Kernel matched subspace detectors for hyperspectral target detection

In this paper, we present a kernel realization of a matched subspace detector (MSD) that is based on a subspace mixture model defined in a high-dimensional feature space associated with a kernel function. The linear subspace mixture model for the MSD is first reformulated in a high-dimensional feature space and then the corresponding expression for the generalized likelihood ratio test (GLRT) is obtained for this model. The subspace mixture model in the feature space and its corresponding GLRT expression are equivalent to a nonlinear subspace mixture model with a corresponding nonlinear GLRT expression in the original input space. In order to address the intractability of the GLRT in the feature space, we kernelize the GLRT expression using the kernel eigenvector representations as well as the kernel trick where dot products in the feature space are implicitly computed by kernels. The proposed kernel-based nonlinear detector, so-called kernel matched subspace detector (KMSD), is applied to several hyperspectral images to detect targets of interest. KMSD showed superior detection performance over the conventional MSD when tested on several synthetic data and real hyperspectral imagery.     

Kernel-based regularized-angle spectral matching for target detection in hyperspectral imagery

Target detection is one of the most important applications of hyperspectral imagery in the field of both civilian and military. In this letter, we firstly propose a new spectral matching method for target detection in hyperspectral imagery, which utilizes a pre-whitening procedure and defines a regularized spectral angle between the spectra of the test sample and the targets. The regularized spectral angle, which possesses explicit geometric sense in multidimensional spectral vector space, indicates a measure to make the target detection more effective. Furthermore Kernel realization of the Angle-Regularized Spectral Matching (KAR-SM, based on kernel mapping) improves detection even more. To demonstrate the detection performance of the proposed method and its kernel version, experiments are conducted on real hyperspectral images. The experimental tests show that the proposed detector outperforms the conventional spectral matched filter and its kernel version.     

核空间的LMS自适应多用户检测技术

提出一种核空间的LMS(KLMS)多用户检测算法,将直接序列扩频码分多址(Direct-sequence code division multiple access,DS-CDMA)接收机收到的信号通过高斯核函数映射到高维特征空间(核空间),再进行线性检测.由于采用了核技巧,所有的计算都在原空间进行,避免了特征空间的复杂运算.KLMS本质是对原空间的信号进行非线性检测,性能更接近最优检测算法.在高斯信道下,仿真结果表明,通过选择合适的核参数,在获得较好稳态误差的同时,KLMS算法具有比其他变步长LMS算法更快的收敛速度.     

Linear and kernel methods for multivariate change detection

The iteratively reweighted multivariate alteration detection (IR-MAD) algorithm may be used both for unsupervised change detection in multi- and hyperspectral remote sensing imagery and for automatic radiometric normalization of multitemporal image sequences. Principal components analysis (PCA), as well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images, both linear and kernel-based (nonlinear), may further enhance change signals relative to no-change background. IDL (Interactive Data Language) implementations of IR-MAD, automatic radiometric normalization, and kernel PCA/MAF/MNF transformations are presented that function as transparent and fully integrated extensions of the ENVI remote sensing image analysis environment. The train/test approach to kernel PCA is evaluated against a Hebbian learning procedure. Matlab code is also available that allows fast data exploration and experimentation with smaller datasets. New, multiresolution versions of IR-MAD that accelerate convergence and that further reduce no-change background noise are introduced. Computationally expensive matrix diagonalization and kernel image projections are programmed to run on massively parallel CUDA-enabled graphics processors, when available, giving an order of magnitude enhancement in computational speed. The software is available from the authors' Web sites.     

