Agricultural crop-type classification of multi-polarization SAR images using a hybrid entropy decomposition and support vector machine technique

This article presents the application of a hybrid classification technique of entropy decomposition and support vector machine (EDSVM) for crop-type categorization. It takes the advantage of the desired parameters from the entropy decomposition (ED) method and the statistical learning method based on the support vector machine (SVM) method that determines the optimal separation between classes in a higher dimensional feature space to improve on the existing classification results. ED is capable of extracting valuable decomposed parameters of entropy H and alpha α for image interpretation with analysis of the underlying scattering mechanisms. H demonstrates the randomness of the underlying scattering mechanisms and α is used to define the type of scattering mechanisms. However, in the application of agricultural crops where the scattering mechanisms of the crops are quite similar to each other, the distribution of the H and α in the H–α feature space overlaps from one class to another. Moreover, the drawback of ED is the arbitrariness of the boundaries for each class. To overcome this issue, SVM classifier is deployed to determine the decision boundaries by projecting the training sets of the classes into higher dimensional feature space. Hence, the hybrid EDSVM is developed to provide an alternative solution to improve the classification accuracy. In this article, EDSVM classifier is applied on a multi-crop field Airborne Synthetic Aperture Radar (AIRSAR) image of Flevoland in the Netherlands and the robustness of the classifier is evaluated. The classification is done with the purpose of separating the different types of crops with the characteristics of the scattering mechanism. At the same time, a hybrid entropy decomposition and neural network (EDNN) classifier method is developed to validate the effectiveness of the EDSVM classifier. As a result, EDSVM is proved to be robust and to yield a superior result compared with neural network (NN), SVM and EDNN classifiers.     

Review Article A review of multi-channel indices of class separability

Abstract

An increasingly common question arising in processing digital multi-channel data from spacecraft and aircraft scanner systems is “which channels contain the best information to separate the classes of interest to the user?”. This may be to identify the best single channel for separating classes in a black and white photographic or line printer output product, or the best three channels for a colour photographic presentation of the data, or the best ‘n’ channels to enter into a classification (being mindful of the ‘trade off’ between improved sub-class separability and increasing usage of computer space and time resources). The only valid way to approach separability using more than one channel is to consider it in multi-channel space utilizing the inter-channel relationship terms. Having defined the classes using some form of hierarchical ordering approach, such as that proposed by Anderson et al. (1972), the user may compile the statistical profiles of the classes of interest from the sensor multi-channel data. Based on these statistics a number of multi-channel separability indices may be derived. Each of these indices quantifies, on the basis of the user-defined multi-channel statistics, the degree of inter-class separability the user can expect as a function of subsets of channels drawn from the overall sensor channel set. This review considers some of the more common multi-channel indices of separability and presents the links between them. Their various properties, and some limitations, are also presented as is an operational approach to their use.     

Improving the efficiency of the dynamic analysis of mass flow networks

Dynamic network analysis algorithms are studied with a view to improving computational efficiency. The main possibility is an appropriate choice of space and time intervals. Using concepts from generalized 4-pole theory t the paper deduces relations for determining near-optimal Δx and Δt values by a prescribed computational error. As an example, the general relations are applied to the analysis of gas pipe networks.     

Spectral separability of riparian forests from small and medium-sized rivers across a latitudinal gradient using multispectral imagery

Spectral discrimination between riparian forests is a challenging issue due to the inherent complexity of species composition and the high spatial structural variability of these vegetation types. This study aimed to evaluate spectral separability among riparian forests, in small and medium-sized river catchment areas, in three bioclimatic zones of Portugal (temperate, transitional, and Mediterranean). We also assess the spectral differences using only the dominant riparian woody species in each riparian forest class, namely Alnus glutinosa, Salix salviifolia, and Nerium oleander.

Pixel values were extracted from high-resolution airborne multispectral imagery (red, green, blue, and near-infrared, 50 cm pixels) of 26 riparian forests located in the three bioclimatic zones. Spectral separability was calculated using the transformed divergence (TD) distance. Discriminant analysis (DA) was used to select the bands that contribute most to the spectral separability and for the classification accuracy assessment of the riparian forests. Species composition and percentage of canopy closure were collected for all the riparian forests in a field campaign and subjected to hierarchical clustering in order to validate the spectral separability analyses. Optical traits derived from field data were used to interpret the spectral differences between riparian forest classes.

