Training pattern replication and weighted class allocation in artificial neural network classification

In some image classifications the importance of classes varies, and it is desirable to weight allocation to selected classes. Often the desire is to weight allocation in favour of classes that are abundant in the area represented by an image at the expense of the less abundant classes. If there is prior knowledge on the distribution of class occurrence, this weighting can be achieved with widely used statistical classifiers by setting appropriate a prioriprobabilities of class membership. With an artificial neural network, the incorporation of prior knowledge is more problematic. An approach to weight class allocation in an artificial neural network classification by replicating selected training patterns is presented. This investigation focuses on a series of classifications in which some classes were more abundant than others, but the same number of training cases were available for each class. By replicating the training patterns of abundant classes the representation of the abundant classes in the training set is increased, reflecting more closely the relative abundance of the classes in an image. Significant increases in classification accuracy were obtained by replicating the training patterns of abundant classes. Furthermore, in comparison against a discriminant analysis for the classification of synthetic aperture radar imagery, the results showed that training pattern replication could be used to weight class allocation with an effect similar to that of incorporating a prioriprobabilities of class membership into the discriminant analysis, and resulted in a significant 20.88%, increase in classification accuracy. This increase in classification accuracy was obtained without any new information, but was the result of making fuller use of what was available.     

A comparison of different optimization algorithms for retrieving aerosol optical depths from satellite data: an example of using a dual-angle algorithm

Optimization techniques are often used in remote sensing retrieval of surface or atmospheric parameters. Nevertheless, different algorithms may exhibit different performances for the same optimization problem. Comparison of some classic optimization approaches in this article aims to select the best method for retrieving aerosol opacity, or even for other parameters, from remotely sensed data. Eight frequently used optimization algorithms were evaluated using both simulated data and actual AATSR (advanced along track scanning radiometer) data. Several typical land cover types and aerosol opacity levels were also considered in the simulations to make the tests more representative. It was observed that the absolute error in retrieval would rise after a certain number of iterations due to the round-off error, and the algorithms showed different performances in the inversions without any a priori knowledge. When combined with reasonable a priori knowledge, the selection of various algorithms only slightly affected the retrieval accuracy. Given a summary of all the comparison tests, a special class named ‘trust-region methods’ (TR) was demonstrated to be the optimal choice in general cases. In contrast, some widely used optimization methods in aerosol research, for example, the Levenberg–Marquardt (LM) algorithm, seemed not to display a persuasive performance.     

Correspondence of projected 3‐D points and lines using a continuous GRASP

The field of computer vision has experienced rapid growth over the past 50 years. Many computer vision problems have been solved using theory and ideas from algebraic projective geometry. In this paper, we look at a previously unsolved problem from object recognition, namely object recognition when the correspondences between the object and image data are not known a priori. We formulate this problem as a mixed‐integer non‐linear optimization problem in terms of the unknown projection relating the object and image, as well as the unknown assignments of object points and lines to those in the image. The global optimum of this problem recovers the relationship between the object points and lines with those in the image. When certain assumptions are enforced on the allowable projections mapping the object into the image, a proof is provided which permits one to solve the optimization problem via a simple decomposition. We illustrate this decomposition approach on some example scenarios.     

Genetic classifiers for remotely sensed images: Comparison with standard methods

In this article the effectiveness of some recently developed genetic algorithm-based pattern classifiers was investigated in the domain of satellite imagery which usually have complex and overlapping class boundaries. Landsat data, SPOT image and IRS image are considered as input. The superiority of these classifiers over k-NN rule, Bayes' maximum likelihood classifier and multilayer perceptron (MLP) for partitioning different landcover types is established. Results based on producer's accuracy (percentage recognition score), user's accuracy and kappa values are provided. Incorporation of the concept of variable length chromosomes and chromosome discrimination led to superior performance in terms of automatic evolution of the number of hyperplanes for modelling the class boundaries, and the convergence time. This non-parametric classifier requires very little a priori information, unlike k-NN rule and MLP (where the performance depends heavily on the value of k and the architecture, respectively), and Bayes' maximum likelihood classifier (where assumptions regarding the class distribution functions need to be made).     

