support vector machines for nonlinear kernel arma system identification nonlinear system identification based on support vector machines svm has been usually addressed by means of the standard svm regression svr which can be seen as an implicit nonlinear autoregressive and moving average arma model in some reproducing kernel hilbert space rkhs the proposal of this letter is twofold first the explicit consideration of an arma model in an rkhs svm arma2k is proposed we show that stating the arma equations in an rkhs leads to solving the regularized normal equations in that rkhs in terms of the autocorrelation and cross correlation of the nonlinearly transformed input and output discrete time processes second a general class of svm based system identification nonlinear models is presented based on the use of composite mercer s kernels this general class can improve model flexibility by emphasizing the input output cross information svm arma4k which leads to straightforward and natural combinations of implicit and explicit arma models svr arma2k and svr arma4k capabilities of these different svm based system identification schemes are illustrated with two benchmark problems

robust lp norm least squares support vector regression with feature selection lp norm least squares support vector regression lp lssvr is proposed for feature selection in regression using the absolute constraint and the lp norm regularization term lp lssvr performs robust against outliers lp lssvr ensures the useful features to be selected based on theoretical analysis lp lssvr only solves a series of linear equations leading to fast training speed in this paper we aim a novel algorithm called robust lp norm least squares support vector regression lp lssvr that is more robust than the traditional least squares support vector regression ls svr using the absolute constraint and the lp norm regularization term our lp lssvr performs robust against outliers moreover though the optimization problem is non convex the sparse solution of lp norm and the lower bonds for nonzero components technique ensure useful features selected by lp lssvr and it helps to find the local optimum of our lp lssvr experimental results show that although lp lssvr is more robust than least squares support vector regression ls svr and much faster than lp norm support vector regression lp svr and svr due to its equality constraint it is slower than ls svr and l1 norm support vector regression l1 svr it is as effective as lp svr l1 svr ls svr and svr in both feature selection and regression

stable periodic solution of a discrete periodic lotka volterra competition system abstract this paper discusses a discrete lotka volterra competition system we first obtain the persistence of the system assuming that the coefficients in the system are periodic we obtain the existence of a periodic solution moreover under some additional conditions this periodic solution is globally stable our results not only reduce to those for the scalar equation when there is no coupling but also improve and complement some in the literature

asymptotic behaviors of support vector machines with gaussian kernel support vector machines svms with the gaussian rbf kernel have been popular for practical use model selection in this class of svms involves two hyperparameters the penalty parameter c and the kernel width this letter analyzes the behavior of the svm classifier when these hyperparameters take very small or very large values our results help in understanding the hyperparameter space that leads to an efficient heuristic method of searching for hyperparameter values with small generalization errors the analysis also indicates that if complete model selection using the gaussian kernel has been conducted there is no need to consider linear svm

reducing the number of support vectors of svm classifiers using the smoothed separable case approximation in this brief we propose a new method to reduce the number of support vectors of support vector machine svm classifiers we formulate the approximation of an svm solution as a classification problem that is separable in the feature space due to the separability the hard margin svm can be used to solve it this approach which we call the separable case approximation sca is very similar to the cross training algorithm explained in which is inspired by editing algorithms the norm of the weight vector achieved by sca can however become arbitrarily large for that reason we propose an algorithm called the smoothed sca ssca that additionally upper bounds the weight vector of the pruned solution and for the commonly used kernels reduces the number of support vectors even more the lower the chosen upper bound the larger this extra reduction becomes upper bounding the weight vector is important because it ensures numerical stability reduces the time to find the pruned solution and avoids overfitting during the approximation phase on the examined datasets ssca drastically reduces the number of support vectors

granular box regression granular computing grc has gained increasing attention in the past decade although not uniquely defined its basic idea is to approximate detailed machine like information by a coarser presentation on a human like level within granular computing the mapping of continuous variables into intervals plays an important role these intervals are often prerequisites for the formulation of linguistic variables in this paper we suggest a piecewise interval approximation and propose granular box regression its objective is to establish relationships between independent and dependent variables by multidimensional boxes we interpret granular box regression as interval regression and show its potential for the extraction of fuzzy rules from data in two experiments we apply granular box regression to an artificial as well as to a real dataset in the field of finance and evaluate its properties

euler s predictor corrector technique for solving the depth integrated shallow water equations abstract euler s predictor corrector technique combined with finite analysis method is applied to solve 2d advection diffusion shallow water equations in this algorithm the momentum equations are calculated by the finite analysis method based on a single mesh while the continuity equation is solved by euler s predictor corrector technique to verify the performance of this approach the simulation of tidal flow in the huangpu estuary is carried out the numerical results are found to be consistent with the field results implying that this proposed method is effective and applicable

bounds on error expectation for support vector machines we introduce the concept of span of support vectors sv and show that the generalization ability of support vector machines svm depends on this new geometrical concept we prove that the value of the span is always smaller and can be much smaller than the diameter of the smallest sphere containing the support vectors used in previous bounds vapnik 1998 we also demonstate experimentally that the prediction of the test error given by the span is very accurate and has direct application in model selection choice of the optimal parameters of the svm

interval regression by tolerance analysis approach in interval linear regression analysis we are given crisp or interval data and we are to determine appropriate interval regression parameters there are various methods for interval regression many of them possess the property that while some of the resulting interval regression parameters are very wide the other parameters are crisp this drawback is the main limiting factor for such methods and much effort has been devoted to overcoming it we propose a method motivated by tolerance analysis in linear systems our method yields intervals for regression parameters the widths of which are proportional to an in advance given vector of parameters moreover the method is computationally very cheap and provides a natural measure of quality of a model first we formulate the method for the basic model of crisp input crisp output data and then extend it to crisp input interval output and interval input interval output models for the interval valued cases we study several formulations of the solution concept possibility strong possibility weak possibility necessity here strong possibility is a new concept proposed as a natural counterpart to the remaining ones we prove that the method provides optimal interval parameters meeting centrality and proportionality requirements we also show that the method provides interval regression parameters satisfying various versions of tanaka lee s inclusion property we also derive a form of a complementarity theorem for the weak possibility and necessity solution concepts since practical problems may be affected by outlying observations we show that our approach is easily adapted to deal with them we illustrate the theory by examples