The greatest spectral separability was observed between the temperate and the Mediterranean riparian forest classes. Global classification accuracy for the DA was 86.3% for riparian forest classes along medium-sized rivers and 70.1% in small-sized ones. The high floristic and spatial structure variability was responsible for the misclassification errors that occurred between the transitional and the other riparian forest classes. The spectral separability using only the dominant species was greater than that obtained using the overall species assemblages of the riparian forests. Alnus glutinosa had the highest level of classification accuracy, and this may be related to its peculiar yellowish-green tone. DA also revealed that all spectral bands were needed in order to distinguish the riparian forest classes.

This study provided evidence that the spectral discrimination of riparian forests can be explained on the basis of differences in species composition and cover, and by a convergence of optical traits, at both leaf and canopy levels. Spectral signatures of these riparian forests and related spectral signatures of key species are useful tools for evaluating the floristic deviations of actual riparian forests from their near-natural benchmarks.

     

A hybrid radial basis function and data envelopment analysis neural network for classification

We propose a hybrid radial basis function network-data envelopment analysis (RBFN-DEA) neural network for classification problems. The procedure uses the radial basis function to map low dimensional input data from input space ℜ to a high dimensional ℜ⁺ feature space where DEA can be used to learn the classification function. Using simulated datasets for a non-linearly separable binary classification problem, we illustrate how the RBFN-DEA neural network can be used to solve it. We also show how asymmetric misclassification costs can be incorporated in the hybrid RBFN-DEA model. Our preliminary experiments comparing the RBFN-DEA with feed forward and probabilistic neural networks show that the RBFN-DEA fares very well.     

面向GF-2遥感影像的U-Net城市绿地分类

目的 高分2号卫星（GF-2）是首颗民用高空间分辨率光学卫星，具有亚米级高空间分辨率与宽覆盖结合的显著特点，为城市绿地信息提取等多领域提供了重要的数据支撑。本文利用GF-2卫星多光谱遥感影像，将一种改进的U-Net卷积神经网络首次应用于城市绿地分类，提出一种面向高分遥感影像的城市绿地自动分类提取技术。方法 先针对小样本训练集容易产生的过拟合问题对U-Net网络进行改进，添加批标准化（batch normalization，BN）和dropout层获得U-Net+模型；再采用随机裁剪和随机数据增强的方式扩充数据集，使得在充分利用影像信息的同时保证样本随机性，增强模型稳定性。结果 将U-Net+模型与最大似然法（maximum likelihood estimation，MLE）、神经网络（neural networks，NNs）和支持向量机（support vector machine，SVM）3种传统分类方法以及U-Net、SegNet和DeepLabv3+这3种深度学习语义分割模型进行分类结果精度对比。改进后的U-Net+模型能有效防止过拟合，模型总体分类精度比改进前提高了1.06%。基于改进的U-Net+模型的城市绿地总体分类精度为92.73%，平均F₁分数为91.85%。各分类方法按照总体分类精度从大到小依次为U-Net+（92.73%）、U-Net （91.67%）、SegNet （88.98%）、DeepLabv3+（87.41%）、SVM （81.32%）、NNs （79.92%）和MLE （77.21%）。深度学习城市绿地分类方法能充分挖掘数据的光谱、纹理及潜在特征信息，有效降低分类过程中产生的"椒盐噪声"，具有较好的样本容错能力，比传统遥感分类方法更适用于城市绿地信息提取。结论 改进后的U-Net+卷积神经网络模型能够有效提升高分遥感影像城市绿地自动分类提取精度，为城市绿地分类提供了一种新的智能解译方法。     

A decomposition approach for the kinematic synthesis of tendon‐driven manipulators

This article describes a decomposition methodology for the kinematic synthesis of tendon‐driven manipulators (TDMs). Based on the QR factorization, the complex transformation between vectors in the tendon‐space and the joint‐space of an n‐DOF TDM with n+1 tendons is decomposed as a two‐step transformation. An orientation matrix is used to characterize the vector transformation between the (n+1)‐dimensional tendon‐space and the n‐dimensional intermediate equivalent tendon‐space. An equivalent structure matrix is also introduced for the vector transformation between the n‐dimensional equivalent tendon‐space and n‐dimensional joint‐space. Design equations for synthesizing a TDM to possess kinematic isotropic transmission characteristics with proper tendon routing and pulley sizes are derived. ©1999 John Wiley & Sons, Inc.     

