Multiple support vector machines (SVMs) with random subspaces [1]-[5] have been performing excellently for hyperspectral image classification to reduce the correlation between features and avoid the Hughes phenomena. In most random subspace methods, features were randomly selected without replacement from the original feature set according to uniform distribution [6]. However, in general, SVM with a Gaussian radial basis function (RBF) kernel is a nonlinear classifier [7]-[8]. It means that if the corresponding feature subset has the largest nonlinear separability with a RBF kernel, then the corresponding SVM can have a better classification performance. Hence, in this study, feature subsets are randomly selected without replacement from a kernel (nonlinear) feature importance [9] determined by the largest nonlinear between-class separability and the smallest nonlinear within-class separability with respect to the RBF kernel. The results from the experiments showed that the proposed method can improve the classification performance using only a few features. In addition, the rate of classification accuracy is higher than those based on the feature subsets determined by the descending order of feature importance.

Many research shows that we will encounter the Highes phenomenon when dealing with the high-dimensional data classification problem. In addition, non-linear support vector machine (SVM) has been shown that it can conquer the problem efficiently. However, the SVM is a black-box model based on the whole features and does not provide the feature importance or “good” feature subset for classification and other applications. In 2012, an automatic kernel parameter selection (APS) based on kernel-based within- and between-class separability measures were proposed. Moreover, the application for determining the kernel parameters of the full bandwidth RBF (FRBF) kernel was proposed. In this study, the bandwidths of the FRBF kernel were considered as the weights of the features when the feature values are rescaled by computing the z-scores. Experimental results on the Indian Pine Site dataset showed that the SVM based on the proposed feature subset outperforms than the SVMs based on the RBF kernel and FRBF kernel.

For hyperspectral image classification, feature extraction is a crucial pre-process for avoiding the Hughes phenomena. Some feature extraction methods such as linear discriminant analysis (LDA), nonparametric weighted feature extraction (NWFE), and their kernel versions, generalized discriminant analysis (GDA) and kernel nonparametric weighted feature extraction method (KNWFE) have been shown that they can improve the classification performance. However, for GDA and KNWFE, it is hard to find the suitable kernel parameters. Hence, although they have been published about 14 or 6 years, respectively, researchers rarely implement them for dealing with hyperspectral image classification problem. An automatic kernel parameter selection method (APS) was proposed to predetermine the appropriate radial basis function (RBF) kernel for support vector machine (SVM) and GDA. In this study, APS was applied to find the suitable RBF kernel function for KNWFE. From the experiment results on PAVIA data set, the classification performance of KNWFE still outperforms those of GDA [10] and SVM [10]. The most important of this research, the kernel parameters of GDA and KNWFE based on RBF kernel can be “automatically” determined and the researcher can implement them directly without tuning the kernel parameter.

Feature extraction can overcome the Hughes phenomenon for hyperspectral image classification. Linear discriminant analysis (LDA) is a basic supervised feature extraction method. However, LDA only cannot extract features more than number of classes. The semi-supervised local discriminant analysis (SELD) was proposed to solve the above problem by combing the scatter matrices of LDA and the neighborhood preserving embedding (NPE). Some unlabeled samples were used to form the scatter matrices of NPE. It can preserve the local geometric property according to the used unlabeled samples. Moreover, the between-class scatter matrix of SELD is nonsingular, and more features can be extracted by applying SELD. However, in SELD, the unlabeled sample were randomly selected. The local geometric property around the training samples cannot be preserved due to the randomly selection. In this study, the concept of the Voronoi diagram is used to determine the regions according to the training samples, and the unlabeled samples are chosen in the regions based on the nearest neighbors. Experimental results on the Indian Pine Site dataset show that the proposed method outperforms SELD with less number of unlabeled samples on the small sample size problem.

The support vector machine (SVM) is widely used in hyperspectral image classification due to the robust to the Hughes phenomenon. However, the performance of SVM highly depends on the kernel parameter selection. Hence, it is hard to apply the SVM based on the kernel with lots of parameters such as the full bandwidth RBF (FRBF) kernel whose number of parameters is equal to the number of features. In our previous study, an automatic kernel parameter selection method (APS) was proposed for the normalized kernel function. The proper kernel parameters are the minimizer of the optimization problem based on the proposed kernel-based class separability measure. In this study, we apply the APS to find the best kernel parameters of the FRBF kernel. Experimental results on the Indian Pine Site dataset show that the SVM based on the FRBF kernel with proper kernel parameters outperforms than the SVM based on the RBF kernel on the small sample size problem.

Most studies showed that most hyperspectral image classification encountered the Hughes phenomenon due to the redundant features, especially in the small sample size problem. Feature extraction method such as linear discriminant analysis (LDA), nonparametric weighted feature extraction (NWFE) is a preprocessing step before classification and used to combine and reduce the original features into a new feature space based on the between-class and with-class separability. Then, the classifier such as the nonlinear support vector machine (SVM) is trained and classifies the unknown samples. However, the separability measurement of LDA and NWFE is for the original space not the kernel-induced feature space. In this study, a kernel-based feature extraction method is proposed. The corresponding transformation matrix for dimension reduction is based on the class separability in the kernel-induced feature space which was proposed in our previous study. Experimental results on the Indian Pine Site dataset show that the proposed method improves the classification performance of the SVM on the small sample size problem.

