An Efficient Method for Supervised Hyperspectral Band Selection
TL;DR: A new supervised band-selection algorithm that uses the known class signatures only without examining the original bands or the need of class training samples is proposed, which can complete the task much faster than traditional methods that test bands or band combinations.
Abstract: Band selection is often applied to reduce the dimensionality of hyperspectral imagery. When the desired object information is known, it can be achieved by finding the bands that contain the most object information. It is expected that these bands can provide an overall satisfactory detection and classification performance. In this letter, we propose a new supervised band-selection algorithm that uses the known class signatures only without examining the original bands or the need of class training samples. Thus, it can complete the task much faster than traditional methods that test bands or band combinations. The experimental result shows that our approach can generally yield better results than other popular supervised band-selection methods in the literature.
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TL;DR: This paper proposes to eliminate the drawbacks of traditional salient band selection methods by manifold ranking and puts the band vectors in the more accurate manifold space and treats the saliency problem from a novel ranking perspective, which is considered to be the main contributions of this paper.
Abstract: Saliency detection has been a hot topic in recent years, and many efforts have been devoted in this area. Unfortunately, the results of saliency detection can hardly be utilized in general applications. The primary reason, we think, is unspecific definition of salient objects, which makes that the previously published methods cannot extend to practical applications. To solve this problem, we claim that saliency should be defined in a context and the salient band selection in hyperspectral image (HSI) is introduced as an example. Unfortunately, the traditional salient band selection methods suffer from the problem of inappropriate measurement of band difference. To tackle this problem, we propose to eliminate the drawbacks of traditional salient band selection methods by manifold ranking. It puts the band vectors in the more accurate manifold space and treats the saliency problem from a novel ranking perspective, which is considered to be the main contributions of this paper. To justify the effectiveness of the proposed method, experiments are conducted on three HSIs, and our method is compared with the six existing competitors. Results show that the proposed method is very effective and can achieve the best performance among the competitors.
444 citations
Cites background from "An Efficient Method for Supervised ..."
...[22] select the bands with an incremental manner....
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05 Feb 2013
TL;DR: An overview of both conventional and advanced feature reduction methods, with details on a few techniques that are commonly used for analysis of hyperspectral data.
Abstract: Hyperspectral sensors record the reflectance from the Earth's surface over the full range of solar wavelengths with high spectral resolution. The resulting high-dimensional data contain rich information for a wide range of applications. However, for a specific application, not all the measurements are important and useful. The original feature space may not be the most effective space for representing the data. Feature mining, which includes feature generation, feature selection (FS), and feature extraction (FE), is a critical task for hyperspectral data classification. Significant research effort has focused on this issue since hyperspectral data became available in the late 1980s. The feature mining techniques which have been developed include supervised and unsupervised, parametric and nonparametric, linear and nonlinear methods, which all seek to identify the informative subspace. This paper provides an overview of both conventional and advanced feature reduction methods, with details on a few techniques that are commonly used for analysis of hyperspectral data. A general form that represents several linear and nonlinear FE methods is also presented. Experiments using two widely available hyperspectral data sets are included to illustrate selected FS and FE methods.
359 citations
Cites methods from "An Efficient Method for Supervised ..."
...In [34], FS is treated as a task to make the class mean signatures the best endmembers (a concept used in spectral unmixing [91])....
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TL;DR: Current hyperspectral band selection methods are reviewed, which can be classified into six main categories: ranking based, searching based, clustering based, sparsity based, embedding-learning based, embedded learning based, and hybrid-scheme based.
Abstract: A hyperspectral imaging sensor collects detailed spectral responses from ground objects using hundreds of narrow bands; this technology is used in many real-world applications. Band selection aims to select a small subset of hyperspectral bands to remove spectral redundancy and reduce computational costs while preserving the significant spectral information of ground objects. In this article, we review current hyperspectral band selection methods, which can be classified into six main categories: ranking based, searching based, clustering based, sparsity based, embedding-learning based, and hybrid-scheme based. With two widely used hyperspectral data sets, we illustrate the classification performances of several popular band selection methods. The challenges and research directions of hyperspectral band selection are also discussed.
246 citations
Cites methods from "An Efficient Method for Supervised ..."
...Similarly, in [49], using class spectral signatures, the minimum estimation abundance covariance (MEAC) algorithm incrementally selected dissimilar bands to preserve the desired information for classification through minimization of the trace of abundance covariance matrix as...
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TL;DR: Zhang et al. as mentioned in this paper proposed a new clustering-based band selection framework to solve the problem of suboptimal solutions toward a specific objective function, which can obtain the optimal clustering result for a particular form of objective under a reasonable constraint.