Classification and dimensional reduction using restricted radial basis function networks

One of the most efficient means to understand complex data is by visualizing them in two- or three-dimensional space. As meaningful data are likely to be high dimensional, visualizing them requires dimensional reduction algorithms, which objective is to map high-dimensional data into low-dimensional space while preserving some of their underlying structures. For labeled data, their low-dimensional representations should embed their classifiability so that their class-structures become visible. It is also beneficial if an algorithm can classify labeled input while at the same time executes dimensional reduction to visually offer information regarding the data’s structure to give rational behind the classification. However, most of the currently available dimensional reduction methods are not usually equipped with classification features, while most classification algorithm lacks transparencies in rationalizing their decisions. In this paper, the restricted radial basis function networks (rRBF), a recently proposed supervised neural network with low-dimensional internal representation, is utilized for visualizing high-dimensional data while also performing classification. The primary focus of this paper is to empirically explain the classifiability and visual transparency of the rRBF.

     

Learning as a nonlinear line of attraction in a recurrent neural network

A method to embed N dimensional, multi-valued patterns into an auto-associative memory represented as a nonlinear line of attraction in a fully connected recurrent neural network is presented in this paper. The curvature of the nonlinear attractor is defined by the Kth degree polynomial line which best fits the training data in N dimensional state space. The width of the nonlinear line is then characterized by the statistical characteristics of the training patterns. Stability of the recurrent network is verified by analyzing the trajectory of the points in the state space during convergence. The performance of the network is benchmarked through the reconstruction of original gray-scale images from their corrupted versions. It is observed that the proposed method can quickly and successfully reconstruct each image with an average convergence rate of 3.10 iterations.     

Unsupervised classification of multispectral Landsat images with multidimensional particle swarm optimization

This article proposes a novel unsupervised classification approach for automatic analysis of multispectral Landsat images. The automatic classification of the information in multidimensional (MD) Landsat data space by dynamic clustering is addressed as an optimization problem and two recently proposed heuristic techniques based on Particle Swarm Optimization (PSO) are applied to determine the optimal (number of) clusters in a given input data space: distance metric and a proper validity index function. The first technique, the so-called MD-PSO, re-forms the native structure of swarm particles (agents) in such a way that they can make inter-dimensional passes with a dedicated dimensional PSO process. Fractional global best formation (FGBF) basically collects all promising dimensional components and fractionally creates an artificial global best (aGB) agent that has the potential to be a better ‘guide’ than the swarm’s native global best position (gbest) agent. In this study, the proposed dynamic clustering approach based on MD-PSO and FGBF techniques is applied to automatically classify the colour-coded representations of the multispectral (MD) Landsat data. The approach has been applied to real-world multispectral data and it provided quite encouraging results compared to the traditional K-means and ISODATA (iterative self-organizing data analysis) clustering methods. The proposed unsupervised technique determines the true number of classes within Landsat data for optimal classification performance while preserving spatial resolution and textural information in the classification map.     

Feedback equivalence for general control systems

We discuss the solution to the problem of local equivalence of control systems with n states and p controls in a neighbourhood of a generic point, under the Lie pseudo-group of local time independent feedback transformations. We have shown earlier that this problem is identical with the problem of simple equivalence of the time optimal variational problem. Here we indicate the way in which this identification may be used to obtain closed loop time critical controls for general systems. We show that the classification of general nonlinear systems depends on the classification of all n−p dimensional affine subspaces of the space of symmetric forms in p variables and that the case of control linear systems depends on the classification of all n−p dimensional affine subspaces of the space of skew forms in p variables. We show that in the latter case the G-structure is the prolongation of one determined by a state space transformation group. We give a complete list of normal forms for control linear systems in the case p=n−1.     

