions are drawn: (1) SVMs yield better outcomes than neural networks regarding accuracy, simplicity, and robustness; (2) training neural and neurofuzzy models is unfeasible when working with high-dimensional input spaces and great amounts of training data; (3) SVMs perform similarly for different training subsets with varying input dimension, which indicates that noisy bands are successfully detected; and (4) a valuable ranking of bands through sensitivity analysis is achieved.