Nonlinear Discriminant Function Research Articles

Deformation pattern classification and energy absorption optimization of the eccentric body centered cubic lattice structures

Lattice structures have shown excellent mechanical properties, such as high energy absorption capacity. In this work, the extended body centered cubic lattice was proposed by offsetting the position of the body center. The pattern recognition method of nonlinear discriminant function was creatively used to classify the proposed eccentric body centered cubic (EBCC) lattice structures according to their deformation patterns. The results indicated that the lattice structures belong to X-Pattern possessed the best energy absorption capability. Further, the relationship between the energy absorption properties and the configuration was captured using a modified symmetric radius basis function (RBF) surrogate model showing higher computational efficiency and approximately equal accuracy compared to the original RBF model. The nondominated sorting genetic algorithm II (NSGA-II) was carried out to obtain the Pareto optimal set, rendering the EBCC structure with balanced properties of high specific energy absorption and low peak crushing force. This work presents a first effort in optimizing the energy absorption of lattice structures through pattern recognition, thus expanding the approaches for designing new lattice structures.

Using the linear and non-linear discriminant function with cluster analysis to study the level of education for the completed stages (governmental – private) In Nineveh Governorate

The basic idea of this research is to study the influential variables that led to the differences between the performance of public and private schools, and through the use of some linear statistical methods, which are the function of discriminatory analysis and nonlinear methods represented by the function of logistic regression and cluster analysis, where the comparison between the two groups of public and community schools and know the appropriateness of each of the methods used with the applied data of the study community, which includes data The finished stage for the school year(2018-2019) of each of the schools (primary- middle- preparatory(Bio)) in the Nineveh Governorate Education Directorate, to determine the group and the best stage in addition to identifying the variables that affect the performance in order to reach improvement and standardization of the educational path.

Discriminante nao linear baseado em mistura de distribuicoes: uma aplicacao no tempo de retorno de observacoes de fluídos máximos heterogéneos na bacia do rio Paranapanema-Brasil

In this work, maximum flows observed in the Paranapanema river basin are modeled by a mixture of two GEV distributions whose components correspond to the summer and winter subpopulations. The nonlinear discriminant function allowed to confirm the assumption of mixture model.The proposed model is then used to determine probabilities of exceedance and return periods associated with extreme flows, which are of fundamental importance for hydraulic projects. The results show significant differences when a mixture model is used and therefore an approach more coherent with the observed data.

Fuzzy DEA-based classifier and its applications in healthcare management.

Nonlinear fuzzy classification models have better classification performance than linear fuzzy classifiers. In many nonlinear fuzzy classification problems, piecewise-linear fuzzy discriminant functions can approximate nonlinear fuzzy discriminant functions. In this paper, we first build fuzzy classifier based on data envelopment analysis (DEA) for incremental separable fuzzy training data, which can be widely applied in the healthcare management with fuzzy attributes, then we apply the proposed fuzzy DEA-based classifier in the diagnosis of Coronary with fuzzy symptoms and the classification of breast cancer dataset with fuzzy disturbance. Numerical experiments show the proposed fuzzy DEA-based classifier is accurate and robust.

Estimation of a nonlinear discriminant function from a mixture of two GEV distributions

ABSTRACTIn this paper, the identifiability of finite mixture of generalized extreme value (GEV) distributions is proved. Next, a procedure for finding maximum likelihood estimates (MLEs) of the parameters of a finite mixture of two generalized extreme value (MGEV) distributions is presented by using classified and unclassified observations. Then, a nonlinear discriminant function for a mixture of two GEV distributions is derived and the performance of the corresponding estimated discriminant function is investigated through a series of simulation experiments. Finally, the methodology is applied to real data.

