A nonparametric classification scheme with mean squared error criterion

A statistical classification scheme for a given set of data requires knowledge of the probability distribution of the observations. Traditional approaches to this problem have revolved around chosen various parametric forms for the probability distribution and evaluating these by goodness of fit methods. Among the difficulties with this method are that it is time consuming, it may not lead to satisfactory results and it may lie beyond the statistical expertise of many practitioners. In this paper, the author's consider the use of a recently developed nonparametric probability density estimator in classification schemes with mean squared error loss criterion. Classical parametric approaches are compared to the nonparametric method on simulated data on the basis of the misclassification probability. Real data from the medical and biological sciences are also used to illustrate the usefulness of the nonparametric method.     

Robustness of radial basis functions

Neural networks are intended to be used in future nanoelectronic technology since these architectures seem to be robust to malfunctioning elements and noise in its inputs and parameters. In this work, the robustness of radial basis function networks is analyzed in order to operate in noisy and unreliable environment. Furthermore, upper bounds on the mean square error under noise contaminated parameters and inputs are determined if the network parameters are constrained. To achieve robuster neural network architectures fundamental methods are introduced to identify sensitive parameters and neurons.     

Robustness of the estimators of transition rates for size-classified matrix models

Matrix models are often used to model the dynamics of age-structured or size-structured populations. The Usher model is an important particular case that relies on the following hypothesis: between time steps t and t+1, individuals either remain in the same class, move up to the following class, or die. There are then two ways of handling data that do not meet this condition: either remove them prior to data analysis or rectify them. These two ways correspond to two estimators of transition parameters. The former, which corresponds to the classical estimator, is obtained from the latter by a data trimming. The two estimators of transition parameters are compared on the basis of their robustness in order to obtain a criterion of choice between the two estimators. The influence curve of both estimators is first computed, then their gross sensitivity and their asymptotic variance. The untrimmed estimator is more robust than the classical one. Its asymptotic variance can be lower or greater than that of the classical estimator depending on the boundaries used for data trimming. The results are applied to a tropical rain forest in French Guiana, with a discussion on the role of the class width.     

基于蒙特卡洛方法的信号转导网络鲁棒性分析

细胞信号转导网络内部结构的复杂性和动力学参数的不确定性影响着系统的动态特性,如何定量地确定系统特性与参数变化的关系,已经成为系统生物研究的重要问题之一.为了研究NF-κB信号转导网络的鲁棒性,应用蒙特卡洛(Monte-Carlo)随机模拟方法,假设参数在其变化范围内服从某一随机分布,通过对模型参数进行随机采样,系统地研究了系统输出NF-κBn关于64个速率参数变化和阶跃输入信号IKK幅值变化的鲁棒性.仿真结果表明,6个鲁棒性较弱的参数k1、k34、k61、k28、k36、k29极大地影响着系统输出NF-κBn的振荡特性,说明这些参数是NF-κB信号转导网络的关键速率常数;同时,输入阶跃信号IKK幅值的变化对系统输出NF-κBn的振荡特性产生了巨大影响.     

Robustness analysis of a hybrid ground coupled heat pump system with model predictive control

MPC of thermal systems usually results in robust operation with respect to uncertainties thanks to some key characteristics of the controller. However, the true limit until which these systems will actually be robust is rarely known explicitly. In this study a Hybrid Ground Coupled Heat Pump (HyGCHP) system with MPC is investigated, for which state estimation and disturbance prediction are highly uncertain, moreover, the system performance is highly sensitive to errors at these points. It has become popular to design control systems which perform explicit computations to assure robustness (e.g. min–max Robust MPC) but this framework is computationally demanding, therefore, not widely applied. An alternative is to perform robustness analysis of an MPC controlled system which is though generally avoided due to complicated theoretical formulations, implicitness and conservativeness of the approach. To tackle these issues an existing framework for robustness analysis is extended and applied to the case of a HyGCHP system with MPC to analyze robustness with respect to state estimation uncertainty. This paper presents an approach to use the original formulation, suggested for regulation/stabilization in order to analyze robustness for the case of set point tracking. The results show that the maximum allowed state estimation uncertainty found by robustness analysis of the regulation problem is confirmed by the simulated HyGCHP system with MPC, which performs set point tracking. In conclusion, the method gives a reliable guarantee for the degree of state estimation uncertainty, up to which the HyGCHP system investigated remains robust. Future research can extend the robustness analysis method towards disturbance prediction uncertainty.     