Time evolution of a system of two valued interacting elements : a microscopic interpretation of birth and death equations

We consider here one of the simplest possible systems with N interacting particles. It has the following features : (i) the state variable of each particle takes the values σ_i(= ?1 ; (ii) the interaction is chosen in such a way to preserve the symmetry of the distribution function p(σ₁, σ₂, [tdot], σ _N ; t) with respect to the σ _i and (iii) the evolution of the system is defined in a stochastic way by the transition probabilities of each particle as depending on the state of all other particles. The master equation of this Markov process is shown to be the equation of a general birth and death process in one dimension. More precisely, the birth and death process is : linear if the particles are independent ; quadratic if there is a binary interaction ; or cubic if there is a third-order interaction. We develop the reduced distribution equations hierarchy (which is the analogue of the BBGKY hierarchy) and we study under what conditions this hierarchy closes. Then we show that for specific systems there is a conserved quantity (in the mean) and we discuss for what kind of intercation there is respectively an H-theorem and a postulate of equal a priori probabilities at equilibrium. It appears in particular that this postulate should not be true in the strong form in which it is usually stated.     

Enforcing stability constraints in set-membership identification of linear dynamic systems

In this paper, we consider the identification of linear systems, a priori known to be stable, from input–output data corrupted by bounded noise. By taking explicitly into account a priori information on system stability, a formal definition of the feasible parameter set for a stable linear system is provided. On the basis of a detailed analysis of the geometrical structure of the feasible set, convex relaxation techniques are presented to solve nonconvex optimization problems arising in the computation of parameter uncertainty intervals. Properties of the computed relaxed bounds are discussed. A simulated example is presented to show the effectiveness of the proposed technique.     

Unambiguous discrimination between two unknown qudit states

We consider the unambiguous discrimination between two unknown qudit states in n-dimensional (n ???2) Hilbert space. By equivalence of unknown pure states to known mixed states and with the Jordan-basis method, we demonstrate that the optimal success probability of the discrimination between two unknown states is independent of the dimension n. We also give a scheme for a physical implementation of the programmable state discriminator that can unambiguously discriminate between two unknown states with optimal probability of success.     

Experimental Goal Regression: A Method for Learning Problem-Solving Heuristics

This research examines the process of learning problem solving with minimal requirements for a priori knowledge and teacher involvement. Experience indicates that knowledge about the problem solving task can be used to improve problem solving performance. This research addresses the issues of what knowledge is useful, how it is applied during problem solving, and how it can be acquired. For each operator used in the problem solving domain, knowledge is incrementally learned concerning why it is useful, when it is applicable, and what transformation it performs. The method of experimental goal regression is introduced for improving the learning rate by approximating the results of analytic learning. The ideas are formalized in an algorithm for learning and problem solving and demonstrated with examples from the domains of simultaneous linear equations and symbolic integration.     

Computing arrival cost parameters in moving horizon estimation using sampling based filters

Moving horizon estimation (MHE) is a numerical optimization based approach to state estimation, where the joint probability density function (pdf) of a finite state trajectory is sought, which is conditioned on a moving horizon of measurements. The joint conditional pdf depends on the a priori state pdf at the start of the horizon, which is a prediction pdf based on historical data outside the horizon. When the joint pdf is maximized, the arrival cost is a penalty term based on the a priori pdf in the MHE objective function. Traditionally, the a priori pdf is assumed as a multivariate Gaussian pdf and the extended Kalman filter (EKF) and smoother are used to recursively update the mean and covariance. However, transformation of moments through nonlinearity is poorly approximated by linearization, which can result in poor initialization of MHE. Sampling based nonlinear filters completely avoid Taylor series approximations of nonlinearities and attempt to approximate the non-Gaussian state pdf using samples and associated weights or probability mass points. The performance gains of sampling based filters over EKF motivate their use to formulate the arrival cost in MHE. The a priori mean and covariance are more effectively propagated through nonlinearities and the resulting arrival cost term can help to keep the horizon small. It is also possible to find closed-form approximations to the non-Gaussian a priori pdf from the sampling based filters. Thus, more realistic nonparametric arrival cost terms can be included by avoiding the Gaussian assumption. In this paper the use of the deterministic sampling based unscented Kalman filter, the class of random sampling based particle filter and the aggregate Markov chain based cell filter are discussed for initializing MHE. Two simulation examples are included to demonstrate the benefits of these methods over the traditional EKF approach.     