fastmmd ensemble of circular discrepancy for efficient two sample test the maximum mean discrepancy mmd is a recently proposed test statistic for the two sample test its quadratic time complexity however greatly hampers its availability to large scale applications to accelerate the mmd calculation in this study we propose an efficient method called fastmmd the core idea of fastmmd is to equivalently transform the mmd with shift invariant kernels into the amplitude expectation of a linear combination of sinusoid components based on bochner s theorem and fourier transform rahimi recht 2007 taking advantage of sampling the fourier transform fastmmd decreases the time complexity for mmd calculation from to where n and d are the size and dimension of the sample set respectively here l is the number of basis functions for approximating kernels that determines the approximation accuracy for kernels that are spherically invariant the computation can be further accelerated to by using the fastfood technique le sarlos smola 2013 the uniform convergence of our method has also been theoretically proved in both unbiased and biased estimates we also provide a geometric explanation for our method ensemble of circular discrepancy which helps us understand the insight of mmd and we hope will lead to more extensive metrics for assessing the two sample test task experimental results substantiate that the accuracy of fastmmd is similar to that of mmd and with faster computation and lower variance than existing mmd approximation methods

new support vector algorithms we propose a new class of support vector algorithms for regression and classification in these algorithms a parameter lets one effectively control the number of support vectors while this can be useful in its own right the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm the accuracy parameter epsilon in the regression case and the regularization constant c in the classification case we describe the algorithms give some theoretical results concerning the meaning and the choice of and report experimental results

bootstrap choice of the smoothing parameter in kernel density estimation summary cross validation based on integrated squared error has already been applied to the choice of smoothing parameter in the kernel method of density estimation in this paper an alternative resampling plan based on the bootstrap is proposed in an attempt to estimate mean integrated squared error this leads to a further data based choice of smoothing parameter the two methods are compared and some simulations and examples demonstrate the relative merits for large samples the bootstrap performs better than cross validation for many distributions

an architecture of neural networks with interval weights and its application to fuzzy regression analysis abstract in this paper we first propose an architecture of neural networks that have interval weights and interval biases a neural network with the proposed architecture maps an input vector of real numbers to an output interval the target output is also given as an interval next we define a cost function using the interval output from the neural network and the corresponding target output a learning algorithm is derived from the cost function in a similar manner as the bp back propagation algorithm we also show two variations of the learning algorithm for the proposed architecture which lead to the inclusion relation between the interval output and the interval target last we apply the learning algorithms to fuzzy regression analysis where target outputs are given as fuzzy numbers

a lattice boltzmann model for the shallow water equations a lattice boltzmann model for the shallow water equations labswe is developed it solves the equations with the source terms such as bed slope bed friction the model has been verified by solving both steady and unsteady flow problems excellent agreement is obtained between numerical predictions and analytical solutions the results show that the labswe is a very competitive method for computational hydraulics or hydrodynamics in terms of computational efficiency and accuracy

application of global optimization methods to model and feature selection many data mining applications involve the task of building a model for predictive classification the goal of this model is to classify data instances into classes or categories of the same type the use of variables not related to the classes can reduce the accuracy and reliability of classification or prediction model superfluous variables can also increase the costs of building a model particularly on large datasets the feature selection and hyper parameters optimization problem can be solved by either an exhaustive search over all parameter values or an optimization procedure that explores only a finite subset of the possible values the objective of this research is to simultaneously optimize the hyper parameters and feature subset without degrading the generalization performances of the induction algorithm we present a global optimization approach based on the use of cross entropy method to solve this kind of problem

k ns a classifier by the distance to the nearest subspace to improve the classification performance of k nn this paper presents a classifier called k ns based on the euclidian distances from a query sample to the nearest subspaces each nearest subspace is spanned by k nearest samples of a same class a simple discriminant is derived to calculate the distances due to the geometric meaning of the grammian and the calculation stability of the discriminant is guaranteed by embedding tikhonov regularization the proposed classifier k ns categorizes a query sample into the class whose corresponding subspace is proximal because the grammian only involves inner products the classifier is naturally extended into the high dimensional feature space induced by kernel functions the experimental results on 13 publicly available benchmark datasets show that k ns is quite promising compared to several other classifiers founded on nearest neighbors in terms of training and test accuracy and efficiency

semi implicit finite difference methods for the two dimensional shallow water equation abstract in this paper a semi implicit finite difference method for the 2 dimensional shallow water equations is derived and discussed a characteristic analysis of the governing equations is carried out first in order to determine those terms to be discretized implicitly so that the stability of the method will not depend upon the celerity such terms are the gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation the convective terms are discretized explicitly the simpler explicit discretization for the convective terms is the upwind discretization which is conditionally stable and introduces some artificial viscosity it is shown that the stability restriction is eliminated and the artificial viscosity is reduced when an eulerian lagrangian approach with large time steps is used to discretize the convective terms this method at each time step requires the solution of a linear symmetric 5 diagonal system such a system is diagonally dominant with positive elements on the main diagonal and negative ones elsewhere thus existence and uniqueness of the numerical solution is assured the resulting algorithm is mass conservative and fully vectorizable for an efficient implementation on modern vector computers the performance of this method is further improved when used in combination with an adi technique which results in two sets of simpler linear 3 diagonal systems and maintains all the properties described above

infinite σ limits for tikhonov regularization we consider the problem of tikhonov regularization with a general convex loss function this formalism includes support vector machines and regularized least squares for a family of kernels that includes the gaussian parameterized by a bandwidth parameter we characterize the limiting solution as in particular we show that if we set the regularization parameter 2p the regularization term of the tikhonov problem tends to an indicator function on polynomials of degree p with residual regularization in the case where p z the proof rests on two key ideas epi convergence a notion of functional convergence under which limits of minimizers converge to minimizers of limits and a value based formulation of learning where we work with regularization on the function output values y as opposed to the function expansion coefficients in the rkhs our result generalizes and unifies previous results in this area

