监督式谱空间分类器

提出了一种非线性的监督式谱空间分类器(supervised spectral space classifier,简称S3C).S3C首先将输入数据映射到融合了训练数据判别信息的低维监督式谱空间中,然后在该监督式谱空间中构造最大化间隔的最优分割超平面,并把测试数据以无监督的方式也映射到与训练数据相同的新特征空间中,最后,直接应用之前构建的分类超平面对映射后的测试数据进行分类.由于S3C使研究者可以直观地观察到变化后的特征空间和映射后的数据,因此有利于对算法的评价和参数的选择.在S3C的基础上,进一步提出了一种监督式谱空间分类器的改进算法(supervised spectral space transformation,简称S3T).S3T通过采用线性子空间变换和强迫一致的方法,将映射到监督式谱空间内的数据再变换到指定的类别指示空间中去,从而获得关于测试数据的类别指示矩阵,并在此基础上对其进行分类.S3T不仅保留了S3C算法的各项优点,而且还可以用于直接处理多分类问题,抗噪声能力更强,性能更加鲁棒.在人工数据集和真实数据集上的大量实验结果显示,S3C和S3T与其他多种著名分类器相比,具有更加优越的分类性能.     

A hybrid classification scheme for mining multisource geospatial data

Supervised learning methods such as Maximum Likelihood (ML) are often used in land cover (thematic) classification of remote sensing imagery. ML classifier relies exclusively on spectral characteristics of thematic classes whose statistical distributions (class conditional probability densities) are often overlapping. The spectral response distributions of thematic classes are dependent on many factors including elevation, soil types, and ecological zones. A second problem with statistical classifiers is the requirement of the large number of accurate training samples (10 to 30 × |dimensions|), which are often costly and time consuming to acquire over large geographic regions. With the increasing availability of geospatial databases, it is possible to exploit the knowledge derived from these ancillary datasets to improve classification accuracies even when the class distributions are highly overlapping. Likewise newer semi-supervised techniques can be adopted to improve the parameter estimates of the statistical model by utilizing a large number of easily available unlabeled training samples. Unfortunately, there is no convenient multivariate statistical model that can be employed for multisource geospatial databases. In this paper we present a hybrid semi-supervised learning algorithm that effectively exploits freely available unlabeled training samples from multispectral remote sensing images and also incorporates ancillary geospatial databases. We have conducted several experiments on Landsat satellite image datasets, and our new hybrid approach shows over 24% to 36% improvement in overall classification accuracy over conventional classification schemes.     

Obtaining initial parameter estimates for nonlinear systems using multicriteria associative memories

Parameter estimation problems for nonlinear systems are typically formulated as nonlinear optimization problems. For such problems, one has the usual difficulty that standard successive approximation schemes require good initial estimates for the parameter vector. This paper develops a simple multicriteria associative memory (MAM) procedure for obtaining useful initial parameter estimates for nonlinear systems. An easily calculated one-parameter family of associative memory matrices is developed; see Equation (25). Each memory matrix is efficient with respect to two criteria: accurate recovery of parameter-output training case associations; and small matrix norm to guard against noise arising from imprecise calculations and observations. For illustration, the MAM procedure is used to obtain initial parameter estimates for a well-known nonlinear economic model, the Solow-Swan growth model. Surprisingly accurate initial parameter estimates are obtained over broad ranges of the family of MAM memory matrices, even when observations are corrupted by i.i.d. or correlated noise.     

Asymptotic error rates of the W and Z statistics when the training observations are dependent

In this paper consideration is given to the properties of the classification statistics W and Z, which were developed for use in discrimination problems with independent training observations. The relative behaviour of these two statistics when the training observations are dependent is investigated. For training observations following a stationary autoregressive process of order p, the asymptotic expansion of the expected error rates associated with W and Z are derived up to and including terms of the second order with respect to the reciprocals of the sample sizes. It is shown that neither Z nor W is absolutely superior to the other. Numerical results are given to show that their relative performance is dependent on the extent of correlation among the training observations and the size of the separation between the two populations, as measured by the Mahalanobis distance.     