The purpose of present study is to develop an automated test assembly tool for Chinese word-segmentation test. Word familiarity and word similarity were both controlled in the experiments. The study examined the effectiveness of automated test by comparing its performance with the traditional test, which was developed by linguistic experts. The results of the present study indicated that the children’s performances on traditional Chinese word-segmentation tests and automated Chinese word-segmentation tests were consistent and comparable. Data collected in different age groups and with larger sample size should be investigated for future research.

A Quantum-Modeled Artificial Bee Colony clustering algorithm for remotely sensed multi-band image segmentation is explored and evaluated. Data sets of interest include remotely sensed multi-band RGB imagery, which subsequent to classification is analyzed and assessed for accuracy. Results demonstrate that the algorithm exhibits improved accuracy, when compared to its classical counterpart. Moreover, solutions are enhanced via introduction of the quantum state machine, which provides random initial food sources and variables as input to the Artificial Bee Colony algorithm, and quantum operators, which bring about convergence and maximize local search space exploration. Typically, the algorithm has shown to produce better solutions.

A Quantum-Modeled Fuzzy C-Means clustering algorithm for remotely sensed multi-band image segmentation is explored and evaluated. Data sets of interest include remotely sensed multi-band imagery, which subsequent to classification is analyzed and assessed for accuracy. Results demonstrate that the algorithm exhibits improved accuracy, when compared to its classical counterpart. Moreover, in general, the solution is enhanced via introduction of the quantum state machine in and of itself, which provides random fuzzy membership input to the Fuzzy C-Means soft partitioning algorithm, while the addition of quantum operators provide additional contributions to solution diversity. Typically, when evaluated for cluster validity, the algorithm has shown to produce effective solutions.

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.

Recent studies show that hyperspectral image classification techniques that use both spectral and spatial information are more suitable, effective, and robust than those that use only spectral information. Using a spatial-contextual term, this study modifies the decision function and constraints of a support vector machine (SVM) and proposes two kinds of spatial-contextual SVMs for hyperspectral image classification. One machine, which is based on the concept of Markov random fields (MRFs), uses the spatial information in the original space (SCSVM). The other machine uses the spatial information in the feature space (SCSVMF), i.e., the nearest neighbors in the feature space. The SCSVM is better able to classify pixels of different class labels with similar spectral values and deal with data that have no clear numerical interpretation. To evaluate the effectiveness of SCSVM, the experiments in this study compare the performances of other classifiers: an SVM, a context-sensitive semisupervised SVM, a maximum likelihood (ML) classifier, a Bayesian contextual classifier based on MRFs (ML_MRF), and nearest neighbor classifier. Experimental results show that the proposed method achieves good classification performance on famous hyperspectral images (the Indian Pine site (IPS) and the Washington, DC mall data sets). The overall classification accuracy of the hyperspectral image of the IPS data set with 16 classes is 95.5%. The kappa accuracy is up to 94.9%, and the average accuracy of each class is up to 94.2%.

Linear discriminant analysis (LDA) is a commonly used feature extraction (FE) method to resolve the Hughes phenomenon for classification. The Hughes phenomenon (also called the curse of dimensionality) is often encountered in classification when the dimensionality of the space grows and the size of the training set is fixed, especially in the small sampling size problem. Recent studies show that the spatial information can greatly improve the classification performance. Hence, for hyperspectral image classification, it is not only necessary to use the available spectral information but also to exploit the spatial information. In this paper, a semisupervised feature extraction method which is based on the scatter matrices of the fuzzy-type LDA and uses the semi-information is proposed. The experimental results on two hyperspectral images, the Washington DC Mall and the Indian Pine Site, show that the proposed method can yield a better classification performance than LDA in the small sampling size problem.

Many studies [1]-[2] show that classification techniques with both spectral and spatial information are effective to overcome the similar spectral properties in hyperspectral image classification problem. Moreover, kernel-based methods have attracted much attention in the area of pattern recognition and machine learning, many researches [3]-[5] show that kernel method is computationally efficient, robust, and stable for pattern analysis. In this study, a novel method which automatically determines the coefficient of the composite kernel [5] that was proposed to join both spectral and spatial information for hyperspectral image classification via an optimail method for selecting an proper kernel function is proposed. The experimental results display the better performance of classification via the composite kernel with this novel method to determine the coefficient than using the RBF kernel function with 5-fold cross-validation method and optimal method to select proper parameter on the famous hyperspectral images, Washington DC Mall.