support vector machinery for infinite ensemble learning ensemble learning algorithms such as boosting can achieve better performance by averaging over the predictions of some base hypotheses nevertheless most existing algorithms are limited to combining only a finite number of hypotheses and the generated ensemble is usually sparse thus it is not clear whether we should construct an ensemble classifier with a larger or even an infinite number of hypotheses in addition constructing an infinite ensemble itself is a challenging task in this paper we formulate an infinite ensemble learning framework based on the support vector machine svm the framework can output an infinite and nonsparse ensemble through embedding infinitely many hypotheses into an svm kernel we use the framework to derive two novel kernels the stump kernel and the perceptron kernel the stump kernel embodies infinitely many decision stumps and the perceptron kernel embodies infinitely many perceptrons we also show that the laplacian radial basis function kernel embodies infinitely many decision trees and can thus be explained through infinite ensemble learning experimental results show that svm with these kernels is superior to boosting with the same base hypothesis set in addition svm with the stump kernel or the perceptron kernel performs similarly to svm with the gaussian radial basis function kernel but enjoys the benefit of faster parameter selection these properties make the novel kernels favorable choices in practice

a variance minimization criterion to feature selection using laplacian regularization in many information processing tasks one is often confronted with very high dimensional data feature selection techniques are designed to find the meaningful feature subset of the original features which can facilitate clustering classification and retrieval in this paper we consider the feature selection problem in unsupervised learning scenarios which is particularly difficult due to the absence of class labels that would guide the search for relevant information based on laplacian regularized least squares which finds a smooth function on the data manifold and minimizes the empirical loss we propose two novel feature selection algorithms which aim to minimize the expected prediction error of the regularized regression model specifically we select those features such that the size of the parameter covariance matrix of the regularized regression model is minimized motivated from experimental design we use trace and determinant operators to measure the size of the covariance matrix efficient computational schemes are also introduced to solve the corresponding optimization problems extensive experimental results over various real life data sets have demonstrated the superiority of the proposed algorithms

persistence and global stability in discrete models of pure delay nonautonomous lotka volterra type abstract consider the persistence and the global asymptotic stability of the following discrete model of pure delay nonautonomous lotka volterra type n i p 1 n i p exp c i p j 1 n l 0 m a ij l p n j p k l p 0 1 2 1 i n n i p n i p 0 p 0 and n i 0 0 1 i n where each ci p and aijl p are bounded for p 0 and inf p 0 l 0 m a ii l p 0 a ij l p 0 i j n 1 i n and k l 0 1 l m in this paper for the above discrete system of pure delay type by improving the former work j math anal appl 273 2002 492 511 which extended the averaged condition offered by s ahmad and a c lazer nonlinear anal 40 2000 37 49 we offer conditions of persistence and considering a lyapunov like discrete function to the above discrete system we establish sufficient conditions of global asymptotic stability

a novel technique for subpixel image classification based on support vector machine this paper presents a novel support vector machine classifier designed for subpixel image classification pixel spectral unmixing the proposed classifier generalizes the properties of svms to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic this results in the definition of a fuzzy input fuzzy output support vector machine f2svm classifier that can 1 process fuzzy information given as input to the classification algorithm for modeling the subpixel information in the learning phase of the classifier and 2 provide a fuzzy modeling of the classification results allowing a relation many to one between classes and pixels the presented binary f2svm can address multicategory problems according to two strategies the fuzzy one against all foaa and the fuzzy one against one foao strategies these strategies generalize to the fuzzy case techniques based upon ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems the effectiveness of the proposed f2svm classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics experimental results confirm the validity of the proposed subpixel classification method

on quantile regression in reproducing kernel hilbert spaces with the data sparsity constraint for spline regressions it is well known that the choice of knots is crucial for the performance of the estimator as a general learning framework covering the smoothing splines learning in a reproducing kernel hilbert space rkhs has a similar issue however the selection of training data points for kernel functions in the rkhs representation has not been carefully studied in the literature in this paper we study quantile regression as an example of learning in a rkhs in this case the regular squared norm penalty does not perform training data selection we propose a data sparsity constraint that imposes thresholding on the kernel function coefficients to achieve a sparse kernel function representation we demonstrate that the proposed data sparsity method can have competitive prediction performance for certain situations and have comparable performance in other cases compared to that of the traditional squared norm penalty therefore the data sparsity method can serve as a competitive alternative to the squared norm penalty method some theoretical properties of our proposed method using the data sparsity constraint are obtained both simulated and real data sets are used to demonstrate the usefulness of our data sparsity constraint

support vector interval regression networks for interval regression analysis in this paper the support vector interval regression networks svirns are proposed for the interval regression analysis the svirns consist of two radial basis function networks one network identifies the upper side of data interval and the other network identifies the lower side of data intervals because the support vector regression svr approach is equivalent to solving a linear constrained quadratic programming problem the number of hidden nodes and the initial values of adjustable parameters can be easily obtained since the selection of a parameter e in the svr approach may seriously affect the modeling performance a two step approach is proposed to properly select the e value after the svr approach with the selected e an initial structure of svirns can be obtained besides outliers will not significantly affect the upper and lower bound interval obtained through the proposed two step approach consequently a traditional back propagation bp learning algorithm can be used to adjust the initial structure networks of svirns under training data sets without or with outliers due to the better initial structure of svirns are obtained by the svr approach the convergence rate of svirns is faster than the conventional networks with bp learning algorithms or with robust bp learning algorithms for interval regression analysis four examples are provided to show the validity and applicability of the proposed svirns

fuzzy regression analysis using neural networks abstract in this paper we propose simple but powerful methods for fuzzy regression analysis using neural networks since neural networks have high capability as an approximator of nonlinear mappings the proposed methods can be applied to more complex systems than the existing lp based methods first we propose learning algorithms of neural networks for determining a nonlinear interval model from the given input output patterns a nonlinear interval model whose outputs approximately include all the given patterns can be determined by two neural networks next we show two methods for deriving nonlinear fuzzy models from the interval model determined by the proposed algorithms nonlinear fuzzy models whose h level sets approximately include all the given patterns can be derived last we show an application of the proposed methods to a real problem

variable selection using svm based criteria we propose new methods to evaluate variable subset relevance with a view to variable selection relevance criteria are derived from support vector machines and are based on weight vector w 2 or generalization error bounds sensitivity with respect to a variable experiments on linear and non linear toy problems and real world datasets have been carried out to assess the effectiveness of these criteria results show that the criterion based on weight vector derivative achieves good results and performs consistently well over the datasets we used