A novel ship classification approach for high resolution SAR images based on the BDA-KELM classification model

Ship classification based on synthetic aperture radar (SAR) images is a crucial component in maritime surveillance. In this article, the feature selection and the classifier design, as two key essential factors for traditional ship classification, are jointed together, and a novel ship classification model combining kernel extreme learning machine (KELM) and dragonfly algorithm in binary space (BDA), named BDA-KELM, is proposed which conducts the automatic feature selection and searches for optimal parameter sets (including the kernel parameter and the penalty factor) for classifier at the same time. Finally, a series of ship classification experiments are carried out based on high resolution TerraSAR-X SAR imagery. Other four widely used classification models, namely k-Nearest Neighbour (k-NN), Bayes, Back Propagation neural network (BP neural network), Support Vector Machine (SVM), are also tested on the same dataset. The experimental results shows that the proposed model can achieve a better classification performance than these four widely used models with an classification accuracy as high as 97% and encouraging results of other three multi-class classification evaluation metrics.     

RBF neural network center selection based on Fisher ratio class separability measure

For classification applications, the role of hidden layer neurons of a radial basis function (RBF) neural network can be interpreted as a function which maps input patterns from a nonlinear separable space to a linear separable space. In the new space, the responses of the hidden layer neurons form new feature vectors. The discriminative power is then determined by RBF centers. In the present study, we propose to choose RBF centers based on Fisher ratio class separability measure with the objective of achieving maximum discriminative power. We implement this idea using a multistep procedure that combines Fisher ratio, an orthogonal transform, and a forward selection search method. Our motivation of employing the orthogonal transform is to decouple the correlations among the responses of the hidden layer neurons so that the class separability provided by individual RBF neurons can be evaluated independently. The strengths of our method are double fold. First, our method selects a parsimonious network architecture. Second, this method selects centers that provide large class separation.     

Fractional-step dimensionality reduction

Linear projections for dimensionality reduction, computed using linear discriminant analysis (LDA), are commonly based on optimization of certain separability criteria in the output space. The resulting optimization problem is linear, but these separability criteria are not directly related to the classification accuracy in the output space. Consequently, a trial and error procedure has to be invoked, experimenting with different separability criteria that differ in the weighting function used and selecting the one that performed best on the training set. Often, even the best weighting function among the trial choices results in poor classification of data in the subspace. In this short paper, we introduce the concept of fractional dimensionality and develop an incremental procedure, called the fractional-step LDA (F-LDA) to reduce the dimensionality in fractional steps. The F-LDA algorithm is more robust to the selection of weighting function and for any given weighting function, it finds a subspace in which the classification accuracy is higher than that obtained using LDA     

Classifying high dimensional data by interactive visual analysis

Data mining techniques such as classification algorithms are applied to data which are usually high dimensional and very large. In order to assist the user to perform a classification task, visual techniques can be employed to represent high dimensional data in a more comprehensible 2D or 3D space. However, such representation of high dimensional data in the 2D or 3D space may unavoidably cause overlapping data and information loss. This issue can be addressed by interactive visualization. With expert domain knowledge, the user can build classifiers that are as competitive as automated ones using a 2D or 3D visual interface interactively. Several visual techniques have been proposed for classifying high dimensional data. However, the user׳s interaction with those techniques is highly dependent on the experience of the user in the visual identification of classifying data, and as a result, the classification results of those techniques may vary and may not be repeatable. To address this deficiency, this article presents an interactive visual approach to the classification of high dimensional data. Our approach employs the enhanced separation feature of a visual technique called HOV³ by which the user plots the training dataset by applying statistical measurements on a 2D space in order to separate data points into groups with the same class labels. A data group with its corresponding statistical measurement which separated it from the others is taken as a visual classifier. Then the user mixes the data points in a classifier with the unlabeled dataset and plots them in HOV³ by the measurement of the classifier. The data points which overlap the labeled ones in the 2D space are assigned the corresponding label. Our approach avoids the randomness in the existing interactive visual classification techniques, as the visual classifier in this approach only depends on the training dataset and its statistical measurement. As a result, this work provides an intuitive and effective approach to classify high dimensional data by interactive visualization.     