Robustness analysis of linear periodic time-varying systems subject to structured uncertainty

In this paper, we show how Floquet theory may be combined with a technique known as Lifting to cast a linear periodically time-varying system subject to structured linear time invariant uncertainty in the form of a linear fractional transformation. The stability and performance robustness of the resulting system may then be analysed using standard μ-analysis methods. A significant advantage of the proposed approach is that it allows the computation of a worst-case destabilising uncertainty combination which may be used to estimate the conservatism of the computed robustness margin. An example is given to illustrate the application of the proposed approach.     

Robustness analysis of exact feedforward linearization based on differential flatness

A methodology to analyze robustness with respect to parametric uncertainty for exact feedforward linearization based on differential flatness is presented. The analysis takes into consideration the tracking error equation and thereafter makes use of a stability result by Kelemen coupled with results issued from interval analysis theory.     

Wavelet-Based Identification of Linear Discrete-Time Systems: Robustness Issue

Discrete-time linear time-varying systems are modeled by discrete-time wavelets. The output of the unknown system is corrupted by noise. The system model parameters are estimated by the least-squares method applied to the output error. Conditions are derived that provide vanishing influence of the output noise to the parameter estimates. Due to the time-frequency selectivity of wavelets, parameter estimates can be robust to narrow-band noise and/or impulse noise. This robustness is confirmed by simulations.     

Robustness analysis of nearfield subband beamformers in the presence of microphone gain and phase errors

Subband beamforming has found many applications in microphone array processing field, due to its advantages over the fullband counterpart. In this paper, the performance of nearfield subband beamformers for arbitrary arrays in the presence of microphone gain and phase errors is studied from the perspective of statistical analysis. Through the bias and variance analysis of array response, some insightful properties on the robustness of nearfield subband beamformers have been derived. It is shown that the robustness of nearfield subband beamformers is dependent on the source-to-array distance, i.e., the robustness will deteriorate when the source is close to microphone arrays. Moreover, the variation in sound speed, i.e., the temperature in homogeneous environments, has little effect on the robustness performance of subband beamformers. The theoretical results are further verified by several numerical examples on nearfield subband beamformers.     

Subclass Discriminant Analysis of morphological and textural features for HEp-2 staining pattern classification

Classifying HEp-2 fluorescence patterns in Indirect Immunofluorescence (IIF) HEp-2 cell imaging is important for the differential diagnosis of autoimmune diseases. The current technique, based on human visual inspection, is time-consuming, subjective and dependent on the operator's experience. Automating this process may be a solution to these limitations, making IIF faster and more reliable. This work proposes a classification approach based on Subclass Discriminant Analysis (SDA), a dimensionality reduction technique that provides an effective representation of the cells in the feature space, suitably coping with the high within-class variance typical of HEp-2 cell patterns. In order to generate an adequate characterization of the fluorescence patterns, we investigate the individual and combined contributions of several image attributes, showing that the integration of morphological, global and local textural features is the most suited for this purpose. The proposed approach provides an accuracy of the staining pattern classification of about 90%.     

On the classification of congenital abnormalities from hand radiographs

Mathematical techniques for the computer classification of congenital abnormalities using metacarpophalageal lengths obtained from hand radiographs have been investigated. Discriminant analysis has been shown to be significantly better than similarity measures in distinguishing the normal condition, Down's syndrome, Turner's syndrome and achondroplasia from one another.     

Additive estimators for probabilities of correct classification

Several methods for estimating a sample-based discriminant's probability of correct classification are compared with respect to bias, variance, robustness, and computation cost. “Smooth” modification of the counting estimator, or sample success proportion, is recommended to reduce bias and variance while retaining robustness. Also the “bootstrap” method of Efron⁽⁸⁾ can approximately correct an additive estimator's bias using an ancillary computer simulation. In contrast, bias reduction achieved by the popular “leave-one-out” modification of counting method is vitiated by corresponding increase in variance.     