The Asymptotic Relative Efficiency of a Nonlinear Discriminant Function from a Mixture of Two Inverse Weibull Distributions

The Asymptotic Relative Efficiency of a Nonlinear Discriminant Function from a Mixture of Two Inverse Weibull Distributions

DEA-Based Piecewise Linear Discriminant Analysis

Nonlinear classification models have better classification performance than the linear classifiers. However, for many nonlinear classification problems, piecewise-linear discriminant functions can approximate nonlinear discriminant functions. In this study, we combine the algorithm of data envelopment analysis (DEA) with classification information, and propose a novel DEA-based classifier to construct a piecewise-linear discriminant function, in this classifier, the nonnegative conditions of DEA model are loosed and class information is added; Finally, experiments are performed using a UCI data set to demonstrate the accuracy and efficiency of the proposed model.

Updating a nonlinear discriminant function estimated from a mixture of two Burr Type III distributions

ABSTRACTThe main contribution of this paper is is updating a nonlinear discriminant function on the basis of data of unknown origin. Specifically a procedure is developed for updating the nonlinear discriminant function on the basis of two Burr Type III distributions (TBIIID) when the additional observations are mixed or classified. First the nonlinear discriminant function of the assumed model is obtained. Then the total probabilities of misclassification are calculated. In addition a Monte carlo simulation runs are used to compute the relative efficiencies in order to investigate the performance of the developed updating procedures. Finally the results obtained in this paper are illustrated through a real and simulated data set.

Estimation of a Discriminant Function from a Mixture of Two Burr Type III Distributions

In this article, we propose the finite mixture of two Burr Type-III distributions (MTBIIID). First, we formulate the proposed model with some properties and prove the identifiability property. Next, we obtain the maximum likelihood estimates (MLEs) of the unknown parameters of MTBIIID under classified and unclassified observations. Also, we estimate the nonlinear discriminant function of the underlying model. In addition, we calculate the total probabilities of misclassification as well as the percentage bias. Further, we investigate the performance of the all results through series of the simulation experiments by the means of the relative efficiencies.

Use of basis images for detection and classification of celiac disease.

Celiac disease commonly occurs in approximately 1% of populations, but it can be difficult to diagnose. The standard method to diagnose celiac disease includes analysis of endoscopy images of the small intestinal mucosa to detect presence of villous atrophy, which can be subtle. We have devised a means to improve the image-based detection of villous atrophy and other abnormality in videocapsule endoscopy by means of incorporating basis images. Basis images were extracted from a series of 200 consecutive image frames acquired over 100 seconds at the level of the duodenal bulb in 13 celiac patients and in 13 controls. They were converted from color to 256 grayscale levels (gsl; 0 = black, 255 = white). Eight basis images were used for analysis. A histogram was constructed for each basis image, and the mean and standard deviation of the histogram values were tabulated. The significance of the difference in histogram mean level for celiacs versus controls was determined. Then the histogram mean was plotted versus the standard deviation, separately for all eight basis images, and also averaged for all bases combined. The mean histogram level for celiacs was 127.59+6.05 gsl versus 129.25+5.53 gsl for controls (p< 0.05). Thus celiac basis images tended to be darker and also more variable as compared with controls. For nonlinear classification, using the average of combined basis images, the sensitivity was 84.6% while the specificity was 92.3%. Using the single most important basis image for nonlinear classification, the sensitivity was 84.6% while the specificity was 76.9%. Construction of basis images can be useful to condense videocapsule image series into salient information, for detection of differences in grayscale level mean and variation in celiac versus control image series, and for classification of celiac versus control videoclips with nonlinear discriminant functions.