In remote sensing researches, the curse of dimensionality is one greatly difficult classification problem. Many studies have demonstrated that multiple classifier systems, such as the random subspace method (RSM), can alleviate small sample size and high dimensionality concern and obtain more outstanding and robust results than a single classifier on extensive pattern recognition issues. A dynamic subspace method (DSM) was proposed for constructing component classifiers with adaptive subspaces to adjust the shortcomings of RSM based on re substitution accuracy by applying each classifier. However, the performances of SVMs are based on choosing the proper kernel functions or proper parameters of a kernel function. The objective of this research is to develop a novel ensemble technique based on support vector machines (SVMs) via the optimal kernel method, and propose a novel subspace selection mechanism, named the kernel-based dynamic subspace method (KDSM), to improve DSM on automatically determining dimensionality and selecting component dimensions for diverse subspaces. Experimental results show a sound performance of classification on the famous hyperspectral images, Washington DC Mall.

Feature extraction plays an essential role in Hyperspectral image classification. Linear discriminant analysis (LDA) is a commonly used feature extraction (FE) method to resolve the Hughes phenomenon for classification. The Hughes phenomenon (also called the curse of dimensionality) is often encountered in classification when the dimensionality of the space grows and the size of the training set is fixed, especially in the small sampling size problem. Recent studies show that the spatial information can greatly improve the classification performance. Hence, for hyperspectral image classification, it is not only necessary to use the available spectral information but also to exploit the spatial information. In this paper, spatial information is acquired by the concept of the Markov random field (MRF), and this spatial information is used to form the membership values of every pixel in the hyperspectral image. The experimental results on two hyperspectral images, the Washington DC Mall and the Indian Pine Site, show that the proposed method can yield a better classification performance than LDA in the small sampling size problem.

This paper presents a new method for fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. First, we present a method for ranking generalized fuzzy numbers with different left heights and right heights. It can overcome the drawbacks of the existing fuzzy ranking methods. Based on the proposed fuzzy ranking method of generalized fuzzy numbers with different left heights and right heights, we propose a new method for fuzzy risk analysis. The proposed fuzzy risk analysis method provides us with a useful way to deal with fuzzy risk analysis problems.

Research has shown fuzzy c-means (FCM) clustering to be a powerful tool to partition samples into different categories. However, the objective function of FCM is based only on the sum of distances of samples to their cluster centers, which is equal to the trace of the within-cluster scatter matrix. In this study, we propose a clustering algorithm based on both within- and between-cluster scatter matrices, extended from linear discriminant analysis (LDA), and its application to an unsupervised feature extraction (FE). Our proposed methods comprise between- and within-cluster scatter matrices modified from the between- and within-class scatter matrices of LDA. The scatter matrices of LDA are special cases of our proposed unsupervised scatter matrices. The results of experiments on both synthetic and real data show that the proposed clustering algorithm can generate similar or better clustering results than 11 popular clustering algorithms: K-means, K-medoid, FCM, the Gustafson-Kessel, Gath-Geva, possibilistic c-means (PCM), fuzzy PCM, possibilistic FCM, fuzzy compactness and separation, a fuzzy clustering algorithm based on a fuzzy treatment of finite mixtures of multivariate Student's t distributions algorithms, and a fuzzy mixture of the Student's t factor analyzers model. The results also show that the proposed FE outperforms principal component analysis and independent component analysis.

In the kernel methods, it is very important to choose a proper kernel function to avoid overlapping data. Based this fact, in this paper we mainly utilize a unified kernel optimization framework on the hyperspectral image classification to augment the margin between different classes, and under the kernel optimization framework, to employ the Fisher discriminant criteria formulated in a pairwise manner as the objective functions to optimize the kernel function in Kernel-based nonparametric weighted feature extraction. The experimental results display the superiority of the optimizing kernel function over the RBF kernel function with 5-fold cross-validation method, especially, in the small sample size problem.

In this study, a novel spatial information based support vector machine for hyperspectral image classification, named spatial-contextual semi-supervised support vector machine (SC3SVM), is proposed. This approach modifies the SVM algorithm by using the spectral information and spatial-contextual information. The concept of SC3SVM is to utilize other information, obtain from the pixels of a neighborhood system in the spatial domain, to modify the effective of each patterns. Experimental results show a sound performance of classification on the famous hyperspectral images, Indian Pine site. Especially, the overall classification accuracy of whole hyperspectral image (Indian Pine site with 16 classes) is up to 96.4%, the kappa accuracy is up to 95.9%.

In this paper, a novel classification processing based on the spatial information and the concept of Adaboost for hyperspectral image classification is proposed. This classification process is named as adaptive feature extraction with spatial information (AdaFESI). The main idea is adaptive in the sense that subsequent feature spaces are tweaked in favor of those instances misclassified by spectral or spatial classifiers in the previous feature space. All training samples are projected into these feature spaces to train various classifiers and then constitute a multiple classifier system. The experimental results based on two hyperspectral data sets show that the proposed algorithm can generate better classification results.