Kernel sparse representation for hyperspectral unmixing based on high mutual coherence spectral library

ABSTRACT

Sparse regression is now a popular method for hyperspectral unmixing relying on a prior spectral library. However, it is limited by the high mutual coherence spectral library which contains high similarity atoms. In order to improve the accuracy of sparse unmixing with a high mutual coherence spectral library, a new algorithm based on kernel sparse representation unmixing model with total variation constraint is proposed in this paper. By constructing an appropriate kernel function to expand similarity measure scale, library atoms and hyperspectral data are mapped to kernel space where sparse regression algorithms are then applied. Experiments conducted with both simulated and real hyperspectral data sets indicate that the proposed algorithm effectively improves the unmixing performance when using a high mutual coherence spectral library because of its ability to precisely extract endmembers in hyperspectral images. Compared with other state-of-the-art algorithms, the proposed algorithm obtains low reconstruction errors in pixels with different mixed degree.     

Nonlinear estimation of subpixel proportion via kernel least square regression

Spectral mixture analysis is an efficient approach to spectral decomposition of hyperspectral remotely sensed imagery, using land cover proportions which can be estimated from pixel values through model inversion. In this paper, a kernel least square regression algorithm has been developed for nonlinear approximation of subpixel proportions. This procedure includes two steps. The first step is to select the feature vectors by defining a global criterion to characterize the image data structure in the feature space and the second step is the projection of pixels onto the feature vectors and the application of classical linear regressive algorithm. Experiments using simulated data, synthetic data and Enhanced Thematic Mapper (ETM)+ data have been carried out, and the results demonstrate that the proposed method can improve proportion estimation. By using the simulated and synthetic data, over 85% of the total pixels in the image are found to lie between the 10% difference lines, and the root mean square error (RMSE) is less than 0.09. Using the real data, the proposed method can also perform satisfactorily with an average RMSE of about 0.12. This algorithm was also compared with other widely used kernel based algorithms, i.e. support vector regression and radial basis function neutral network and the results show that the proposed algorithm outperforms other algorithms about 5% in subpixel proportion estimation.     

高光谱图像非线性解混方法的研究进展

由于空间分辨率的限制,高光谱遥感图像中存在大量混合像元,对混合像元的解混是实现地物精确分类和识别的前提。与传统的线性解混方法相比,非线性解混方法在寻找组成混合像元的端元以及每个端元的丰度时具有较高的精度。分析了光谱非线性混合的原理,总结了近年来提出的非线性解混算法,重点对双线性模型、神经网络、基于核函数的非线性解混算法以及基于流形学习的非线性解混算法进行了介绍和分析。最后总结了混合像元非线性解混未来发展的趋势。     

Kernel-Based State-Space Kriging for Predictive Control

In this paper, we extend the state-space kriging(SSK) modeling technique presented in a previous work by the authors in order to consider non-autonomous systems. SSK is a data-driven method that computes predictions as linear combinations of past outputs. To model the nonlinear dynamics of the system, we propose the kernel-based state-space kriging(K-SSK), a new version of the SSK where kernel functions are used instead of resorting to considerations about the locality of the data. Also, a Kalma...     

A kernel optimization method based on the localized kernel Fisher criterion

It is widely recognized that whether the selected kernel matches the data determines the performance of kernel-based methods. Ideally it is expected that the data is linearly separable in the kernel induced feature space, therefore, Fisher linear discriminant criterion can be used as a cost function to optimize the kernel function. However, the data may not be linearly separable even after kernel transformation in many applications, e.g., the data may exist as multimodally distributed structure, in this case, a nonlinear classifier is preferred, and obviously Fisher criterion is not a suitable choice as kernel optimization rule. Motivated by this issue, we propose a localized kernel Fisher criterion, instead of traditional Fisher criterion, as the kernel optimization rule to increase the local margins between embedded classes in kernel induced feature space. Experimental results based on some benchmark data and measured radar high-resolution range profile (HRRP) data show that the classification performance can be improved by using the proposed method.     