A probabilistic SVM approach for hyperspectral image classification using spectral and texture features

New hyperspectral sensors can collect a large number of spectral bands, which provide a capability to distinguish various objects and materials on the earth. However, the accurate classification of these images is still a big challenge. Previous studies demonstrate the effectiveness of combination of spectral data and spatial information for better classification of hyperspectral images. In this article, this approach is followed to propose a novel three-step spectral–spatial method for classification of hyperspectral images. In the first step, Gabor filters are applied for texture feature extraction. In the second step, spectral and texture features are separately classified by a probabilistic Support Vector Machine (SVM) pixel-wise classifier to estimate per-pixel probability. Therefore, two probabilities are obtained for each pixel of the image. In the third step, the total probability is calculated by a linear combination of the previous probabilities on which a control parameter determines the efficacy of each one. As a result, one pixel is assigned to one class which has the highest total probability. This method is performed in multivariate analysis framework (MAF) on which one pixel is represented by a d-dimensional vector, d is the number of spectral or texture features, and in functional data analysis (FDA) on which one pixel is considered as a continuous function. The proposed method is evaluated with different training samples on two hyperspectral data. The combination parameter is experimentally obtained for each hyperspectral data set as well as for each training samples. This parameter adjusts the efficacy of the spectral versus texture information in various areas such as forest, agricultural or urban area to get the best classification accuracy. Experimental results show high performance of the proposed method for hyperspectral image classification. In addition, these results confirm that the proposed method achieves better results in FDA than in MAF. Comparison with some state-of-the-art spectral–spatial classification methods demonstrates that the proposed method can significantly improve classification accuracies.     

The effects of ecologically determined spatial complexity on the classification accuracy of simulated coral reef images

Numerous studies have been conducted to compare the classification accuracy of coral reef maps produced from satellite and aerial imagery with different sensor characteristics such as spatial or spectral resolution, or under different environmental conditions. However, in additional to these physical environment and sensor design factors, the ecologically determined spatial complexity of the reef itself presents significant challenges for remote sensing objectives. While previous studies have considered the spatial resolution of the sensors, none have directly drawn the link from sensor spatial resolution to the scale and patterns in the heterogeneity of reef benthos. In this paper, we will study how the accuracy of a commonly used maximum likelihood classification (MLC) algorithm is affected by spatial elements typical of a Caribbean atoll system present in high spectral and spatial resolution imagery.The results indicate that the degree to which ecologically determined spatial factors influence accuracy is dependent on both the amount of coral cover on the reef and the spatial resolution of the images being classified, and may be a contributing factor to the differences in the accuracies obtained for mapping reefs in different geographical locations. Differences in accuracy are also obtained due to the methods of pixel selection for training the maximum likelihood classification algorithm. With respect to estimation of live coral cover, a method which randomly selects training samples from all samples in each class provides better estimates for lower resolution images while a method biased to select the pixels with the highest substrate purity gave better estimations for higher resolution images.     

A method for calibrated maximum likelihood classification of forest types

A modification to the maximum likelihood algorithm was developed for classification of forest types in Sweden's part of the CORINE land cover mapping project. The new method, called the “calibrated maximum likelihood classification” involves an automated and iterative adjustment of prior weights until class frequency in the output corresponds to class frequency as calculated from objective (field-inventoried) estimates. This modification compensates for the maximum likelihood algorithm's tendency to over-represent dominant classes and under-represent less frequent ones. National forest inventory plot data measured from a five-year period are used to estimate relative frequency of class occurrence and to derive spectral signatures for each forest class. The classification method was implemented operationally within an automated production system which allowed rapid production of a country-wide forest type map from Landsat TM/ETM+ satellite data. The production system automated the retrieval and updating of forest inventory plots, a plot-to-image matching routine, illumination and haze correction of satellite imagery, and classification into forest classes using the calibrated maximum likelihood classification. This paper describes the details of the method and demonstrates the result of using an iterative adjustment of prior weights versus unadjusted prior weights. It shows that the calibrated maximum likelihood algorithm adjusts for the overclassification of classes that are well represented in the training data as well as for other classes, resulting in an output where class proportions are close to those as expected based on forest inventory data.     

基于区域生长的多尺度遥感图像分割算法

图像分割是图像解译的关键一步,仅仅利用光谱信息的传统分割方法已不能有效地对高分辨遥感图像进行分割。鉴于高分辨率遥感图像提供了地物光谱、形状和纹理等大量信息,文章提出了一种基于区域生长结合多种特征的多尺度分割算法。首先利用图像梯度信息选取种子点;其次综合高分辨率遥感图像地物的局部光谱信息和全局形状信息作为区域生长的准则进行区域生长。迭代这两个过程,直到所有区域的平均面积大于设定的尺度面积参数则停止生长。该算法用VC实现,实验结果表明该算法能获得不同尺度下的分割结果且分割效率高、分割效果好。     

Asymptotic solution of a discrete optimal control problem for one class of weakly controllable systems

An asymptotic expansion in integer nonnegative powers of small parameter for a solution of a discrete optimal control problem for one class of weakly controllable systems is constructed by substituting an assumed asymptotic expansion into the problem conditions and obtaining a series of problems in the coefficients of the asymptotics. Conditions of existence of a solution to the perturbed problem for sufficiently small values of the parameter are found. Estimates of closeness of the approximate and exact solutions in terms of trajectory, control, and functional are obtained. The values of the minimized functional are proven not to increase when higher-order asymptotic approximations of the optimal control are used. The discussion is illustrated by examples.     