Support vector machine (SVM) is one of the most powerful techniques for supervised classification. However, the performances of SVMs are based on choosing the proper kernel functions or proper parameters of a kernel function. It is extremely time consuming by applying the k-fold cross-validation (CV) to choose the almost best parameter. Nevertheless, the searching range and fineness of the grid method should be determined in advance. In this paper, an automatic method for selecting the parameter of the RBF kernel function is proposed. In the experimental results, it costs very little time than k-fold cross-validation for selecting the parameter by our proposed method. Moreover, the corresponding SVMs can obtain more accurate or at least equal performance than SVMs by applying k-fold cross-validation to determine the parameter.

Growing numbers of traffic accidents had become a serious social safety problem in recent years. The main factor of the high fatalities was the obvious decline of the driver's cognitive state in their perception, recognition and vehicle control abilities while being sleepy. The key to avoid the terrible consequents is to build a detecting system for ongoing assessment of driver's cognitive state. A quickly growing research, brain-computer interface (BCI), offers a solution offering great assistance to those who require alternative communicatory and control mechanisms. In this study, we propose an alertness/drowsiness classification system based on investigating electroencephalographic (EEG) brain dynamics in lane-keeping driving experiments in a virtual reality (VR) driving environment with a motion platform. The core of the classification system is composed of dimension reduction technique and classifier learning algorithm. In order to find the suitable method for better describing the data structure, we explore the performances using different feature extraction and feature selection methods with different classifiers. Experiment results show that the accuracy is over 80% in most combinations and even near 90% under Principal Component Analysis (PCA) and Nonparametric Weighted Feature Extraction (NWFE) going with Gaussian Maximum Likelihood classifier (ML) and k-Nearest-Neighbor classifier (kNN), respectively. In addition, this developed classification system can also solve the individual brain dynamic differences caused from different subjects and overcome the subject dependent limitation. The optimized solution with better accuracy performance out of all combinations can be considered to implement in the kernel brain-computer interface.

Past studies reported that the main electrogastrography (EEG) dynamic changes related to motion sickness (MS) were occurred in occipital, parietal, and somatosensory brain area, especially in the power increasing of the alpha band (8-13 Hz) and theta band (4-7 Hz) which had positive correlation with the subjective MS level. Depend on these main findings correlated with MS, we attempt to develop an EEG based classification system to automatically classify subject's MS level and find the suitable EEG features via common feature extraction, selection and classifiers technologies in this study. If we can find the regulations and then develop an algorithm to predict MS occurring, it would be a great benefit to construct a safe and comfortable environment for all drivers and passengers when they are cruising in the car, bus, ship or airplane. EEG is one of the best methods for monitoring the brain dynamics induced by motion-sickness because of its high temporal resolution and portability. After collecting the EEG signals and subjective MS level in a realistic driving environment, we first do the data pre-processing part including ICA, component clustering analysis and time-frequency analysis. Then we adopt three common feature extractions and two feature selections (FE/FS) technologies to extract or select the correlated features such as principal component analysis (PCA), linear discriminate analysis (LDA), nonparametric weighted feature extraction (NWFE), forward feature selections (FFS) and backward feature selections (BFS) and feed the feature maps into three classifiers (Gaussian Maximum Likelihood Classifier (ML), k-Nearest-Neighbor Classifier (kNN) and Support Vector Machine (SVM)). Experimental results show that classification performance of all our proposed technologies can be reached almost over 95%. It means it is possible to apply the effective technology combination to predict the subject's MS level in the real life applications. The better combination in this study is using LDA and Gaussian based ML classifier. This advantage can be widely used in machine learning area for developing the prediction algorithms in the future.

The 24 papers in this special issue focus on hyperspectral image and signal processing.

For the classification among different land-cover types in a hyperspectral image, particularly in the small-sample-size situation, a feature-extraction method is an approach for reducing the dimensionality and increasing the classification accuracy. Fisher's linear discriminant analysis (LDA) is one of the most popular feature-extraction methods. However, it cannot be applied directly to the classification of hyperspectral image because of several natures of Fisher's criterion. Nonparametric discriminant analysis (NDA) and nonparametric weighted feature extraction, on the other hand, are two extensions of LDA with a creative idea about emphasizing the boundary structure of class distributions. However, the overlap situation was not considered in these methods and thus decreased the robustness of these methods. In this paper, a new feature-extraction method is introduced based on a structure named double nearest proportion. This structure enables the proposed method to reduce the effect of overlap, allows a new regularization technique to be embedded, and includes LDA and NDA as special cases. These properties enable the proposed method to be more robust and thus, generally, have better performance.

Many studies have demonstrated that multiple classifier systems, such as the random subspace method (RSM), obtain more outstanding and robust results than a single classifier on extensive pattern recognition issues. In this paper, we propose a novel subspace selection mechanism, named the dynamic subspace method (DSM), to improve RSM on automatically determining dimensionality and selecting component dimensions for diverse subspaces. Two importance distributions are proposed to impose on the process of constructing ensemble classifiers. One is the distribution of subspace dimensionality, and the other is the distribution of band weights. Based on the two distributions, DSM becomes an automatic, dynamic, and adaptive ensemble. The real data experimental results show that the proposed DSM obtains sound performances than RSM, and that the classification maps remarkably produce fewer speckles.