A MULTI-CLASS SUPPORT VECTOR MACHINE: THEORY AND MODEL

A multi-class support vector machine (M-SVM) is developed, its dual is derived, its dual is mapped to high dimensional feature spaces using inner product kernels, and its performance is tested. The M-SVM is formulated as a quadratic programming model. Its dual, also a quadratic programming model, is very elegant and is easier to solve than the primal. The discriminant functions can be directly constructed from the dual solution. By using inner product kernels, the M-SVM can be built and nonlinear discriminant functions can be constructed in high dimensional feature spaces without carrying out the mappings from the input space to the feature spaces. The size of the dual, measured by the number of variables and constraints, is independent of the dimension of the input space and stays the same whether the M-SVM is built in the input space or in a feature space. Compared to other models published in the literature, this M-SVM is equally or more effective. An example is presented to demonstrate the dual formulation and solution in feature spaces. Very good results were obtained on benchmark test problems from the literature.

Hierarchical Discriminant Analysis and Its Application

This article presents a new discriminant analysis method and tries to improve the accuracy of discriminant problems without reducing variables. This method establishes two layers of discriminant functions. For the first layer, a linear discriminant function is constructed to determine the sample type. Those samples’ type are not determined at the first layer, they will be distinguished as sub-samples, then a second layer of a nonlinear discriminant function will be established to determine the sub-sample type. The examples show that this method can handle discriminant problems of complex data, and results of this method are better than some common methods.

Estimation of a discriminant function from a mixture of two inverse Weibull distributions

The classification of a random variable based on a mixture can be meaningfully discussed only if the class of all finite mixtures is identifiable. In this paper, we find the maximum-likelihood estimates of the parameters of the mixture of two inverse Weibull distributions by using classified and unclassified observations. Next, we estimate the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification as well as the percentage bias. In addition, we investigate the performance of all results through a series of simulation experiments by means of relative efficiencies. Finally, we analyse some simulated and real data sets through the findings of the paper.

A neural network-based infection screening system that uses vital signs and percutaneous oxygen saturation for rapid screening of patients with influenza

Objective: Influenza is a highly infectious viral disease, which occurs epidemically almost every winter in Japan. Rapid screening of patients with suspected influenza in places of mass gathering is important to delay or prevent transmission of the infection. The aim of this study was to assess the effectiveness of our newly developed infection screening system that employed vital signs and percutaneous oxygen saturation (SpO2) as parameters in a clinical setting. Methods: Since SpO2 accurately reflects respiratory status during influenza virus infection, we upgraded our previous system by adding SpO2 as a new parameter to improve the screening accuracy. This system instantly measures SpO2 and vital signs (i.e., heart rate, respiration rate, and facial temperature), which automatically detects infected individuals via a neural network-based nonlinear discriminant function using these derived parameters. We tested the system on 45 patients with seasonal influenza (35.8℃ 2 as a screening parameter, we achieved superior sensitivity and NPV compared to that reported in our previous paper (sensitivity = 88%; NPV = 82%). Conclusions: Our results suggest that SpO2 is a good screening parameter that improves the accuracy of infection screening. The proposed system has the potential to efficiently identify infected individuals, thereby delaying or preventing the spread of infection during epidemic seasons.

Updating a nonlinear discriminant function estimated from a mixture of two inverse Weibull distributions

In this paper, we investigate the problem of updating a discriminant function on the basis of data of unknown origin. We consider the updating procedure for the nonlinear discriminant function on the basis of two inverse Weibull distributions in situations when the additional observations are mixed or classified. Then, we introduce the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification. In addition, we investigate the performance of the updating procedures through series of simulation experiments by means of the relative efficiencies. Finally, we analyze a simulated data set by using the findings of the paper.

Nonlinear Discriminant Functions for Mixed Random Walk Models

A procedure is presented for finding maximum likelihood estimates of the parameters of a mixture of two random walk distributions in two cases, using classified and unclassified observations. Based on small sample size, estimation of nonlinear discriminant functions is considered. Throughout simulation experiments, the performance of the corresponding estimated nonlinear discriminant functions is investigated. The total probabilities of misclassification and percentage biases are evaluated and discussed.