Upper-bound estimates for classifiers based on a dissimilarity function

Approaches to calculating upper-bound estimates of recognition probability are proposed that can be used for a more general class of models. One of estimates determines the stability of object coverage by classification algorithms on the basis of distribution of distances between objects, and another estimate is underlain by leave-one-out cross-validation. This considerably simplifies and facilitates the construction of estimates.     

The effect of the atmosphere on the classification of satellite observations to identify surface features

The effect of differences in atmospheric turbidity on the classification of Landsat 1 observations of a rural scene is presented. The observations are classified by an unsupervised clustering technique. These clusters serve as a training set for use of a maximum likelihood algorithm. The measured radiances in each of the four spectral bands are then changed by amounts measured by Landsat 1. These changes can be associated with a 1.3 decrease in atmospheric turbidity. The classification of 22% of the pixels changes as a result of the modification. The modified observations are then reclassified as an independent set. Only 3% of the pixels have a different classification than the unmodified set. Hence, if classification errors of rural areas are not to exceed 15%, a new training set has to be developed whenever the difference in turbidity between the training and test sets reaches one.     

Optimization at multi-spectral land cover classification with fuzzy clustering and the Kohonen feature map

The number and structure of land cover classes separatable in a region on the basis of multi-spectral satellite images are usually known. The method presented here is capable of combining information from the spectral and nonspectral channels of multi-spectral images in a way that offers a possibility to cover all spectrally separable classes. The method also enables the determination of the representativeness of the available training areas with respect to these classes. In the course of the procedure, 5-35 classes are iteratively determined in succession for different channel combinations with the Kohonen feature map and the fuzzy c-means clustering algorithm. The maximum Jeffries-Matusita (JM) distance between these classes indicates the optimum class number of unambiguously separable classes for the entire multi-spectral image. In a simple step, the available training areas are grouped by the fuzzy c-means clustering algorithm. In this case, the maximum JM distance indicates the class number that ensures optimum separation of training areas. If this class number is smaller than the optimum class number determined for the entire scene, then further training areas must be defined in order to improve the results of a subsequent supervised land cover classification. The method's efficiency is demonstrated by the example of land cover classification for the region around Perpignan.     

Multiplicative update rules for incremental training of multiclass support vector machines

We present a new method for the incremental training of multiclass support vector machines that can simultaneously modify each class separating hyperplane and provide computational efficiency for training tasks where the training data collection is sequentially enriched and dynamic adaptation of the classifier is required over time. An auxiliary function has been designed, that incorporates some desired characteristics in order to provide an upper bound for the objective function, which summarizes the multiclass classification task. A novel set of multiplicative update rules is proposed, which is independent from any kind of learning rate parameter, provides computational efficiency compared to the conventional batch training approach and is easy to implement. Convergence to the global minimum is guaranteed, since the optimization problem is convex and the global minimizer for the enriched dataset is found using a warm-start algorithm. Experimental evidence on various data collections verified that our method is faster than retraining the classifier from scratch, while the achieved classification accuracy rate is maintained at the same level.     

Autoregressive modeling and power spectral estimate of R-R interval time series in arrhythmic patients

The signal constituted by the successive R-R intervals in the ECG tracing carries important information about the control mechanisms of heart rate. The present paper describes advanced methods of parameter extraction from the R-R duration time series which use autoregressive (AR) modeling and power spectral estimates applied to patients in the MIT-BIH arrhythmia data base. The described methodologies enhance information which characterize the most common rhythm disturbances (A-V block, bigeminy/trigeminy, atrial and ventricular flutter, atrial fibrillation, etc.). Important applications of such methods are in the area of the pathophysiological comprehension of cardiac rhythm control mechanisms in the research side and the classification of abnormal rhythms as well in the clinical side. A few examples from the data base are illustrated which show interesting properties of signal processing and classification in respect to the more traditional methods.     

A multiresolution spectral angle‐based hyperspectral classification method

Due to the lack of training samples, hyperspectral classification often adopts the minimum distance classification method based on spectral metrics. This paper proposes a novel multiresolution spectral‐angle‐based hyperspectral classification method, where band subsets will be selected to simultaneously minimize the average within‐class spectral angle and maximize the average between‐class spectral angle. The method adopts a pairwise classification framework (PCF), which decomposes the multiclass problem into two‐class problems. Based on class separability criteria, the original set of bands is recursively decomposed into band subsets for each two‐class problem. Each subset is composed of adjacent bands. Then, the subsets with high separability are selected to generate subangles, which will be combined to measure the similarity. Following the PCF, the outputs of all the two‐class classifiers are combined to obtain the final output. Tested with an Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data set for a six‐class problem, the results demonstrate that our method outperforms the previous spectral metric‐based classification methods.     