Feature extraction plays an essential role in hyperspectral image classification. Nonparametric feature extraction algorithms have more advantages than parametric ones and are well suited for nonnormally distributed data along with being able to extract more features than the classic linear discriminant analysis. In this paper, a novel nonparametric feature extraction method, namely, cosine-based nonparametric feature extraction (CNFE), is proposed, in which the weight function embedded in the within-class and between-class scatter matrices is developed based on cosine distance. Moreover, a powerful K-nearest neighbor (KNN) classification algorithm based on the distance metric formed by CNFE features is also developed, which is called the CNFE-based KNN (CKNN) classifier. The effectiveness of the proposed CNFE and CKNN is evaluated by two hyperspectral real data sets. The experimental results demonstrate that both the proposed CNFE and CKNN achieve remarkable performances on various types of training sample sizes, including the small-sample-size cases.

Many existing pattern recognition techniques require the estimation of the covariance matrix. When the number of available samples is sufficient large relative to the dimension the features, a maximum likelihood estimator or a related unbiased covariance matrix estimator can be applied. In the classification task of the hyperspectral image, however, the number of available observations is very limited or even smaller than the number of bands due to the access of the ground truth samples is costly and valuable. In this case, the performance of the maximum likelihood related estimators will be poor. Thus, the classification accuracy of the corresponding classification methods is unsatisfied. Based on the idea of combining several different structures in an estimator, a new covariance matrix estimator called localized shrinkage covariance estimator (LSCE) is proposed in this study. The performance of LSCE is evaluated via the classification accuracy of the linear discriminant classifier (LDC) using LSCE as the estimator of its covariance matrix. The results of the simulation studies show that LSCE is an ideal covariance estimator and the classical method LDC can be a very competitive classifier comparing to other popular techniques in hyperspectral data classification.

Combining multiple classifiers is a natural way to discover useful information and improve the performances of individual classifiers. It's based on the combination of the outputs of an ensemble of different classifiers. When interactions exist in combining multiple classifiers, fuzzy integral would be a valid method to fuse multiple classifiers. In this fuzzy fusion approach, the fuzzy measure plays an important role. Liu proposed a novel fuzzy measure, L-measure, which is more sensitive than some common measures, like ¿-measure, P-measure and V-measure. In this paper, we would combine the multiple classifiers by Choquet integral wtih this Z-measure.

In recent years, many studies show that kernel methods are computationally efficient, robust, and stable for pattern analysis. Many kernel-based classifiers were designed and applied to classify remote-sensed data, and some results show that kernel-based classifiers have satisfying performances. Many studies about hyperspectral image classification also show that nonparametric weighted feature extraction (NWFE) is a powerful tool for extracting hyperspectral image features. However, NWFE is still based on linear transformation. In this paper, the kernel method is applied to extend NWFE to kernel-based NWFE (KNWFE). The new KNWFE possesses the advantages of both linear and nonlinear transformation, and the experimental results show that KNWFE outperforms NWFE, decision-boundary feature extraction, independent component analysis, kernel-based principal component analysis, and generalized discriminant analysis.

The k-nearest neighbor classifier is a simple and appealing approach to classification problems. It expects the class conditional probabilities to be locally constant, and suffers from bias in high dimensional situation. Using a locally adaptive metric becomes crucial in order to keep class conditional probabilities close to uniform, thereby minimizing the bias of estimates. A technique that computes a locally flexible metric by means of the decision boundaries of support vector machines (SVMs) is proposed. Then the modified neighborhoods can be shrunk in directions orthogonal to these decision boundaries and elongated parallel to the boundaries. Thereafter, any neighborhood-based classifier can use the modified neighborhoods.

AdaBoost algorithm is one of the very successful classifier combining methods in recent years. To imply the AdaBoost method for hyperspectral image classification problem, especially when the sample size is limited (small), a proper feature extraction method might be very helpful for increasing the accuracy rate. In this research, a scheme is proposed to properly joint the nonparametric weighted feature extraction (NWFE) with the AdaBoost algorithm. The performance of the proposed scheme is evaluated via the real spectral image, Washington DC Mall. Results showed that the proposed method do reduce the classification error rate.

This paper introduces a new adaptive fuzzy clustering algorithm which combines the capability of fuzzy mathematics and adaptation. This adaptive capability is achieved by using the mechanism of splitting and merging. Unlike most of the fuzzy clustering algorithms which require a priori knowledge about the number of classes in the dataset, this new algorithm can learn the number of classes dynamically. It also gives the higher accuracy of clustering results with fuzzy mathematics. A comparison with the K-Means, ISODATA, Fuzzy C-Means and Possibilistic C-Means shows that the algorithm is effective in image segmentation. The algorithm also enhances the adaptive capability of the ISODATA.