Support vector machine classification with noisy data: a second order cone programming approach

In this paper, we investigate the stability of linear and quadratic programming support vector machines (SVMs) with bounded noise in the input data using a robust optimisation model. For a linear discriminant function, this model is expressed as a second order cone optimisation problem. Using the concept of the kernel function, we generalise for nonlinear discriminant functions. Intuitively, it looks quite clear that large margin classifiers are robust in terms of bounded input noise. However, there is no theoretical analysis investigating this behaviour. We show that the SVM solution is stable under bounded perturbations of the data both in the linear programming and quadratic programming. Computational results are also presented for toy and real-world data.

Estimation of a Discriminant Function Based on Small Sample Size from a Mixture of Two Gumbel Distributions

The identifiability of finite mixture of Gumbel distributions is proved. A procedure is presented for finding maximum likelihood estimates for the four parameters of a mixture of two Gumbel distributions, using classified and unclassified observations. A nonlinear discriminant function for a mixture of two Gumbel distributions is derived and estimated based on small sample size. Throughout simulation experiments, the performance of the corresponding estimated nonlinear discriminant function is investigated.

Distinguishing patients with celiac disease by quantitative analysis of videocapsule endoscopy images

Background Although videocapsule endoscopy images are helpful in the evaluation of celiac disease, their interpretation is subjective. Quantitative disease markers could assist in determining the extent of villous atrophy and response to treatment. Method Capsule endoscopy images were acquired from celiac patients with small bowel pathology ( N = 11) and from control patients ( N = 10). Image resolution was 576 × 576 pixels in dimension, 256 grayscale levels, and had a 2 s −1 frame rate. Pixel brightness and image texture were measured over 10 × 10 pixel subimages and then averaged for 56 × 56 subimages per frame. Measurements were obtained at five locations from proximal to distal small intestine in each patient. At each location, measurements were calculated using 200 consecutive image frames (100 s). Mean frame-to-frame pixel brightness, image texture, and periodicity in brightness, an estimate of wall motion or intestinal motility, were computed and used for classification with a nonlinear discriminant function. Results From pooled data, celiac images had greater texture than did images from control patients ( p < 0.001) and exhibited more frame-to-frame brightness variation as well ( p = 0.032). The dominant period of brightness was longer in celiacs ( p = 0.001), possibly indicating decreased motility. Using the markers for three-dimensional nonlinear classification of celiacs versus controls, sensitivity was 92.7% and specificity was 93.5%. The relationship between dominant period and small intestinal transit time was approximately linear for both celiacs and controls ( r 2 = 0.42 and r 2 =0 .55, respectively). Conclusions Videocapsule images can be quantified to detect villous atrophy throughout the small intestine, and to distinguish individuals with celiac disease from individuals lacking mucosal atrophy.

Margin-Maximizing Feature Elimination Methods for Linear and Nonlinear Kernel-Based Discriminant Functions

Feature selection for classification in high-dimensional spaces can improve generalization, reduce classifier complexity, and identify important, discriminating feature "markers." For support vector machine (SVM) classification, a widely used technique is recursive feature elimination (RFE). We demonstrate that RFE is not consistent with margin maximization, central to the SVM learning approach. We thus propose explicit margin-based feature elimination (MFE) for SVMs and demonstrate both improved margin and improved generalization, compared with RFE. Moreover, for the case of a nonlinear kernel, we show that RFE assumes that the squared weight vector 2-norm is strictly decreasing as features are eliminated. We demonstrate this is not true for the Gaussian kernel and, consequently, RFE may give poor results in this case. MFE for nonlinear kernels gives better margin and generalization. We also present an extension which achieves further margin gains, by optimizing only two degrees of freedom--the hyperplane's intercept and its squared 2-norm--with the weight vector orientation fixed. We finally introduce an extension that allows margin slackness. We compare against several alternatives, including RFE and a linear programming method that embeds feature selection within the classifier design. On high-dimensional gene microarray data sets, University of California at Irvine (UCI) repository data sets, and Alzheimer's disease brain image data, MFE methods give promising results.