Training sets and a priori probabilities with the nearest neighbour method of pattern recognition

This paper considers whether the nearest neighbour (NN) classifier takes proper account of a priori class probabilities. If the frequencies with which the different classes arise naturally in the whole population of patterns are retained during training, it is found that a priori probabilities are automatically incorporated: this will not be so if (for example) equal numbers of training patterns are selected from each class.     

The dynamic optimization approach to locomotion dynamics: human-like gaits from a minimally-constrained biped model

This work presents a unifying framework to study energy-efficient optimal gaits for a bipedal model without elastic elements. The model includes a torso, flat feet, and telescoping legs, equipped with rotational hip and ankle joints. Two general types of gaits are studied: with and without a flight phase. The support surface can be level ground, sloped, or staircase. The algorithm achieves the optimum within the admissible space by using a minimal set of realistic physical constraints, and avoiding a priori assumptions on kinetic and kinematic parameters such as extended or instantaneous double-support, collisional or collisionless foot-ground contact, step length, step period, etc. The gait optimization for this simple model predicts many features of human locomotion including the optimality of pendular walking and impulsive running at slow and fast progression speeds, ankle push-off prior to touch-down, swing leg retraction, landing on a near vertical leg in gaits with flight phase, and burst hip torques at both ends of the swing phase.     

Partial-state feedback control of high-order cascade systems with unknown control direction

Without a priori knowledge of the signs of control directions, this paper investigates the robust asymptotic regulating problem for a class of high-order non-linear cascade systems with both dynamic and static uncertainties. Under some weaker assumptions, a partial-state feedback controller is proposed which ensures that all the signals of closed-loop system are globally uniformly bounded and all states can be regulated to the origin. The design procedure is illustrated through an example.     

基于半定规划的量子状态最优无错区分

对于一般的量子状态最优无错区分问题.很难得到最优量子测量的解析形式.因此,有必要寻求有效实用的数值方法.基于半定规划理论,证明了无错状态区分的最优量子测肇的设计问题可以转化为标准的半定规划问题,以及能直接应用半定规划的最优性条件,从而更简明地推导了.一组无错状态区分的最优性条件;通过求解标准的半定规划问题.可在多项式时间内直接得到最优量子测量的数值解以及成功区分状态的最大概率值.实例仿真表明,方法易于计算机实现,能有效地设计出无错状态区分的最优量子测量算子.     

Decision Making with Second‐Order Imprecise Probabilities

In decision analysis, uncertainty is usually described in the framework of probability. However, a large number of experimental and theoretical studies showed that a single nature of probability does not accurately capture human preferences. To avoid this drawback, they use imprecise probabilities. But, as decision maker is usually uncertain about first‐order imprecise probabilities, imprecise hierarchical probability models are used. For most of such models, the second levels are precise. There also exist studies on two‐level imprecise hierarchical models, which use imprecise probabilities or possibilities at the second level. Most of these works are based on lower prevision theory leading to a large number of optimization problems. In the present paper, we propose an imprecise hierarchical decision‐making model where the first and the second level are described by interval probabilities. The method associates with the construction of a nonadditive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function.     

Aggregation in the generalized transportation problem

We develop an a posteriori error bound on error induced by aggregating subsets of sources or sinks in generalized transportation problems. It is shown that the structure of the problem does not lend itself to the development of a priori error bounds as in ordinary transportation problems. These results can be useful to practitioners in solving large problems on commercial software.     