the generalized lasso in the last few years the support vector machine svm method has motivated new interest in kernel regression techniques although the svm has been shown to exhibit excellent generalization properties in many experiments it suffers from several drawbacks both of a theoretical and a technical nature the absence of probabilistic outputs the restriction to mercer kernels and the steep growth of the number of support vectors with increasing size of the training set in this paper we present a different class of kernel regressors that effectively overcome the above problems we call this approach generalized lasso regression it has a clear probabilistic interpretation can handle learning sets that are corrupted by outliers produces extremely sparse solutions and is capable of dealing with large scale problems for regression functionals which can be modeled as iteratively reweighted least squares irls problems we present a highly efficient algorithm with guaranteed global convergence this defies a unique framework for sparse regression models in the very rich class of irls models including various types of robust regression models and logistic regression performance studies for many standard benchmark datasets effectively demonstrate the advantages of this model over related approaches

training hard margin support vector machines using greedy stagewise algorithm hard margin support vector machines hm svms suffer from getting overfitting in the presence of noise soft margin svms deal with this problem by introducing a regularization term and obtain a state of the art performance however this disposal leads to a relatively high computational cost in this paper an alternative method greedy stagewise algorithm for svms named gs svms is presented to cope with the overfitting of hm svms without employing the regularization term the most attractive property of gs svms is that its computational complexity in the worst case only scales quadratically with the size of training samples experiments on the large data sets with up to 400 000 training samples demonstrate that gs svms can be faster than libsvm 2 83 without sacrificing the accuracy finally we employ statistical learning theory to analyze the empirical results which shows that the success of gs svms lies in that its early stopping rule can act as an implicit regularization term

permanence for a discrete time lotka volterra type food chain model with delays abstract considered is a delayed discrete time lotka volterra type food chain model sufficient conditions are established for the permanence and the feasibility of the obtained results are illustrated with an example

top k feature selection framework using robust 0 1 integer programming feature selection fs which identifies the relevant features in a data set to facilitate subsequent data analysis is a fundamental problem in machine learning and has been widely studied in recent years most fs methods rank the features in order of their scores based on a specific criterion and then select the k top ranked features where k is the number of desired features however these features are usually not the top k features and may present a suboptimal choice to address this issue we propose a novel fs framework in this article to select the exact top k features in the unsupervised semisupervised and supervised scenarios the new framework utilizes the l0 2 norm as the matrix sparsity constraint rather than its relaxations such as the l1 2 norm since the l0 2 norm constrained problem is difficult to solve we transform the discrete l0 2 norm based constraint into an equivalent 0 1 integer constraint and replace the 0 1 integer constraint with two continuous constraints the obtained top k fs framework with two continuous constraints is theoretically equivalent to the l0 2 norm constrained problem and can be optimized by the alternating direction method of multipliers admm unsupervised and semisupervised fs methods are developed based on the proposed framework and extensive experiments on real world data sets are conducted to demonstrate the effectiveness of the proposed fs framework

tuning kernel parameters for svm based on expected square distance ratio the performance of a support vector machine svm depends highly on the selection of the kernel function type and relevant parameters to choose the kernel parameters properly methods analyzing the class separability have been widely adopted for their efficiency compared with other methods such as the popular grid search algorithm this paper proposes a novel index called the expected square distance ratio esdr which can serve as a better class separability criterion than the existing ones experiments on real world datasets show that compared with common kernel parameter selection methods that utilize the between class separation the variations in esdr with respect to the kernel parameter are much more in line with those of the classification accuracy leading to better kernel parameters moreover esdr takes the exact data distribution into account and can thus be used to study the model selection problem of an svm for certain forms of data distribution as an example we employ the esdr to analyze the selection of rbf radial basis function kernel parameters for gaussian data classification

interval regression analysis using support vector networks support vector machines svms have been very successful in pattern classification and function estimation problems for crisp data in this paper the v support vector interval regression network v svirn is proposed to evaluate interval linear and nonlinear regression models for crisp input and output data as it is difficult to select an appropriate value of the insensitive tube width in e support vector regression network the proposed v svirn alleviates this problem by utilizing a new parametric insensitive loss function the proposed v svirn automatically adjusts a flexible parametric insensitive zone of arbitrary shape and minimal size to include the given data besides the proposed method can achieve automatic accuracy control in the interval regression analysis task for a priori chosen v at most a fraction v of the data points lie outside the interval model constructed by the proposed v svirn to be more precise v is an upper bound on the fraction of training errors and a lower bound on the fraction of support vectors hence the selection of v is more intuitive moreover the proposed algorithm here is a model free method in the sense that we do not have to assume the underlying model function experimental results are then presented which show the proposed v svirn is useful in practice especially when the noise is heteroscedastic that is the noise strongly depends on the input value x

analysis of the distance between two classes for tuning svm hyperparameters an important step in the construction of a support vector machine svm is to select optimal hyperparameters this paper proposes a novel method for tuning the hyperparameters by maximizing the distance between two classes dbtc in the feature space with a normalized kernel function we find that dbtc can be used as a class separability criterion since the between class separation and the within class data distribution are implicitly taken into account employing dbtc as an objective function we develop a gradient based algorithm to search the optimal kernel parameter on the basis of the geometric analysis and simulation results we find that the optimal algorithm and the initialization problem become very simple experimental results on the synthetic and real world data show that the proposed method consistently outperforms other existing hyperparameter tuning methods

dual possibilistic regression analysis using support vector networks abstract this study proposes a novel and efficient dual regression model for possibilistic regression analysis that incorporates the principles of support vector machine svm theory the dual regression model which comprises an upper model and a lower model approximates the observed fuzzy phenomena from the outside and inside directions respectively such that the inclusion relationship between those two models holds the proposed dual regression model better explains the inherent vagueness that exists in a given dataset it provides the outer and inner bounds for the estimated vagueness region and allows an estimation of the degree of confidence in the predicted fuzzy output using the principles for a twin support vector machine tsvm the upper and lower models are estimated by solving two smaller svm type quadratic programming problems qpps instead of a single larger qpp this strategy significantly increases the learning speed for the proposed algorithm the structural risk minimization principle of svm makes the proposed method to yield better generalization ability the kernel function method offers a model independent framework for the proposed dual regression model this paper focuses on the class of radial kernels which enables the proposed method to conquer the problem of increasing spreads the radial kernel also gives the proposed method a unified framework that allows both crisp and fuzzy inputs the experimental results verify the effectiveness and efficiency of the proposed method in comparison with previous svm based dual regression model the proposed approach significantly improves the sparsity prediction speed and training speed