Robustness of Fourier estimator of integrated volatility in the presence of microstructure noise

The finite sample properties of the Fourier estimator of integrated volatility under market microstructure noise are studied. Analytic expressions for the bias and the mean squared error (MSE) of the contaminated estimator are derived. These formulae can be practically used to design optimal MSE-based estimators, which are very robust and efficient in the presence of noise. Moreover an empirical analysis based on a simulation study and on high-frequency logarithmic prices of the Italian stock index futures (FIB30) validates the theoretical results.     

Stable estimation of a covariance matrix guided by nuclear norm penalties

Estimation of a covariance matrix or its inverse plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. The current paper introduces a novel prior to ensure a well-conditioned maximum a posteriori (MAP) covariance estimate. The prior shrinks the sample covariance estimator towards a stable target and leads to a MAP estimator that is consistent and asymptotically efficient. Thus, the MAP estimator gracefully transitions towards the sample covariance matrix as the number of samples grows relative to the number of covariates. The utility of the MAP estimator is demonstrated in two standard applications–discriminant analysis and EM clustering–in challenging sampling regimes.     

Multi-class supervised classification of electrical borehole wall images using texture features

Electrical borehole wall images represent micro-resistivity measurements at the borehole wall. The lithology reconstruction is often based on visual interpretation done by geologists. This analysis is very time-consuming and subjective. Different geologists may interpret the data differently. In this work, linear discriminant analysis (LDA) in combination with texture features is used for an automated lithology reconstruction of ODP (Ocean Drilling Program) borehole 1203A drilled during Leg 197. Six rock groups are identified by their textural properties in resistivity data obtained by a Formation MircoScanner (FMS). Although discriminant analysis can be used for multi-class classification, non-optimal decision criteria for certain groups could emerge. For this reason, we use a combination of 2-class (binary) classifiers to increase the overall classification accuracy. The generalization ability of the combined classifiers is evaluated and optimized on a testing dataset where a classification rate of more than 80% for each of the six rock groups is achieved. The combined, trained classifiers are then applied on the whole dataset obtaining a statistical reconstruction of the logged formation. Compared to a single multi-class classifier the combined binary classifiers show better classification results for certain rock groups and more stable results in larger intervals of equal rock type.     

具有形状信息的多传感器群目标跟踪算法

针对多传感器环境下具有形状信息的扩展/群目标跟踪问题,提出了两种融合算法,即高斯逆韦氏并行PHD滤波算法和高斯逆韦氏序贯PHD滤波算法。新算法分别结合并行滤波和序贯滤波算法思想,能够对扩展/群目标的质心状态进行跟踪,对形状进行有效估计。高斯逆韦氏并行PHD滤波算法将各个传感器产生的量测集合并到一个量测集中,统一对量测集进行划分。在滤波更新阶段,对划分后的量测集进行扩维,从而在形式上将多传感器环境下的跟踪问题转化为单传感器环境下的跟踪问题。高斯逆韦氏序贯PHD滤波算法则先对各个传感器产生的量测集依次进行划分,再依次对每一个划分后的量测集进行滤波,从而达到融合多个传感器量测的目的。仿真结果表明该算法的可行性和有效性。     

Deterioration of visual information in face classification using Eigenfaces and Fisherfaces