Optimal unambiguous discrimination of pure qudits

Linearly independent pure quantum states can be discriminated unambiguously, while linearly dependent states cannot. We use a physical accessible unitary transformation to map the nonorthogonal quantum states onto a set of orthogonal ones so that measuring the output states can discriminate the initial states with the deterministic and inconclusive results. The failure states that give an inconclusive result are linearly dependent ones. In finding the optimal unambiguous discrimination (UD), we show that a main constraint condition that the determinant constructed by the complex inner products of the failure states must be zero, along with two additional conditions, can provide solutions to the problem of the optimal UD for pure qudits. For any d, we give one analytical solution as all the Berry phases being zero. We also derive the lowest bound of the total failure probability of the optimal UD.     

States of a Map Flow of Events: Optimal Estimation by the Maximal a Posteriori State Probability Criterion

The Optimal estimation of the states of a MAP—a particular case of the BMAP—flow of events is studied. Expressions for the a posteriori probabilities of the states of the control process of the MAP flow are derived. An optimal estimation algorithm for determining the states from the maximal a posteriori state probabilities is designed and the numerical results it generated in imitation modelling of an event flow are presented.     

Incorporating global-local a Priori knowledge into expectation-maximization for SAR image change detection

Speckle is one of the inevitable obstacles related to synthetic aperture radar (SAR) image change detection; it increases the overlap between changed and unchanged pixels in the histogram of a difference image. This makes the selection of a statistic model more difficult for describing opposite classes. To address this issue, this article developed an unsupervised change-detection approach for multitemporal SAR images that specifies a priori knowledge about the spatial characteristics of the classes through Dempster-Shafer evidence theory and embeds it into the Expectation-Maximization (EM) iteration process. It is based on the consideration that each pixel in the difference image is unique due to its neighbourhood, although some of them may have the same pixel value. Thus, under the hypothesis that local and global a priori knowledge are independent sources, a global-local a priori model is developed through Dempster-Shafer evidence theory. The EM algorithm allows one to estimate the statistical parameters of the opposite classes associated with this a priori model. As a consequence, the change-detection result can be obtained within the framework of Bayes. Visual and quantitative results obtained on real multitemporal SAR image data sets confirm the effectiveness of the proposed method compared with state-of-the-art ones for SAR image change detection.     

New measures for comparing optimization algorithms on dynamic optimization problems

Dynamic optimization problems have emerged as an important field of research during the last two decades, since many real-world optimization problems are changing over time. These problems need fast and accurate algorithms, not only to locate the optimum in a limited amount of time but also track its trajectories as close as possible. Although lots of research efforts have been given in developing dynamic benchmark generator/problems and proposing algorithms to solve these problems, the role of numerical performance measurements have been barely considered in the literature. Several performance criteria have been already proposed to evaluate the performance of algorithms. However, because they only take confined aspects of the algorithms into consideration, they do not provide enough information about the effectiveness of each algorithm. In this paper, at first we review the existing performance measures and then we present a set of two measures as a framework for comparing algorithms in dynamic environments, named fitness adaptation speed and alpha–accuracy. A comparative study is then conducted among different state-of-the-art algorithms on moving peaks benchmark via proposed metrics, along with several other performance measures, to demonstrate the relative advantages of the introduced measures. We hope that the collected knowledge in this paper opens a door toward a more comprehensive comparison among algorithms for dynamic optimization problems.

     

A new efficient CAD technique for inductive reactance coupled waveguide bandpass filters

This article presents a computer-aided synthesis technique for E-plane and iris-coupled waveguide bandpass filters. This technique uses fewer optimization variables than are required by the existing techniques. The designer begins with an accurate a priori knowledge of the search direction and uses an efficient penalty function. The closed-form expressions for waveguide discontinuities, for the initial computation of the K-inverter values in the optimization procedure, greatly enhances the design speed. The technique has been implemented on a personal computer and has been found to be as accurate as the existing methods implemented on mainframe computers. Results are presented for several Ku and Ka-band iris-coupled and E-plane filters. © 1993 John Wiley & Sons, Inc.