Performance characteristics of the indicator classifier on simulated image data

Classification of remotely sensed imagery into groups of pixels having similar spectral reflectance characteristics is conducted classically by comparing the spectral signature of unknown pixels with those of training pixels of known ground cover type. Thus classification methods use only the spectral characteristics of image data without considering the spatial aspects or the relative location of an unknown pixel with respect to pixels from the training data set. An indicator classifier was introduced in 1992 that combines spatial and spectral information in a decision model. In this Letter the performance of this classifier is tested on simulated image data with known mineral targets and varying spatial variability and noise. It is demonstrated that incorporating spatial continuity into the classification process may largely increase the accuracy of the resulting classified images.     

On The Eigenvalues of the Spectral Second Order Differentiation Operator and Application to the Boundary Observability of the Wave Equation

The behaviour of the eigenvalues of the spectral second-order differentiation operator is studied and the results are used to investigate the boundary observability of the one dimensional wave equation approximated with a spectral Galerkin method. New explicit estimates of the discrete eigenvalues are given. These estimates improve the previous results on the subject especially for the portion of eigenvalues converging exponentially to those of the continuous problem. Although the boundary observability property of the discretized wave equation is not uniform with respect to the discretization parameter, we show that a uniform observability estimate can be obtained by filtering out the highest eigenmodes.      

Adjusting the outputs of a classifier to new a priori probabilities: a simple procedure.

It sometimes happens (for instance in case control studies) that a classifier is trained on a data set that does not reflect the true a priori probabilities of the target classes on real-world data. This may have a negative effect on the classification accuracy obtained on the real-world data set, especially when the classifier's decisions are based on the a posteriori probabilities of class membership. Indeed, in this case, the trained classifier provides estimates of the a posteriori probabilities that are not valid for this real-world data set (they rely on the a priori probabilities of the training set). Applying the classifier as is (without correcting its outputs with respect to these new conditions) on this new data set may thus be suboptimal. In this note, we present a simple iterative procedure for adjusting the outputs of the trained classifier with respect to these new a priori probabilities without having to refit the model, even when these probabilities are not known in advance. As a by-product, estimates of the new a priori probabilities are also obtained. This iterative algorithm is a straightforward instance of the expectation-maximization (EM) algorithm and is shown to maximize the likelihood of the new data. Thereafter, we discuss a statistical test that can be applied to decide if the a priori class probabilities have changed from the training set to the real-world data. The procedure is illustrated on different classification problems involving a multilayer neural network, and comparisons with a standard procedure for a priori probability estimation are provided. Our original method, based on the EM algorithm, is shown to be superior to the standard one for a priori probability estimation. Experimental results also indicate that the classifier with adjusted outputs always performs better than the original one in terms of classification accuracy, when the a priori probability conditions differ from the training set to the real-world data. The gain in classification accuracy can be significant.     

Assessment of local influence in elliptical linear models with longitudinal structure

The aim of this paper is to derive local influence curvatures under various perturbation schemes for elliptical linear models with longitudinal structure. The elliptical class provides a useful generalization of the normal model since it covers both light- and heavy-tailed distributions for the errors, such as Student-t, power exponential, contaminated normal, among others. It is well known that elliptical models with longer-than-normal tails may present robust parameter estimates against outlying observations. However, little has been investigated on the robustness aspects of the parameter estimates against perturbation schemes. We use appropriate derivative operators to express the normal curvatures in tractable forms for any correlation structure. Estimation procedures for the position and variance-covariance parameters are also presented. A data set previously analyzed under a normal linear mixed model is reanalyzed under elliptical models. Local influence graphics are used to select less sensitive models with respect to some perturbation schemes.     

A CMOS binary pattern classifier based on Parzen''s method

Biological circuitry in the brain that has been associated with the Parzen method of classification inspired an analog CMOS binary pattern classifier. The circuitry resides on three separate chips. The first chip computes the closeness of a test vector to each training vector stored on the chip where "vector closeness" is defined as the number of bits two vectors have in common above some thresholds. The second chip computes the closeness of the test vector to each possible category where "category closeness" is defined as the sum of the closenesses of the test vector to each training vector in a particular category. Category closenesses are coded by currents which feed into an "early bird" winner-take-all circuit on the third chip that selects the category closest to the test vector. Parzen classifiers offer superior classification accuracy than the common nearest neighbor Hamming networks. A high degree of parallelism allows for O(1) time complexity and the chips are tillable for increased training vector storage capacity. Proof-of-concept chips were fabricated through the MOSIS chip prototyping service and successfully tested.