Comparative study between a new nonlinear model and common linear model for analysing laboratory simulated‐forest hyperspectral data

The spectral unmixing of mixed pixels is a key factor in remote sensing images, especially for hyperspectral imagery. A commonly used approach to spectral unmixing has been linear unmixing. However, the question of whether linear or nonlinear processes dominate spectral signatures of mixed pixels is still an unresolved matter. In this study, we put forward a new nonlinear model for inferring end‐member fractions within hyperspectral scenes. This study focuses on comparing the nonlinear model with a linear model. A detail comparative analysis of the fractions ‘sunlit crown’, ‘sunlit background’ and ‘shadow’ between the two methods was carried out through visualization, and comparing with supervised classification using a database of laboratory simulated‐forest scenes. Our results show that the nonlinear model of spectral unmixing outperforms the linear model, especially in the scenes with translucent crown on a white background. A nonlinear mixture model is needed to account for the multiple scattering between tree crowns and background.     

Comparison of spectral and spatial windows for local anomaly detection in hyperspectral imagery

A new way of implementing two local anomaly detectors in a hyperspectral image is presented in this study. Generally, most local anomaly detector implementations are carried out on the spatial windows of images, because the local area of the image scene is more suitable for a single statistical model than for global data. These detectors are applied by using linear projections. However, these detectors are quite improper if the hyperspectral dataset is adopted as the nonlinear manifolds in spectral space. As multivariate data, the hyperspectral image datasets can be considered to be low-dimensional manifolds embedded in the high-dimensional spectral space. In real environments, the nonlinear spectral mixture occurs more frequently, and these manifolds could be nonlinear. In this case, traditional local anomaly detectors are based on linear projections and cannot distinguish weak anomalies from background data. In this article, local linear manifold learning concepts have been adopted, and anomaly detection algorithms have used spectral space windows with respect to the linear projection. Output performance is determined by comparison between the proposed detectors and the classic spatial local detectors accompanied by the hyperspectral remote-sensing images. The result demonstrates that the effectiveness of the proposed algorithms is promising to improve detection of weak anomalies and to decrease false alarms.     

A fast kernel-based nonlinear discriminant analysis for multi-class problems

Nonlinear discriminant analysis may be transformed into the form of kernel-based discriminant analysis. Thus, the corresponding discriminant direction can be solved by linear equations. From the view of feature space, the nonlinear discriminant analysis is still a linear method, and it is provable that in feature space the method is equivalent to Fisher discriminant analysis. We consider that one linear combination of parts of training samples, called “significant nodes”, can replace the total training samples to express the corresponding discriminant vector in feature space to some extent. In this paper, an efficient algorithm is proposed to determine “significant nodes” one by one. The principle of determining “significant nodes” is simple and reasonable, and the consequent algorithm can be carried out with acceptable computation cost. Depending on the kernel functions between test samples and all “significant nodes”, classification can be implemented. The proposed method is called fast kernel-based nonlinear method (FKNM). It is noticeable that the number of “significant nodes” may be much smaller than that of the total training samples. As a result, for two-class classification problems, the FKNM will be much more efficient than the naive kernel-based nonlinear method (NKNM). The FKNM can be also applied to multi-class via two approaches: one-against-the-rest and one-against-one. Although there is a view that one-against-one is superior to one-against-the-rest in classification efficiency, it seems that for the FKNM one-against-the-rest is more efficient than one-against-one. Experiments on benchmark and real datasets illustrate that, for two-class and multi-class classifications, the FKNM is effective, feasible and much efficient.     

A spectral-spatial method based on low-rank and sparse matrix decomposition for hyperspectral anomaly detection

Recently, some methods based on low-rank and sparse matrix decomposition (LRASMD) have been developed to improve the performance of hyperspectral anomaly detection (AD). However, these methods mainly take advantage of the spectral information in hyperspectral imagery (HSI), and ignore the spatial information. This article proposes an LRASMD-based spectral-spatial (LS-SS) method for hyperspectral AD. First, the Go Decomposition (GoDec) algorithm is employed to solve the low-rank background component and the sparse anomaly component. Next, the sparse component is explored to calculate the spectral sparsity divergence index (SDI). Based on spectral SDI, the detection result in the spectral domain and the reliable background points, which are employed as training data to construct the background manifold by linear local tangent space alignment (LLTSA), can also be obtained. Then, based on the background manifold and the transformation matrix, the low-dimensional manifold of the whole data is computed by linear mapping. After that, the kernel collaborative representation detector (KCRD) is used in the low-dimensional manifold of the whole data for the spatial SDI. Finally, SS SDI is computed for the final detection result. The theoretical analysis and experimental results demonstrate that the proposed LS-SS can achieve better performance when compared with the comparison algorithms.     