effects of kernel function on nu support vector machines in extreme cases how we should choose a kernel function in support vector machines svms is an important but difficult problem in this paper we discuss the properties of the solution of the spl nu svm s a variation of svm s for normalized feature vectors in two extreme cases all feature vectors are almost orthogonal and all feature vectors are almost the same in the former case the solution of the spl nu svm is nearly the center of gravity of the examples given while the solution is approximated to that of the spl nu svm with the linear kernel in the latter case although extreme kernels are not employed in practice analyzes are helpful to understand the effects of a kernel function on the generalization performance

persistence and global stability in a delayed gause type predator prey system without dominating instantaneous negative feedbacks abstract a delayed gause type predator prey system without dominating instantaneous negative feedbacks is investigated it is proved that the system is uniformly persistent under some appropriate conditions by means of constructing a suitable lyapunov functional sufficient conditions are derived for the local and global asymptotic stability of the positive equilibrium of the system

possibilistic linear regression with fuzzy data tolerance approach with prior information abstract we introduce the tolerance approach to the construction of fuzzy regression coefficients of a possibilistic linear regression model with fuzzy data both input and output the method is very general the only assumption is that cuts of the fuzzy data are efficiently computable we take into account possible prior restrictions of the parameters space we assume that the restrictions are given by linear and quadratic constraints the method for construction of the possibilistic regression coefficients is in a reduction of the fuzzy valued model to an interval valued model on a given cut which is further reduced to a linear time method i e running in time o n p computing with endpoints of the intervals here n is the number of observations and p is the number of regression parameters the speed of computation makes the method applicable for huge datasets unlike various approaches based on mathematical programming formulations the tolerance based construction preserves central tendency of the resulting regression coefficients in addition we prove further properties if inputs are crisp and outputs are fuzzy then the construction preserves piecewise linearity and convex shape of fuzzy numbers we derive an o n 2 p algorithm for enumeration of breakpoints of the membership function of the estimated coefficients similar results are also derived for the fuzzy input and output model we illustrate the theory for the case of triangular and asymmetric gaussian fuzzy inputs and outputs of an inflation consumption model

fuzzy regression wiht radial basis function network radial basis function network is used in fuzzy regression analysis without predefined functional relationship between the input and the output the proposed approach is a fuzzification of the connection weights between the hidden and the output layers this fuzzy network is trained by a hybrid learning algorithm where self organized learning is used for training the parameters of the hidden units and supervised learning is used for updating the weights between the hidden and the output layers the c mean clustering method and the k nearest neighbor heuristics are used for the self organized learning the supervised learning is carried out by solving a linear possibilistic programming problem techniques for the generalization of the network are also proposed numerical examples are used to illustrate and to test the performances of the approach

feature subset selection by bayesian network based optimization abstract a new method for feature subset selection in machine learning fss ebna feature subset selection by estimation of bayesian network algorithm is presented fss ebna is an evolutionary population based randomized search algorithm and it can be executed when domain knowledge is not available a wrapper approach over naive bayes and id3 learning algorithms is used to evaluate the goodness of each visited solution fss ebna based on the eda estimation of distribution algorithm paradigm avoids the use of crossover and mutation operators to evolve the populations in contrast to genetic algorithms in absence of these operators the evolution is guaranteed by the factorization of the probability distribution of the best solutions found in a generation of the search this factorization is carried out by means of bayesian networks promising results are achieved in a variety of tasks where domain knowledge is not available the paper explains the main ideas of feature subset selection estimation of distribution algorithm and bayesian networks presenting related work about each concept a study about the overfitting problem in the feature subset selection process is carried out obtaining a basis to define the stopping criteria of the new algorithm

a discrete particle swarm optimization method for feature selection in binary classification problems abstract this paper investigates the feature subset selection problem for the binary classification problem using logistic regression model we developed a modified discrete particle swarm optimization pso algorithm for the feature subset selection problem this approach embodies an adaptive feature selection procedure which dynamically accounts for the relevance and dependence of the features included the feature subset we compare the proposed methodology with the tabu search and scatter search algorithms using publicly available datasets the results show that the proposed discrete pso algorithm is competitive in terms of both classification accuracy and computational performance

fuzzy linear regression with fuzzy intervals abstract in this paper we introduce a new class of fuzzy linear regression models based on tanaka s approach unlike in the tanaka model here all training data influence the estimated interval the crisp lp of tanaka s approach is generalized to a fuzzy linear programming problem with the proposed model an adaptation of the fuzzy regression equation to new data becomes possible

training ν support vector classifiers theory and algorithms the support vector machine svm for classification proposed by scholkopf smola williamson and bartlett 2000 has the advantage of using a parameter on controlling the number of support vectors in this article we investigate the relation between svm and c svm in detail we show that in general they are two different problems with the same optimal solution set hence we may expect that many numerical aspects of solving them are similar however compared to regular c svm the formulation of svm is more complicated so up to now there have been no effective methods for solving large scale svm we propose a decomposition method for svm that is competitive with existing methods for c svm we also discuss the behavior of svm by some numerical experiments

permanence for a delayed discrete ratio dependent predator prey system with holling type functional response abstract sufficient conditions are established for the permanence in a delayed discrete predator prey model with holling type iii functional response n 1 k 1 n 1 k exp b 1 k a 1 k n 1 k 1 1 k n 1 k n 2 k n 1 2 k m 2 n 2 2 k n 2 k 1 n 2 k exp b 2 k 2 k n 1 2 k 2 n 1 2 k 2 m 2 n 2 2 k 2 our investigation confirms that when the death rate of the predator is rather small as well as the intrinsic growth rate of the prey is relatively large the species could coexist in the long run

a local information based feature selection algorithm for data regression this paper presents a novel feature selection algorithm for data regression with a lot of irrelevant features the proposed method is based on well established machine learning technique without any assumption about the underlying data distribution the key idea in this method is to decompose an arbitrarily complex nonlinear problem into a set of locally linear ones through local information and to learn globally feature relevance within the least squares loss framework in contrast to other feature selection algorithms for data regression the learning of this method is efficient since the solution can be readily found through gradient descent with a simple update rule experiments on some synthetic and real world data sets demonstrate the viability of our formulation of the feature selection problem and the effectiveness of our algorithm