Many studies have demonstrated that multiple classifier systems, such as random subspace method, obtain more outstanding and robust results than a single classifier. In this study, we propose a novel RSM framework which is composed of two parts. The first part is the construction of a weighted RSM, where weights are given by two classifier-based distributions. One is the feature weighting distribution, and the other is the subspace dimensionality distribution that helps for dynamically selecting the size of subspace with respect to the employed classifiers. The second part is to introduce the spatial information estimated by the Markov random filed theory into the Bayesian classifiers used in the framework. The real data experimental results show that the proposed framework obtains satisfactory performances, and the classification maps remarkably produce fewer speckles.

In this paper, a new fuzzy clustering, namely fuzzy c-weighted mean (FCWM), is being proposed. The cost function of the classical fuzzy c-mean (FCM) is defined by the distances from data to the cluster centers with their fuzzy memberships. Another idea for estimating the cluster centers originating form the idea of weighted mean applied in nonparametric weighted feature extraction (NWFE) is introduced to established a novel FCM-like clustering algorithm in this study. The real data experimental results show that the proposing FCWM outperforms the original FCM.

In this study, two kernel-based classifiers are applied to hyperspectral image classification. One is the kernel Gaussian classifier, and the other is the kernel k-nearest-neighbor classifier. For classification in feature space, the data are mapped from the input-space into a higher dimensional feature space by utilizing a nonlinear transformation, and then we can perform the k-nearest-neighbor classifier and the Gaussian classifier on the mapped images in that space. Fortunately, instead of doing the expensive transformation of samples, the classification can be performed via inner products in feature space and use the kernel function to efficiently compute the inner products which is the so-called kernel trick. The effectiveness of the proposed classifiers is evaluated by real datasets and other classifiers are included for comparison. The experimental results show that the kernel Gaussian classifier outperforms the others.

Usually feature extraction is applied for dimension reduction in hyperspectral data classification problems. Many studies show that nonparametric weighted feature extraction (NWFE) is a powerful tool for extracting hyperspectral image features. The detection of class boundaries is an important part in NWFE and the weighted mean was defined for this purpose. In this paper, a kernel-based feature extraction is proposed based on a new class boundary detection mechanism. The soft-margin support vector machine (SVM) binary classifier and the support vector domain description (SVDD) are applied to detect the boundaries between two classes and one class, respectively. The results of real data experiments show that the proposed method outperforms original NWFE.

Each pixel of the hyperspectral image is composed of hundreds of individual bands. Usually, these pixels are considered as high dimensional vectors. NWFE is a very robust and superior feature extraction method in this aspect of view of image pixel. On the other hand, since adjacent bands in a pixel are usually highly correlated, each pixel can also be viewed as a time series or signal. Therefore, the classification of hyperspectral data becomes the problem of distinguishing between different time series. As the consequence, time series discrimination methods, such as SLEX related time series methods, can then be applied in the classification of hyperspectral image. In this paper, a selection ensemble of NWFE and SLEX is proposed for classifying multi-group hyperspectral image. The performance of the proposed scheme is compared to SLEX and NWFE both by simulation data set and real hyperspectral image dataset, Washington DC Mall. These results show that the proposed scheme has higher testing data classification accuracy than others.

This paper explores the effectiveness of the rough set theory in multispectral image classification. A new multispectral image classification approach is proposed based on the rough set theory which uses upper and lower bounds for the class description. Rough set theory is used for classification rules extraction. A comparison of this method with the parallelepiped classifier, where the former uses the concept of cuts and the later uses the maximum and minimum values, is compared. Preliminary experimental results show that the proposed classifier is effective for multispectral image classification.

In this study, we proposed some alternatives for building a binary hierarchical classification (BHC) systems. Two criteria for building the hierarchical tree under the idea of max-cut are addressed and two additional classification architectures based on the constructed trees are also proposed. The performances of these BHC schemes on Indian Pine Site hyperspectral image will be compared by means of using different base classifiers maximum likelihood (ML),support vector machine (SVM) and 1-nearest-neighbor (INN). The experimental results show that the addressed criteria and classification architectures have satisfactory performances.

Kernel nonparametric feature extraction (KNWFE) is a power tool for hyperspectral image classification in feature space. However, the performances of KNWFE largely depend on the choices of kernels. In this paper, a method is proposed for optimizing kernel function using the weighted means of KNWFE and the Fisher scalar with respect to KNWFE. The idea is to obtain a feature space with the largest nonparametric separability of training samples between classes by employing the parameters of a conformal transformation of a basic kernel. Experimental results show that the proposed method has a remarkable improvement of KNWFE for real data for two-classe problem.