Extremist vs. centrist decision behavior: quasi-convex utility functions for interactive multi-objective linear programming problems

This paper presents the fundamental theory and algorithms for identifying the most preferred alternative for a decision maker (DM) having a non-centrist (or extremist) preferential behavior. The DM is requested to respond to a set of questions in the form of paired comparison of alternatives. The approach is different than other methods that consider the centrist preferential behavior.In this paper, an interactive approach is presented to solve the multiple objective linear programming (MOLP) problem. The DM's underlying preferential function is represented by a quasi-convex value (utility) function, which is to be maximized. The method presented in this paper solves MOLP problems with quasi-convex value (utility) functions by using paired comparison of alternatives in the objective space. From the mathematical point of view, maximizing a quasi-convex (or a convex) function over a convex set is considered a difficult problem to solve, while solutions for quasi-concave (or concave) functions are currently available. We prove that our proposed approach converges to the most preferred alternative.We demonstrate that the most preferred alternative is an extreme point of the MOLP problem, and we develop an interactive method that guarantees obtaining the global most preferred alternative for the MOLP problem. This method requires only a finite number of pivoting operations using a simplex-based method, and it asks only a limited number of paired comparison questions of alternatives in the objective space. We develop a branch and bound algorithm that extends a tree of solutions at each iteration until the MOLP problem is solved. At each iteration, the decision maker has to identify the most preferred alternatives from a given subset of efficient alternatives that are adjacent extreme points to the current basis. Through the branch and bound algorithm, without asking many questions from the decision maker, all branches of the tree are implicitly enumerated until the most preferred alternative is obtained. An example is provided to show the details of the algorithm. Some computational experiments are also presented.Scope and purposeThis paper presents the fundamental theory, algorithm, and examples for identifying the most preferred alternative (solution) for a decision maker (DM) having a non-centrist (or extremist) preferential behavior for Multiple Objective Linear Programming (MOLP) problems. The DM is requested to respond to a set of questions in the form of paired comparison of alternatives.Although widely applied, Linear Programming is limited to a single objective function. In many real world situations, DMs are faced with multiple objective problems in that several competing and conflicting objectives have to be considered. For these problems, there exist many alternatives that are feasible and acceptable. However, the DM is interested in finding “the most preferred alternative”. In the past three decades, many methods have been developed for solving MOLP problems.One class of these methods is called “interactive”, in which the DM responds to a set of questions interactively so that his/her most preferred alternative can be obtained. In most of these methods, the value (utility) function (that presents the DM's preference) is assumed to be linear or additive, concave, pseudo-concave, or quasi-concave. However, for MOLP problems, there has not been any effort to recognize and solve the quasi-convex utility functions, which are among the most difficult class of problems to solve. The quasi-convex class of utility functions represents an extremist preferential behavior, while the other aforementioned methods (such as quasi-concave) represent a conservative behavioral preference. It is shown that the method converges to the optimal (the most preferred) alternative. The approach is computationally feasible for moderately sized problems.     

An end-user-oriented framework for the classification of multitemporal SAR images

In this article, we present an end-user-oriented framework for multitemporal synthetic aperture radar (SAR) data classification. It accepts as input the recently introduced Level-1α products, whose peculiarities are a high degree of interpretability and increased class separability with respect to single greyscale images. These properties make the Level-1α products very attractive in the application of simple supervised classification algorithms. Specifically, (1) the high degree of interpretability of the maps makes the training phase extremely simple; and (2) the good separation between classes gives excellent results using simple discrimination rules. The end product is a simple, fast, accurate, and repeatable framework.     

Towards Incremental Fuzzy Classifiers

Fuzzy classification systems (FCS) are traditionally built from observations (data points) in an off-line one shot-experiment. Once the learning phase is exhausted, the classifier is no more capable to learn further knowledge from new observations nor is it able to update itself in the future. This paper investigates the problem of incremental learning in the context of FCS. It shows how, in contrast to off-line or batch learning, incremental learning infers knowledge in the form of fuzzy rules from data that evolves over time. To accommodate incremental learning, appropriate mechanisms are applied in all steps of the FCS construction: (1) Incremental supervised clustering to generate granules in a progressive manner, (2) Systematic and automatic update of fuzzy partitions, (3) Incremental feature selection using an incremental version of Fisher’s interclass separability criterion. The effect of incrementality on various aspects is demonstrated via a numerical evaluation.