an alternative method of cross validation for the smoothing of density estimates cross validation with kullback leibler loss function has been applied to the choice of a smoothing parameter in the kernel method of density estimation a framework for this problem is constructed and used to derive an alternative method of cross validation based on integrated squared error recently also proposed by rudemo 1982 hall 1983 has established the consistency and asymptotic optimality of the new method for small and moderate sized samples the performances of the two methods of cross validation are compared on simulated data and specific examples

feature selection using probabilistic prediction of support vector regression this paper presents a new wrapper based feature selection method for support vector regression svr using its probabilistic predictions the method computes the importance of a feature by aggregating the difference over the feature space of the conditional density functions of the svr prediction with and without the feature as the exact computation of this importance measure is expensive two approximations are proposed the effectiveness of the measure using these approximations in comparison to several other existing feature selection methods for svr is evaluated on both artificial and real world problems the result of the experiments show that the proposed method generally performs better than or at least as well as the existing methods with notable advantage when the dataset is sparse

the dynamic behavior of n species cooperation system with continuous time delays and feedback controls in this paper we consider a n species cooperation system with continuous time delays and feedback controls for general nonautonomous case by using differential inequality theory and constructing a suitable lyapunov functional we obtain sufficient conditions which guarantee the permanence and the global attractivity of the system for the periodic case we obtain sufficient conditions which guarantee the existence uniqueness and stability of a positive periodic solution for the almost periodic case by using the razumikhin type theorem we obtain the sufficient conditions which guarantee the existence of a positive almost periodic solution of the system

on asymptotic stability of delay difference systems in this paper we obtain some criteria for determining the asymptotic stability of the zero solution for some classes of delay difference systems by using a discrete version of the second lyapunov method our results can be well suited for computational purposes

uniform persistence and periodic solutions for a discrete predator prey system with delays abstract in this paper we deal with a discrete predator prey system with delay we first give a sufficient condition for the uniform persistence of the system assuming that the coefficients in the system are periodic by generalizing the yoshizawa s theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays we obtain the existence of a periodic solution basing on the uniform persistence result

from fuzzy regression to gradual regression interval based analysis and extensions abstract this paper proposes an analysis of parametric interval based regression methodologies according to ontic and epistemic visions of intervals when assuming an epistemic point of view a new interpretation of fuzzy regression through the notion of gradual intervals is developed which leads to gradual regression gradual regression is viewed as an extension of the imprecise interval based regression which is obtained by integrating an uncertain dimension gradual intervals can yield improved specificity compared to conventional intervals and jointly consider the concepts of imprecision and uncertainty through a single and coherent formalism the formulation of the gradual regression problem its resolution and the propagation of the information through the obtained regressive models are carried out via gradual interval arithmetic the proposed method allows not only the extension of the interval vision to the gradual case but also interesting interpretations according to non additive confidence measure theories possibility and belief functions

a positive finite difference advection scheme abstract this paper examines a class of explicit finite difference advection schemes derived along the method of lines an important application field is large scale atmospheric transport the paper therefore focuses on the demand of positivity for the spatial discretization attention is confined to conservative schemes using five points per direction the fourth order central scheme and the family of schemes comprising the second order central the second order upwind and the third order upwind biased are studied positivity is enforced through flux limiting it is concluded that the limited third order upwind discretization is the best candidate from the four examined for the time integration attention is confined to a number of explicit runge kutta methods of orders two up to four with regard to the demand of positivity these integration methods turn out to behave almost equally and no best method could be identified

interval regression analysis by quadratic programming approach when we use linear programming in possibilistic regression analysis some coefficients tend to become crisp because of the characteristic of linear programming on the other hand a quadratic programming approach gives more diverse spread coefficients than a linear programming one therefore to overcome the crisp characteristic of linear programming we propose interval regression analysis based on a quadratic programming approach another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression by changing the weights of the quadratic function we can analyze the given data from different viewpoints for data with crisp inputs and interval outputs the possibility and necessity models can be considered therefore the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed even though there always exist possibility estimation models the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model thus we consider polynomials as regression models since any curve can be represented by the polynomial approximation using polynomials we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models furthermore from the obtained possibility and necessity regression models a trapezoidal fuzzy output can be constructed

permanence and stability of equilibrium for a two prey one predator discrete model in this letter a predator prey system of two prey one predator discrete model is investigated it is proved that the system is permanence under some appropriate conditions by jacobian matrix method a sufficient and necessary condition is derived for the local asymptotic stability of a equilibrium of the system meanwhile we give a suitable example for supporting our theoretical result

subset selection in multiple linear regression models a hybrid of genetic and simulated annealing algorithms the question of variable selection in a multiple linear regression model is a major open research topic in statistics the subset selection problem in multiple linear regression deals with the selection of a minimal subset of input variables without loss of explanatory power in this paper we adapt the genetic and simulated annealing algorithms for variable selection in multiple linear regression the performance of this hybrid heuristic method is compared to those obtained by forward selection backward elimination and classical genetic algorithm search a comparative analysis on the literature data sets and simulation data shows that our hybrid heuristic method may suggest efficient alternative to traditional subset selection methods for the variable selection problem in multiple linear regression models

robust interval regression analysis using neural networks abstract as a very important tool for dealing with both crisp data and fuzzy data fuzzy regression analysis based on interval regression analysis has become an active area of research some neural network related methods for nonlinear interval regression analysis have been proposed on the assumption that given training data are totally good data the performance of these methods will significantly worsen when the training data are spoiled by outliers in this paper we introduce the concepts of polarity and quality of the training data on the basis of which we propose two robust learning algorithms for determining a robust nonlinear interval regression model which makes a feature of a new cost function for reflecting not only the polarity of the training data but also the estimated knowledge about the quality of the training data the two robust algorithms are derived in a manner similar to the back propagation bp algorithm simulation results show that our robust algorithms outperform the existing methods remarkably in two aspects when outliers are present 1 they are robust against outliers 2 their rates of convergence are improved to some extent

exact simplification of support vector solutions this paper demonstrates that standard algorithms for training support vector machines generally produce solutions with a greater number of support vectors than are strictly necessary an algorithm is presented that allows unnecessary support vectors to be recognized and eliminated while leaving the solution otherwise unchanged the algorithm is applied to a variety of benchmark data sets for both classification and regression and in most cases the procedure leads to a reduction in the number of support vectors in some cases the reduction is substantial