In this paper, a novel non-parametric weighted linear feature extraction method has been developed for classifying hyperspectral image data with limited training samples. Within this framework, we found two important vectors for each training sample and calculated the magnitude of projection of the two vectors to weight it when designing the within-class and between-class scatter matrix. The effectiveness of the proposed feature extraction scheme as compared to two other nonparametric feature extraction methods, nonparametric weighted feature extraction (NWFE), and nonparametric discriminant analysis (NDA), is demonstrated using Washington DC Mall data. From the experimental results, the proposed method is remarkably powerful and robust.

Accidents caused by errors and failures in human performance among traffic fatalities have a high rate causing death and become an important issue in public security. The key problem causing these car accidents is mainly because that the drivers failed to perceive the changes of the traffic lights or the unexpected conditions happening accidentally on the roads. In this paper, we devised a quantitative analysis for ongoing assessment of driver's cognitive responses by investigating the neurobiological information underlying electroencephalographic (EEG) brain dynamics in traffic-light experiments in a virtual-reality (VR) dynamic driving environment. Three different feature extraction methods including nonparametric weighted feature extraction (NWFE), principal component analysis (PCA), discriminant analysis feature extraction (DAFE) are applied to reduce the feature dimension and project the measured EEG signals to a feature space spanned by their eigenvectors. After that, the mapped data can be classified with fewer features and their classification results are compared by utilizing three different classifiers including Gaussian classifier (GC), k nearest neighbor classification (KNNC), and naive Bayes classifier (NBC). Experimental results show that the successful rate of nonparametric weighted feature extraction combined with Gaussian classifier is higher more than 10% compared with other combinations. It also demonstrates the feasibility of detecting and analyzing single-trail ERP signals that represent operators' cognitive states and responses to task events.

Much research has shown that the definitions of within-class and between-class scatter matrices and regularization technique are the key components to design a feature extraction for small sample size problems. In this paper, we illustrate the importance of another key component, eigenvalue decomposition method, and a new regularization technique was proposed. In the hyperspectral image experiment, the effects of these three components of feature extraction are explored on ill-posed and poorly posed conditions. The experimental results show that different regularization methods need to cooperate with different eigenvalue decomposition methods to reach the best performance, the proposed regularization method, regularized feature extraction (RFE) outperform others, and the best feature extraction for a small sample size classification problem is RFE with nonparametric weighted scatter matrices.

In this paper, a new discrimination scheme is proposed for classifying multi-group hyperspectral image. The smooth localized complex exponentials (SLEX) library and a modified Bottom-Up Generalized Local Discriminant Bases (MGLDB-BU) algorithm are adopted for extracting ideal features for discrimination. With the extracted features, a mechanism based on Chernoff information is employed for classification. The effectiveness of the proposed scheme as compared to DAFE and NWFE is reported using real hyperspectral image dataset, Washington DC Mall.

In this study, the performances of hyperspectral image classification using three max-cut based BHC schemes are compared. The first one is original BHC scheme and the second is applied feature extraction in the root node. The last is applied feature extraction in the each non-leaf node. The real data experimental results show that applying feature extraction in the each non-leaf node is the best strategy. Among the combinations of two feature extraction methods, DAFE and NWFE and three base classifiers, using NWFE and ML base classifier can reach the best performance.

Feature extraction is often applied for dimensionality reduction in hyperspectral data classification problems to mitigate the Hughes phenomenon. Some studies had proven that nonparametric weighted feature extraction (NWFE) is a powerful tool to extract well-described features for classification. NWFE concentrates only on the separability of spectral data, however, in many remotely sensed images, objects on the ground are much greater than one pixel. Hence, neighboring pixels are more likely to belong to the same class and form a homogeneous region. We present a scheme to fuse spatial information into NWFE, and from the real data experiments, we can find the proposed method outperforms the original NWFE.

Usually feature extraction is applied for dimension reduction in hyperspectral data classification problems. Some studies show that nonparametric weighted feature extraction (NWFE; Kuo and Landgrebe, 2004) is a powerful tool to extract hyperspectral image features for classification. Recently, some studies also show that kernel-based methods are computationally efficient, robust and stable for pattern analysis. In this study, a kernel-based NWFE (KNWFE) is proposed for hyperspectral image classification. In this paper, we show that KNWFE is a generalization of original NWFE.

In this paper, semi-supervised classification concept is applied to Discriminant Analysis Feature Extraction (DAFE) and Nonparametric Weighted Feature Extraction (NWFE). The proposed semi-supervised DAFE and NWFE use the information of both labeled and unlabeled data in an iterative process. Experimental results of hyperspectral data show that the proposed feature extraction methods can improve the classification performance significantly with limited training samples.

In this paper, a weighted random subspace method (RSM) with automatic subspace dimensionality selection has been proposed for classifying hyperspectral image data. The dimensionality selection method is based on the importance distribution of dimensionality estimated by kernel smoothing technique during the algorithm training. Two feature weighting methods based on normalized re-substitution accuracy and Fisher's LDA separability are introduced for improving the original RSM. Experimental result shows that the proposed algorithm outperforms the original random subspace method.