Abstract: Band selection, by choosing a set of representative bands in a hyperspectral image, is an effective method to reduce the redundant information without compromising the original contents. Recently, various unsupervised band selection methods have been proposed, but most of them are based on approximation algorithms which can only obtain suboptimal solutions toward a specific objective function. This paper focuses on clustering-based band selection and proposes a new framework to solve the above dilemma, claiming the following contributions: 1) an optimal clustering framework, which can obtain the optimal clustering result for a particular form of objective function under a reasonable constraint; 2) a rank on clusters strategy, which provides an effective criterion to select bands on existing clustering structure; and 3) an automatic method to determine the number of the required bands, which can better evaluate the distinctive information produced by certain number of bands. In experiments, the proposed algorithm is compared with some state-of-the-art competitors. According to the experimental results, the proposed algorithm is robust and significantly outperforms the other methods on various data sets.
195 citations
TL;DR: A multigraph determinantal point process (MDPP) model is proposed to capture the full structure between different bands and efficiently find the optimal band subset in extensive hyperspectral applications.
Abstract: Band selection, as a special case of the feature selection problem, tries to remove redundant bands and select a few important bands to represent the whole image cube. This has attracted much attention, since the selected bands provide discriminative information for further applications and reduce the computational burden. Though hyperspectral band selection has gained rapid development in recent years, it is still a challenging task because of the following requirements: 1) an effective model can capture the underlying relations between different high-dimensional spectral bands; 2) a fast and robust measure function can adapt to general hyperspectral tasks; and 3) an efficient search strategy can find the desired selected bands in reasonable computational time. To satisfy these requirements, a multigraph determinantal point process (MDPP) model is proposed to capture the full structure between different bands and efficiently find the optimal band subset in extensive hyperspectral applications. There are three main contributions: 1) graphical model is naturally transferred to address band selection problem by the proposed MDPP; 2) multiple graphs are designed to capture the intrinsic relationships between hyperspectral bands; and 3) mixture DPP is proposed to model the multiple dependencies in the proposed multiple graphs, and offers an efficient search strategy to select the optimal bands. To verify the superiority of the proposed method, experiments have been conducted on three hyperspectral applications, such as hyperspectral classification, anomaly detection, and target detection. The reliability of the proposed method in generic hyperspectral tasks is experimentally proved on four real-world hyperspectral data sets.
174 citations
Cites background from "An Efficient Method for Supervised ..."
...4) Extensive empirical studies with four publicly available data sets are conducted on three important applications, such as hyperspectral classification [48], anomaly detection [49], and target detection [50] (Section IV)....
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References
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Book•
01 Jan 1982
TL;DR: In this article, the authors present an overview of the basic concepts of multivariate analysis, including matrix algebra and random vectors, as well as a strategy for analyzing multivariate models.
Abstract: (NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.) I. GETTING STARTED. 1. Aspects of Multivariate Analysis. Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments. 2. Matrix Algebra and Random Vectors. Some Basics of Matrix and Vector Algebra. Positive Definite Matrices. A Square-Root Matrix. Random Vectors and Matrices. Mean Vectors and Covariance Matrices. Matrix Inequalities and Maximization. Supplement 2A Vectors and Matrices: Basic Concepts. 3. Sample Geometry and Random Sampling. The Geometry of the Sample. Random Samples and the Expected Values of the Sample Mean and Covariance Matrix. Generalized Variance. Sample Mean, Covariance, and Correlation as Matrix Operations. Sample Values of Linear Combinations of Variables. 4. The Multivariate Normal Distribution. The Multivariate Normal Density and Its Properties. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation. The Sampling Distribution of 'X and S. Large-Sample Behavior of 'X and S. Assessing the Assumption of Normality. Detecting Outliners and Data Cleaning. Transformations to Near Normality. II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS. 5. Inferences About a Mean Vector. The Plausibility of ...m0 as a Value for a Normal Population Mean. Hotelling's T 2 and Likelihood Ratio Tests. Confidence Regions and Simultaneous Comparisons of Component Means. Large Sample Inferences about a Population Mean Vector. Multivariate Quality Control Charts. Inferences about Mean Vectors When Some Observations Are Missing. Difficulties Due To Time Dependence in Multivariate Observations. Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids. 6. Comparisons of Several Multivariate Means. Paired Comparisons and a Repeated Measures Design. Comparing Mean Vectors from Two Populations. Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects. Two-Way Multivariate Analysis of Variance. Profile Analysis. Repealed Measures, Designs, and Growth Curves. Perspectives and a Strategy for Analyzing Multivariate Models. 7. Multivariate Linear Regression Models. The Classical Linear Regression Model. Least Squares Estimation. Inferences About the Regression Model. Inferences from the Estimated Regression Function. Model Checking and Other Aspects of Regression. Multivariate Multiple Regression. The Concept of Linear Regression. Comparing the Two Formulations of the Regression Model. Multiple Regression Models with Time Dependant Errors. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model. III. ANALYSIS OF A COVARIANCE STRUCTURE. 8. Principal Components. Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. Large-Sample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation. 9. Factor Analysis and Inference for Structured Covariance Matrices. The Orthogonal Factor Model. Methods of Estimation. Factor Rotation. Factor Scores. Perspectives and a Strategy for Factor Analysis. Structural Equation Models. Supplement 9A Some Computational Details for Maximum Likelihood Estimation. 10. Canonical Correlation Analysis Canonical Variates and Canonical Correlations. Interpreting the Population Canonical Variables. The Sample Canonical Variates and Sample Canonical Correlations. Additional Sample Descriptive Measures. Large Sample Inferences. IV. CLASSIFICATION AND GROUPING TECHNIQUES. 11. Discrimination and Classification. Separation and Classification for Two Populations. Classifications with Two Multivariate Normal Populations. Evaluating Classification Functions. Fisher's Discriminant Function...nSeparation of Populations. Classification with Several Populations. Fisher's Method for Discriminating among Several Populations. Final Comments. 12. Clustering, Distance Methods and Ordination. Similarity Measures. Hierarchical Clustering Methods. Nonhierarchical Clustering Methods. Multidimensional Scaling. Correspondence Analysis. Biplots for Viewing Sample Units and Variables. Procustes Analysis: A Method for Comparing Configurations. Appendix. Standard Normal Probabilities. Student's t-Distribution Percentage Points. ...c2 Distribution Percentage Points. F-Distribution Percentage Points. F-Distribution Percentage Points (...a = .10). F-Distribution Percentage Points (...a = .05). F-Distribution Percentage Points (...a = .01). Data Index. Subject Index.
11,697 citations
"An Efficient Method for Supervised ..." refers background in this paper
...According to [9], the stochastic features of α̂ include...
[...]
...According to [9], the first- and second-order moments of α̂ become...
[...]
TL;DR: In this article, the authors present an overview of the basic concepts of multivariate analysis, including matrix algebra and random vectors, as well as a strategy for analyzing multivariate models.
Abstract: (NOTE: Each chapter begins with an Introduction, and concludes with Exercises and References.) I. GETTING STARTED. 1. Aspects of Multivariate Analysis. Applications of Multivariate Techniques. The Organization of Data. Data Displays and Pictorial Representations. Distance. Final Comments. 2. Matrix Algebra and Random Vectors. Some Basics of Matrix and Vector Algebra. Positive Definite Matrices. A Square-Root Matrix. Random Vectors and Matrices. Mean Vectors and Covariance Matrices. Matrix Inequalities and Maximization. Supplement 2A Vectors and Matrices: Basic Concepts. 3. Sample Geometry and Random Sampling. The Geometry of the Sample. Random Samples and the Expected Values of the Sample Mean and Covariance Matrix. Generalized Variance. Sample Mean, Covariance, and Correlation as Matrix Operations. Sample Values of Linear Combinations of Variables. 4. The Multivariate Normal Distribution. The Multivariate Normal Density and Its Properties. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation. The Sampling Distribution of 'X and S. Large-Sample Behavior of 'X and S. Assessing the Assumption of Normality. Detecting Outliners and Data Cleaning. Transformations to Near Normality. II. INFERENCES ABOUT MULTIVARIATE MEANS AND LINEAR MODELS. 5. Inferences About a Mean Vector. The Plausibility of ...m0 as a Value for a Normal Population Mean. Hotelling's T 2 and Likelihood Ratio Tests. Confidence Regions and Simultaneous Comparisons of Component Means. Large Sample Inferences about a Population Mean Vector. Multivariate Quality Control Charts. Inferences about Mean Vectors When Some Observations Are Missing. Difficulties Due To Time Dependence in Multivariate Observations. Supplement 5A Simultaneous Confidence Intervals and Ellipses as Shadows of the p-Dimensional Ellipsoids. 6. Comparisons of Several Multivariate Means. Paired Comparisons and a Repeated Measures Design. Comparing Mean Vectors from Two Populations. Comparison of Several Multivariate Population Means (One-Way MANOVA). Simultaneous Confidence Intervals for Treatment Effects. Two-Way Multivariate Analysis of Variance. Profile Analysis. Repealed Measures, Designs, and Growth Curves. Perspectives and a Strategy for Analyzing Multivariate Models. 7. Multivariate Linear Regression Models. The Classical Linear Regression Model. Least Squares Estimation. Inferences About the Regression Model. Inferences from the Estimated Regression Function. Model Checking and Other Aspects of Regression. Multivariate Multiple Regression. The Concept of Linear Regression. Comparing the Two Formulations of the Regression Model. Multiple Regression Models with Time Dependant Errors. Supplement 7A The Distribution of the Likelihood Ratio for the Multivariate Regression Model. III. ANALYSIS OF A COVARIANCE STRUCTURE. 