global attractivity of non autonomous lotka volterra competition system without instantaneous negative feedback abstract we consider a non autonomous lotka volterra competition system with distributed delays but without instantaneous negative feedbacks i e pure delay systems we establish some 3 2 type and m matrix type criteria for global attractivity of the positive equilibrium of the system which generalise and improve the existing ones

building support vector machines with reduced classifier complexity support vector machines svms though accurate are not preferred in applications requiring great classification speed due to the number of support vectors being large to overcome this problem we devise a primal method with the following properties 1 it decouples the idea of basis functions from the concept of support vectors 2 it greedily finds a set of kernel basis functions of a specified maximum size dmax to approximate the svm primal cost function well 3 it is efficient and roughly scales as o ndmax2 where n is the number of training examples and 4 the number of basis functions it requires to achieve an accuracy close to the svm accuracy is usually far less than the number of svm support vectors

choosing the kernel parameters for support vector machines by the inter cluster distance in the feature space determining the kernel and error penalty parameters for support vector machines svms is very problem dependent in practice a popular method to deciding the kernel parameters is the grid search method in the training process classifiers are trained with different kernel parameters and only one of the classifiers is required for the testing process this makes the training process time consuming in this paper we propose using the inter cluster distances in the feature spaces to choose the kernel parameters calculating such distance costs much less computation time than training the corresponding svm classifiers thus the proper kernel parameters can be chosen much faster experiment results show that the inter cluster distance can choose proper kernel parameters with which the testing accuracy of trained svms is competitive to the standard ones and the training time can be significantly shortened

a necessary and sufficient condition for permanence of a lotka volterra discrete system with delays abstract in this paper we consider the permanence of the following lotka volterra discrete competition system with delays k1 k2 l1 and l2 x n 1 x n exp r1 1 x n k1 1y n k2 y n 1 y n exp r2 1 2x n l1 y n l2 we show the system is permanent for all nonnegative integers k1 k2 l1 and l2 if and only if 1

formulations of support vector machines a note from an optimization point of view in this article we discuss issues about formulations of support vector machines svm from an optimization point of view first svms map training data into a higher maybe infinite dimensional space currently primal and dual formulations of svm are derived in the finite dimensional space and readily extend to the infinite dimensional space we rigorously discuss the primal dual relation in the infinite dimensional spaces second svm formulations contain penalty terms which are different from unconstrained penalty functions in optimization traditionally unconstrained penalty functions approximate a constrained problem as the penalty parameter increases we are interested in similar properties for svm formulations for two of the most popular svm formulations we show that one enjoys properties of exact penalty functions but the other is only like traditional penalty functions which converge when the penalty parameter goes to infinity

biased and unbiased cross validation in density estimation abstract nonparametric density estimation requires the specification of smoothing parameters the demands of statistical objectivity make it highly desirable to base the choice on properties of the data set in this article we introduce some biased cross validation criteria for selection of smoothing parameters for kernel and histogram density estimators closely related to one investigated in scott and factor 1981 these criteria are obtained by estimating l 2 norms of derivatives of the unknown density and provide slightly biased estimates of the average squared l 2 error or mean integrated squared error these criteria are roughly the analog of wahba s 1981 generalized cross validation procedure for orthogonal series density estimators we present the relationship of the biased cross validation procedure to the least squares cross validation procedure which provides unbiased estimates of the mean integrated squared error both methods are shown to be based on u statistics we compare the two metho

some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

a possibilistic regression based on gradual interval b splines application for hyperspectral imaging lake sediments abstract according to an epistemic view of intervals this paper proposes a possibilistic regression based on gradual interval b splines to represent the input output data mapping in this context an improvement of the parametric fuzzy regression through the notion of gradual interval b splines is proposed the proposed gradual regression based on b splines can be regarded as an extension of the nonparametric interval based regression where an uncertain dimension is integrated the proposed method is validated through illustrative and comparative examples moreover it is applied for modeling the input output behavior between reflectance and wavelengths in an application for hyperspectral imaging for lake sediments

fuzzy linear regression and its applications to forecasting in uncertain environment abstract linear regression has been used for many years in developing mathematical models for application in marketing management and sales forecasting in this paper two different sales forecasting techniques are discussed the first technique involves non fuzzy abstract methods of linear regression and econometrics a study of the international market sales of cameras done in 1968 by john scott armstrong utilized these non fuzzy forecasting techniques the second sales forecasting technique uses fuzzy linear regression introduced by h tanaka s uejima and k asai in 1980 in this paper a study of the computer and peripheral equipment sales in the united states is discussed using fuzzy linear regression moreover fuzzy linear regression is applied to forecasting in an uncertain environment finally some possible improvements and suggestions for further study are mentioned

supervised aggregated feature learning for multiple instance classification this paper introduces a novel algorithm called supervised aggregated feature learning or safe which combines both local instance level and global bag level information in a joint framework to address the multiple instance classification task in this realm the collective assumption is used to express the relationship between the instance labels and the bag labels by means of taking the sum as aggregation rule the proposed model is formulated within a least squares support vector machine setting where an unsupervised core model either kernel pca or kernel spectral clustering at the instance level is combined with a classification loss function at the bag level the corresponding dual problem consists of solving a linear system and the bag classifier is obtained by aggregating the instance scores synthetic experiments suggest that safe is advantageous when the instances from both positive and negative bags can be naturally grouped in the same cluster moreover real life experiments indicate that safe is competitive with the best state of the art methods

use of the zero norm with linear models and kernel methods we explore the use of the so called zero norm of the parameters of linear models in learning minimization of such a quantity has many uses in a machine learning context for variable or feature selection minimizing training error and ensuring sparsity in solutions we derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero norm the method boils down to implementing a simple modification of vanilla svm namely via an iterative multiplicative rescaling of the training data applications we investigate which aid our discussion include variable and feature selection on biological microarray data and multicategory classification