The parallelepiped classifier is one of the widely used supervised classification algorithms for multispectral images. The threshold of each spectral (class) signature is defined in the training data, which is to determine whether a given pixel within the class or not. To avoid involving the analyst for the training data selection, this paper is to study whether the threshold of parallelepiped classifier can be automatically determined by using natural evolution process - genetic algorithms (GAs). In other words, our goal is to create an unsupervised multispectral parallelepiped classifier with the help of genetic algorithms. In this algorithm, we also use a new approach to estimate the initial range. Preliminary experimental results with different parameters for genetic algorithms and a comparison with the supervised parallelepiped classifier are provided.

In this study, a two-stage feature extraction algorithm cooperated with feature selection is proposed for improving hyperspectral data classification. The first stage feature extraction extracts the features for separating all classes and second stage feature extraction extracts the features for separating individual pair of classes, which cannot be well separated in first stage feature space. Then, feature selection is applied for selecting the best features. Real data experimental result show that the proposed 2-stage feature extraction outperforms single stage feature extraction

A new hybrid algorithm based on bagging and random subspace methods is proposed for improving hyperspectral data classification problem. The effects of using original data and transformed data in bagging, random subspace and the proposed algorithm are also explored. Real data experiment result shows that the proposed method performs well in both original and NWFE feature spaces.

In this paper, a new nonparametric feature extraction method is proposed for high-dimensional multiclass pattern recognition problems. It is based on a nonparametric extension of scatter matrices. There are at least two advantages to using the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired and to reduce the effect of the singularity problem. This is in contrast to parametric discriminant analysis, which usually only can extract L-1 (number of classes minus one) features. In a real situation, this may not be enough. Second, the nonparametric nature of scatter matrices reduces the effects of outliers and works well even for nonnormal datasets. The new method provides greater weight to samples near the expected decision boundary. This tends to provide for increased classification accuracy.

New Gaussian mixture classifiers are designed by replacing the maximum likelihood covariance estimator with regularized covariance estimator in both parameters estimation and model selection steps. The results of simulated and real data experiments suggested that nearest mean clustering and Bayesian information criterion with regularized covariance estimator is a better choice to build a Gaussian mixture classifier.

In this paper, a new nonparametric feature extraction method is proposed for high dimensional multiclass pattern recognition problems. It is based on a nonparametric extension of scatter matrices. There are at least two advantages to using the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired and to reduce the effect of the singularity problem. This is in contrast to parametric discriminant analysis, which usually only can extract L-1 (number of classes minus one) features. In a real situation, this may not be enough. Second, the nonparametric nature of scatter matrices reduces the effects of outliers and works well even for non-normal data sets. The new method provides greater weight to samples near the expected decision boundary. This tends to provide for increased classification accuracy.

The main purpose of this work is to find an improved regularized covariance estimator of each class with the advantages of LOOC, and BLOOC, which are useful for high dimensional pattern recognition problems. The searching ranges of LOOC and BLOOC are between the linear combinations of three pair covariance estimators. The first proposed covariance estimator (mixed-LOOC1) extended the searching range and is a general case of LOOC and BLOOC. By observing that the optimal value of leave-one-out likelihood function of LOOC usually occurs at near the end point of the parameter domain, the second covariance estimator (mixed-LOOC2), which needs less computation, was proposed. Using the proposed covariance estimator to improve the linear feature extraction methods when the multivariate data are singular or nearly so is demonstrated.

A key to successful classification of multivariate data is the defining of an accurate quantitative model of each class. This is especially the case when the dimensionality of the data is high, and the problem is exacerbated when the number of training samples is limited. For the commonly used quadratic maximum-likelihood classifier, the class mean vectors and covariance matrices are required and must be estimated from the available training samples. In high dimensional cases, it has been found that feature extraction methods are especially useful, so as to transform the problem to a lower dimensional space without loss of information, however, here too class statistics estimation error is significant. Finding a suitable regularized covariance estimator is a way to mitigate these estimation error effects. The main purpose of this work is to find an improved regularized covariance estimator of each class with the advantages of Leave-One-Out Covariance Estimator (LOOC) and Bayesian LOOC (BLOOC). Besides, using the proposed covariance estimator to improve the linear feature extraction methods when the multivariate data is singular or nearly so is demonstrated. This work is specifically directed at analysis methods for hyperspectral remote sensing data.

There are many factors to consider in carrying out a hyperspectral data classification. Perhaps chief among them are class training sample size, dimensionality, and distribution separability. The intent of this study is to design a classification procedure that is robust and maximally effective, but which provides the analyst with significant assists, thus simplifying the analyst's task. The result is a quadratic mixture classifier based on Mixed-LOOC2 regularized discriminant analysis and nonparametric weighted feature extraction. This procedure has the advantage of providing improved classification accuracy compared to typical previous methods but requires minimal need to consider the factors mentioned above. Experimental results demonstrating these properties are presented.