嵌入式深度神经网络高光谱图像聚类

目的 高光谱图像的高维特性和非线性结构给聚类任务带来了"维数灾难"和线性不可分问题，以往的工作将特征提取过程与聚类过程互相剥离，难以同时优化。为了解决上述问题，提出了一种新的嵌入式深度神经网络模糊C均值聚类方法（EDFCC）。方法 EDFCC算法为了提取更加有效的深层特征，联合优化高光谱图像的特征提取和聚类过程，将模糊C均值聚类算法嵌入至深度自编码器网络中，可以保持两任务联合优化的优势，同时利用深度自编码器网络降维以及逼近任意非线性函数的能力，逐步将原始数据映射到潜在特征空间，提取数据的深层特征。所提方法采用模糊C均值聚类算法约束特征提取过程，学习适用于聚类的高光谱数据深层特征，动态调整聚类指示矩阵。结果 实验结果表明，EDFCC算法在Indian Pines和Pavia University两个高光谱数据集上的聚类精度分别达到了42.95%和60.59%，与当前流行的低秩子空间聚类算法（LRSC）相比分别提高了3%和4%，相比于基于自编码器的数据聚类算法（AEKM）分别提高了2%和3%。结论 EDFCC算法能够从高光谱图像的高维光谱信息中提取更加有效的深层特征，提升聚类精度，并且由于EDFCC算法不需要额外的训练过程，大大提升了聚类效率。     

Feature extraction method based on spectral dimensional edge preservation filtering for hyperspectral image classification

ABSTRACT

A large amount of spectral and spatial information contained in hyperspectral imagery has provided a great opportunity to effectively characterize and identify the surface materials of interest. Feature extraction plays a very important role for hyperspectral data classification, which can reduce noise from the original data and improve the separability of land classes. A novel feature extraction technique based on spectral dimensional edge preserving filter is proposed in this paper. A series of Gaussian filters are applied in the spatial domain of the hyperspectral image to produce the guidance image, then, the edge preserving filter which is guided by the guidance image is adopted and applied in the spectral domain of the hyperspectral data to get the feature. For the feature is produced by filtering in the spectral domain, the spectral curves of the feature are more continues, which avoids the spectral discontinuity problems result from the traditional two-dimensional spatial filter. The guidance image is obtained by filtering the original image in the spatial domain, so, the spatial and the spectral information are integrated together in the following spectral edge preserving filtering process. We carefully adjusted the parameters of the filter and applied it to different real hyperspectral remote sensing images, with the support vector machine, multinomial logistic regression, and random forest serving as the classifier, by comparing with other feature extraction methods presented in recent literature, the results indicate that the proposed methodology always has a great performance in different kinds of cases.     

Choosing parameters of kernel subspace LDA for recognition of face images under pose and illumination variations.

This paper addresses the problem of automatically tuning multiple kernel parameters for the kernel-based linear discriminant analysis (LDA) method. The kernel approach has been proposed to solve face recognition problems under complex distribution by mapping the input space to a high-dimensional feature space. Some recognition algorithms such as the kernel principal components analysis, kernel Fisher discriminant, generalized discriminant analysis, and kernel direct LDA have been developed in the last five years. The experimental results show that the kernel-based method is a good and feasible approach to tackle the pose and illumination variations. One of the crucial factors in the kernel approach is the selection of kernel parameters, which highly affects the generalization capability and stability of the kernel-based learning methods. In view of this, we propose an eigenvalue-stability-bounded margin maximization (ESBMM) algorithm to automatically tune the multiple parameters of the Gaussian radial basis function kernel for the kernel subspace LDA (KSLDA) method, which is developed based on our previously developed subspace LDA method. The ESBMM algorithm improves the generalization capability of the kernel-based LDA method by maximizing the margin maximization criterion while maintaining the eigenvalue stability of the kernel-based LDA method. An in-depth investigation on the generalization performance on pose and illumination dimensions is performed using the YaleB and CMU PIE databases. The FERET database is also used for benchmark evaluation. Compared with the existing PCA-based and LDA-based methods, our proposed KSLDA method, with the ESBMM kernel parameter estimation algorithm, gives superior performance.     