In the area of biometrics, face classification becomes one of the most appealing and commonly used approaches for personal identification. There has been an ongoing quest for designing systems that exhibit high classification rates and portray significant robustness. This feature becomes of paramount relevance when dealing with noisy and uncertain images. The design of face recognition classifiers capable of operating in presence of deteriorated (noise affected) face images requires a careful quantification of deterioration of the existing approaches vis-à-vis anticipated form and levels of image distortion. The objective of this experimental study is to reveal some general relationships characterizing the performance of two commonly used face classifiers (that is Eigenfaces and Fisherfaces) in presence of deteriorated visual information. The findings obtained in our study are crucial to identify at which levels of noise the face classifiers can still be considered valid. Prior knowledge helps us develop adequate face recognition systems. We investigate several typical models of image distortion such as Gaussian noise, salt and pepper, and blurring effect and demonstrate their impact on the performance of the two main types of the classifiers. Several distance models derived from the Minkowski family of distances are investigated with respect to the produced classification rates. The experimental environment concerns a well-known standard in this area of face biometrics such as the FERET database. The study reports on the performance of the classifiers, which is based on a comprehensive suite of experiments and delivers several design hints supporting further developments of face classifiers. Gabriel Jarillo Alvarado obtained his B.Sc. degree in Biomedical Engineering from the Universidad Iberoamericana, Mexico. In 2003 he obtained his M.Sc. degree from the University of Alberta at the Department of Electrical and Computer Engineering, he is currently enrolled in the Ph.D. program at the same University. His research interests involve machine learning, pattern recognition, and evolutionary computation with particular interest to biometrics for personal identification. Witold Pedrycz is a Professor and Canada Research Chair (CRC) in Computational Intelligence) in the Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada. His research interests involve Computational Intelligence, fuzzy modeling, knowledge discovery and data mining, fuzzy control including fuzzy controllers, pattern recognition, knowledge-based neural networks, relational computing, and Software Engineering. He has published numerous papers in this area. He is also an author of 9 research monographs. Witold Pedrycz has been a member of numerous program committees of conferences in the area of fuzzy sets and neurocomputing. He currently serves on editorial board of numereous journals including IEEE Transactions on Systems Man and Cybernetics, Pattern Recognition Letters, IEEE Transactions on Fuzzy Systems, Fuzzy Sets & Systems, and IEEE Transactions on Neural Networks. He is an Editor-in-Chief of Information Sciences. Marek Reformat received his M.Sc. degree from Technical University of Poznan, Poland, and his Ph.D. from University of Manitoba, Canada. His interests were related to simulation and modeling in time-domain, as well as evolutionary computing and its application to optimization problems For three years he worked for the Manitoba HVDC Research Centre, Canada, where he was a member of a simulation software development team. Currently, Marek Reformat is with the Department of Electrical and Computer Engineering at University of Alberta. His research interests lay in the areas of application of Computational Intelligence techniques, such as neuro-fuzzy systems and evolutionary computing, as well as probabilistic and evidence theories to intelligent data analysis leading to translating data into knowledge. He applies these methods to conduct research in the areas of Software and Knowledge Engineering. He has been a member of program committees of several conferences related to Computational Intelligence and evolutionary computing. Keun-Chang Kwak received B.Sc., M.Sc., and Ph.D. degrees in the Department of Electrical Engineering from Chungbuk National University, Cheongju, South Korea, in 1996, 1998, and 2002, respectively. During 2002–2003, he worked as a researcher in the Brain Korea 21 Project Group, Chungbuk National University. His research interests include biometrics, computational intelligence, pattern recognition, and intelligent control.     

A program for machine learning of counting criteria: empirical induction of logic-based classification rules

A program has been developed which derives classification rules from empirical observations and expresses these rules in a knowledge representation format called 'counting criteria'. Decision rules derived in this format are often more comprehensible than rules derived by existing machine learning programs such as AQ11. Use of the program is illustrated by the inference of discrimination criteria for certain types of bacteria based upon their biochemical characteristics. The program may be useful for the conceptual analysis of data and for the automatic generation of prototype knowledge bases for expert systems.     

A novel hybrid classification model of artificial neural networks and multiple linear regression models

The classification problem of assigning several observations into different disjoint groups plays an important role in business decision making and many other areas. Developing more accurate and widely applicable classification models has significant implications in these areas. It is the reason that despite of the numerous classification models available, the research for improving the effectiveness of these models has never stopped. Combining several models or using hybrid models has become a common practice in order to overcome the deficiencies of single models and can be an effective way of improving upon their predictive performance, especially when the models in combination are quite different. In this paper, a novel hybridization of artificial neural networks (ANNs) is proposed using multiple linear regression models in order to yield more general and more accurate model than traditional artificial neural networks for solving classification problems. Empirical results indicate that the proposed hybrid model exhibits effectively improved classification accuracy in comparison with traditional artificial neural networks and also some other classification models such as linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), K-nearest neighbor (KNN), and support vector machines (SVMs) using benchmark and real-world application data sets. These data sets vary in the number of classes (two versus multiple) and the source of the data (synthetic versus real-world). Therefore, it can be applied as an appropriate alternate approach for solving classification problems, specifically when higher forecasting accuracy is needed.     

A bootstrap method of distribution mixture proportion determination

A simulation-based methodology for distribution mixture proportion determination is presented. A Monte Carlo study using Gaussian population data and cosmic-ray-experiments data proved the reliability of the methods proposed.