improving over fitting in ensemble regression by imprecise probabilities in this paper generalized versions of two ensemble methods for regression based on variants of the original adaboost algorithm are proposed the generalization of these regression methods consists in restricting the unit simplex for the weights of the instances to a smaller set of weighting probabilities various imprecise statistical models can be used to obtain a restricted set of weighting probabilities whose sizes each depend on a single parameter for particular choices of this parameter the proposed algorithms reduce to standard adaboost based regression algorithms or to standard regression the main advantage of the proposed algorithms compared to the basic adaboost based regression methods is that they have less tendency to over fitting because the weights of the hard instances are restricted several simulations and applications furthermore indicate a better performance of the proposed regression methods in comparison with the corresponding standard regression methods

very sparse lssvm reductions for large scale data least squares support vector machines lssvms have been widely applied for classification and regression with comparable performance with svms the lssvm model lacks sparsity and is unable to handle large scale data due to computational and memory constraints a primal fixed size lssvm pfs lssvm introduce sparsity using nystrom approximation with a set of prototype vectors pvs the pfs lssvm model solves an overdetermined system of linear equations in the primal however this solution is not the sparsest we investigate the sparsity error tradeoff by introducing a second level of sparsity this is done by means of l 0 norm based reductions by iteratively sparsifying lssvm and pfs lssvm models the exact choice of the cardinality for the initial pv set is not important then as the final model is highly sparse the proposed method overcomes the problem of memory constraints and high computational costs resulting in highly sparse reductions to lssvm models the approximations of the two models allow to scale the models to large scale datasets experiments on real world classification and regression data sets from the uci repository illustrate that these approaches achieve sparse models without a significant tradeoff in errors

a reliable data based bandwidth selection method for kernel density estimation we present a new method for data based selection of the bandwidth in kernel density estimation which has excellent properties it improves on a recent procedure of park and marron which itself is a good method in various ways first the new method has superior theoretical performance second it also has a computational advantage third the new method has reliably good performance for smooth densities in simulations performance that is second to none in the existing literature these methods are based on choosing the bandwidth to approximately minimize good quality estimates of the mean integrated squared error the key to the success of the current procedure is the reintroduction of a non stochastic term which was previously omitted together with use of the bandwidth to reduce bias in estimation without inflating variance

l1 regularization path algorithm for generalized linear models summary we introduce a path following algorithm for l1 regularized generalized linear models the l1 regularization procedure is useful especially because it in effect selects variables according to the amount of penalization on the l1 norm of the coefficients in a manner that is less greedy than forward selection backward deletion the generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor corrector method of convex optimization selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths we suggest intuitive and flexible strategies for choosing appropriate values we demonstrate the implementation with several simulated and real data sets

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

support vector interval regression machine for crisp input and output data support vector regression svr has been very successful in function estimation problems for crisp data in this paper we propose a robust method to evaluate interval regression models for crisp input and output data combining the possibility estimation formulation integrating the property of central tendency with the principle of standard svr the proposed method is robust in the sense that outliers do not affect the resulting interval regression furthermore the proposed method is model free method since we do not have to assume the underlying model function for interval nonlinear regression model with crisp input and output in particular this method performs better and is conceptually simpler than support vector interval regression networks svirns which utilize two radial basis function networks to identify the upper and lower sides of data interval five examples are provided to show the validity and applicability of the proposed method

decomposition methods for linear support vector machines in this letter we show that decomposition methods with alpha seeding are extremely useful for solving a sequence of linear support vector machines svms with more data than attributes this strategy is motivated by keerthi and lin 2003 who proved that for an svm with data not linearly separable after c is large enough the dual solutions have the same free and bounded components we explain why a direct use of decomposition methods for linear svms is sometimes very slow and then analyze why alpha seeding is much more effective for linear than nonlinear svms we also conduct comparisons with other methods that are efficient for linear svms and demonstrate the effectiveness of alpha seeding techniques in model selection

global stability of discrete population models with time delays and fluctuating environment the global stability of a discrete population model of volterra type is studied the model incorporates time delays and allows for a fluctuating environment by linearization of the model at positive solutions and construction of liapunov functionals sufficient conditions are obtained to ensure a positive solution of the model is stable and attracts all positive solutions

learning rates for classification with gaussian kernels this letter aims at refined error analysis for binary classification using support vector machine svm with gaussian kernel and convex loss our first result shows that for some loss functions su

input space versus feature space in kernel based methods this paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector sv kernel functions we first discuss the geometry of feature space in particular we review what is known about the shape of the image of input space under the feature space map and how this influences the capacity of sv methods following this we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel using the example of the class of inhomogeneous polynomial kernels which are often used in sv pattern recognition we then discuss the connection between feature space and input space by dealing with the question of how one can given some vector in feature space find a preimage exact or approximate in input space we describe algorithms to tackle this issue and show their utility in two applications of kernel methods first we use it to reduce the computational complexity of sv decision functions second we combine it with the kernel pca algorithm thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real world data

asymptotic behavior of solutions in nonautonomous predator prey patchy system with beddington type functional response abstract in this paper we study the asymptotic behavior of solutions in nonautonomous predator prey patchy system with beddington type functional response it is proved that the system is permanent under some appropriate conditions furthermore if the system is a n almost periodic one a set of easily verifiable sufficient conditions which guarantee the existence uniqueness and global asymptotic stability of a positive almost periodic solutions of system are obtained

the normalized interval regression model with outlier detection and its real world application to house pricing problems tanaka and his colleagues initially proposed fuzzy linear regression models in 1982 from then on fuzzy regression analysis has been widely studied by many researchers since tanaka s model uses the inclusion relationship between the given data and the estimated data it was pointed out that tanaka s model is sensitive to outliers how to deal with the outlier problem has been a very important issue and attracted much attention from fuzzy regression researchers given crisp multiple independent variables and single interval dependent variable we introduce the normalized upper and lower interval regression models and propose two outlier detection approaches for them the dual problem of the normalized upper interval regression model is used to find out potential outliers for the normalized lower interval regression model the existence of the outliers makes it infeasible the relaxation approach is proposed to find out the outliers by deleting the outliers we can find out the possibilistic functional relationship of the major data a case study involving a house pricing problem is analyzed in detail household size loan ratio and annual household income are identified as the independent variables and acceptable purchase price is the interval dependent variable with the data collected from the survey in shanghai the normalized upper and lower interval regression models are built with deleting the outliers the proposed models provide managerial insights into the real estate market and important policy implications in regulating urban land development