An unsupervised approach to learn the kernel functions: from global influence to local similarity

Recently there has been a steep growth in the development of kernel-based learning algorithms. The intrinsic problem in such algorithms is the selection of the optimal kernel for the learning task of interest. In this paper, we propose an unsupervised approach to learn a linear combination of kernel functions, such that the resulting kernel best serves the objectives of the learning task. This is achieved through measuring the influence of each point on the structure of the dataset. This measure is calculated by constructing a weighted graph on which a random walk is performed. The measure of influence in the feature space is probabilistically related to the input space that yields an optimization problem to be solved. The optimization problem is formulated in two different convex settings, namely linear and semidefinite programming, dependent on the type of kernel combination considered. The contributions of this paper are twofold: first, a novel unsupervised approach to learn the kernel function, and second, a method to infer the local similarity represented by the kernel function by measuring the global influence of each point toward the structure of the dataset. The proposed approach focuses on the kernel selection which is independent of the kernel-based learning algorithm. The empirical evaluation of the proposed approach with various datasets shows the effectiveness of the algorithm in practice.     

Local normalized linear summation kernel for fast and robust recognition

Kernel-based methods are effective for object detection and recognition. However, the computational cost when using kernel functions is high, except when using linear kernels. To realize fast and robust recognition, we apply normalized linear kernels to local regions of a recognition target, and the kernel outputs are integrated by summation. This kernel is referred to as a local normalized linear summation kernel. Here, we show that kernel-based methods that employ local normalized linear summation kernels can be computed by a linear kernel of local normalized features. Thus, the computational cost of the kernel is nearly the same as that of a linear kernel and much lower than that of radial basis function (RBF) and polynomial kernels. The effectiveness of the proposed method is evaluated in face detection and recognition problems, and we confirm that our kernel provides higher accuracy with lower computational cost than RBF and polynomial kernels. In addition, our kernel is also robust to partial occlusion and shadows on faces since it is based on the summation of local kernels.     

Efficient tracking of the dominant eigenspace of a normalized kernel matrix

Various machine learning problems rely on kernel-based methods. The power of these methods resides in the ability to solve highly nonlinear problems by reformulating them in a linear context. The dominant eigenspace of a (normalized) kernel matrix is often required. Unfortunately, the computational requirements of the existing kernel methods are such that the applicability is restricted to relatively small data sets. This letter therefore focuses on a kernel-based method for large data sets. More specifically, a numerically stable tracking algorithm for the dominant eigenspace of a normalized kernel matrix is proposed, which proceeds by an updating (the addition of a new data point) followed by a downdating (the exclusion of an old data point) of the kernel matrix. Testing the algorithm on some representative case studies reveals that a very good approximation of the dominant eigenspace is obtained, while only a minimal amount of operations and memory space per iteration step is required.     

Kernel-based discriminative elastic embedding algorithm

A nonlinear version of discriminative elastic embedding (DEE) algorithm is presented, called kernel discriminative elastic embedding (KDEE). In this paper, we concretely fulfill the following works: (1) class labels and linear projection matrix are integrated into the kernel-based objective function; (2) two different strategies are adopted for optimizing the objective function of KDEE, and accordingly the final algorithms are termed as KDEE1 and KDEE2 respectively; (3) a deliberately selected Laplacian search direction is adopted in KDEE1 for faster convergence. Experimental results on several publicly available databases demonstrate that the proposed algorithm achieves powerful pattern revealing capability for complex manifold data.