8. Principal Components. Population Principal Components. Summarizing Sample Variation by Principal Components. Graphing the Principal Components. Large-Sample Inferences. Monitoring Quality with Principal Components. Supplement 8A The Geometry of the Sample Principal Component Approximation. 9. Factor Analysis and Inference for Structured Covariance Matrices. The Orthogonal Factor Model. Methods of Estimation. Factor Rotation. Factor Scores. Perspectives and a Strategy for Factor Analysis. Structural Equation Models. Supplement 9A Some Computational Details for Maximum Likelihood Estimation. 10. Canonical Correlation Analysis Canonical Variates and Canonical Correlations. Interpreting the Population Canonical Variables. The Sample Canonical Variates and Sample Canonical Correlations. Additional Sample Descriptive Measures. Large Sample Inferences. IV. CLASSIFICATION AND GROUPING TECHNIQUES. 11. Discrimination and Classification. Separation and Classification for Two Populations. Classifications with Two Multivariate Normal Populations. Evaluating Classification Functions. Fisher's Discriminant Function...nSeparation of Populations. Classification with Several Populations. Fisher's Method for Discriminating among Several Populations. Final Comments. 12. Clustering, Distance Methods and Ordination. Similarity Measures. Hierarchical Clustering Methods. Nonhierarchical Clustering Methods. Multidimensional Scaling. Correspondence Analysis. Biplots for Viewing Sample Units and Variables. Procustes Analysis: A Method for Comparing Configurations. Appendix. Standard Normal Probabilities. Student's t-Distribution Percentage Points. ...c2 Distribution Percentage Points. F-Distribution Percentage Points. F-Distribution Percentage Points (...a = .10). F-Distribution Percentage Points (...a = .05). F-Distribution Percentage Points (...a = .01). Data Index. Subject Index.
10,148 citations
Book•
01 Jan 2008
TL;DR: In this paper, the authors present an introduction to quantitative evaluation of satellite and aircraft derived from remotely retrieved data, without detailed mathematical treatment of computer based algorithms, but in a manner conductive to an understanding of their capabilities and limitations.
Abstract: From the Publisher:
The book provides the non-specialist with an introduction to quantitative evaluation of satellite and aircraft derived from remotely retrieved data. Each chapter covers the pros and cons of digital remotely sensed data, without detailed mathematical treatment of computer based algorithms, but in a manner conductive to an understanding of their capabilities and limitations. Problems conclude each chapter.
3,532 citations
TL;DR: Sequential search methods characterized by a dynamically changing number of features included or eliminated at each step, henceforth "floating" methods, are presented and are shown to give very good results and to be computationally more effective than the branch and bound method.
3,104 citations
"An Efficient Method for Supervised ..." refers methods in this paper
..., sequential forward selection (SFS) and sequential forward floating selection (SFFS), can be used [7]....
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TL;DR: A technique which simultaneously reduces the data dimensionality, suppresses undesired or interfering spectral signatures, and detects the presence of a spectral signature of interest is described.
Abstract: Most applications of hyperspectral imagery require processing techniques which achieve two fundamental goals: 1) detect and classify the constituent materials for each pixel in the scene; 2) reduce the data volume/dimensionality, without loss of critical information, so that it can be processed efficiently and assimilated by a human analyst. The authors describe a technique which simultaneously reduces the data dimensionality, suppresses undesired or interfering spectral signatures, and detects the presence of a spectral signature of interest. The basic concept is to project each pixel vector onto a subspace which is orthogonal to the undesired signatures. This operation is an optimal interference suppression process in the least squares sense. Once the interfering signatures have been nulled, projecting the residual onto the signature of interest maximizes the signal-to-noise ratio and results in a single component image that represents a classification for the signature of interest. The orthogonal subspace projection (OSP) operator can be extended to k-signatures of interest, thus reducing the dimensionality of k and classifying the hyperspectral image simultaneously. The approach is applicable to both spectrally pure as well as mixed pixels. >
1,570 citations
"An Efficient Method for Supervised ..." refers methods in this paper
...In order to evaluate the amount of class information and class separability in the selected bands, a supervised classification algorithm, such as orthogonal subspace projection (OSP) [14], constrained linear discriminant analysis (CLDA) [15], or SVM, can be applied....
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...The OSP classifier was chosen for soft classification, and spatial correlation coefficient was calculated between the corresponding classifications maps using all the original bands and the selected bands....
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...This is doable only if no training or test is required for classification (e.g., OSP and CLDA)....
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