an iterative algorithm learning the maximal margin classifier abstract a simple learning algorithm for maximal margin classifiers also support vector machines with quadratic cost function is proposed we build our iterative algorithm on top of the schlesinger kozinec algorithm s k algorithm from 1981 which finds a maximal margin hyperplane with a given precision for separable data we suggest a generalization of the s k algorithm i to the non linear case using kernel functions and ii for non separable data the requirement in memory storage is linear to the data this property allows the proposed algorithm to be used for large training problems the resulting algorithm is simple to implement and as the experiments showed competitive to the state of the art algorithms the implementation of the algorithm in matlab is available we tested the algorithm on the problem aiming at recognition poor quality numerals

stabilization of partitioned solution procedure for pore fluid soil interaction analysis on montre que la solution decalee conventionnelle des problemes d interaction fluide sol dans les pores souffre de restrictions sur la stabilite on presente une forme stabilisee de la procedure de solution decalee de ce probleme on recommande cette procedure pour l implementation des problemes d interaction sol fluide

a fast iterative nearest point algorithm for support vector machine classifier design in this paper we give a new fast iterative algorithm for support vector machine svm classifier design the basic problem treated is one that does not allow classification violations the problem is converted to a problem of computing the nearest point between two convex polytopes the suitability of two classical nearest point algorithms due to gilbert and mitchell et al is studied ideas from both these algorithms are combined and modified to derive our fast algorithm for problems which require classification violations to be allowed the violations are quadratically penalized and an idea due to cortes and vapnik and friess is used to convert it to a problem in which there are no classification violations comparative computational evaluation of our algorithm against powerful svm methods such as platt s sequential minimal optimization shows that our algorithm is very competitive

unconditionally stable staggered solution procedure for soil pore fluid interaction problems this paper presents a simple procedure for modifying the dynamic coupled soil pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used the solution method is simpler than an alternative suggested by park15 and has a direct physical interpretation this stabilized procedure is efficient in numerical time domain analysis of soil pore fluid occurring in earthquake and consolidation problems numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure

evaluation of three and two field finite element methods for the dynamic response of saturated soil the three field formulation u p u is presented and is applied to solve dynamic equations for saturated porous media in order to evaluate the accuracy and the performance of this three field approximation the u u and the u w formulations are also considered and a few one and two dimensional examples are solved using the three methods problems for which both the pore fluid and the solid grains are incompressible are also considered and are solved using the u p u approximation accuracy was determined by a comparison of the finite element results with the analytical solution given by gajo and mongiovi 19 for a wide range of permeability

clifford support vector machines for classification regression and recurrence this paper introduces the clifford support vector machines csvm as a generalization of the real and complex valued support vector machines using the clifford geometric algebra in this framework we handle the design of kernels involving the clifford or geometric product in this approach one redefines the optimization variables as multivectors this allows us to have a multivector as output therefore we can represent multiple classes according to the dimension of the geometric algebra in which we work we show that one can apply csvm for classification and regression and also to build a recurrent csvm the csvm is an attractive approach for the multiple input multiple output processing of high dimensional geometric entities we carried out comparisons between csvm and the current approaches to solve multiclass classification and regression we also study the performance of the recurrent csvm with experiments involving time series the authors believe that this paper can be of great use for researchers and practitioners interested in multiclass hypercomplex computing particularly for applications in complex and quaternion signal and image processing satellite control neurocomputation pattern recognition computer vision augmented virtual reality robotics and humanoids

optimal interval estimation for a family of lower truncated distribution under progressive censoring in this paper based on progressively type ii censored sample different types of interval estimates of a general lower truncated distribution are constructed exact confidence intervals and joint exact confidence regions are derived for unknown model parameter and the lower truncated threshold bound optimal criteria are also provided for choosing the best confidence interval and confidence region among obtained estimates two real life examples and a numerical study are presented to illustrate the performance of our results

a quadratically constrained map classifier using the mixture of gaussians models as a weight function in this paper we propose classifiers derived from quadratically constrained maximum a posteriori qcmap estimation the qcmap consists of the maximization of the expectation of a cost function which is derived from the maximum a posteriori probability and a quadratic constraint this criterion is highly general since its forms include least squares regressions and a support vector machine furthermore the criterion provides a novel classifier the gaussian qcmap the qcmap procedure still has large theoretical interest and its full extensibility has yet to be explored in this paper we propose using the mixture of gaussian distributions as the qcmap weight function the mixture of gaussian distributions has wide ranging applicability and encompasses forms such as a normal distribution model and a kernel density model we propose four types of mixture of gaussian functions for qcmap classifiers and conduct experiments to demonstrate their advantages

a novel geometric approach to binary classification based on scaled convex hulls geometric methods are very intuitive and provide a theoretical foundation to many optimization problems in the fields of pattern recognition and machine learning in this brief the notion of scaled convex hull sch is defined and a set of theoretical results are exploited to support it these results allow the existing nearest point algorithms to be directly applied to solve both the separable and nonseparable classification problems successfully and efficiently then the popular s k algorithm has been presented to solve the nonseparable problems in the context of the sch framework the theoretical analysis and some experiments show that the proposed method may achieve better performance than the state of the art methods in terms of the number of kernel evaluations and the execution time

rapid and brief communication unified dual for bi class svm approaches svm theory was originally developed on the basis of a separable binary classification problem and other approaches have been later introduced in this paper we demonstrated that all these approaches admit the same dual problem formulation

geometric intuition and algorithms for ev svm in this work we address the ev svm model proposed by perez cruz et al as an extension of the traditional v support vector classification model v svm through an enhancement of the range of admissible values for the regularization parameter v the ev svm has been shown to be able to produce a wider variety of decision functions giving rise to a better adaptability to the data however while a clear and intuitive geometric interpretation can be given for the v svm model as a nearest point problem in reduced convex hulls rch npp no previous work has been made in developing such intuition for the ev svm model in this paper we show how ev svm can be reformulated as a geometrical problem that generalizes rch npp providing new insights into this model under this novel point of view we propose the rapminos algorithm able to solve ev svm more efficiently than the current methods furthermore we show how rapminos is able to address the ev svm model for any choice of regularization norm lp 1 seamlessly which further extends the svm model flexibility beyond the usual ev svm models

clipping algorithms for solving the nearest point problem over reduced convex hulls the nearest point problem npp i e finding the closest points between two disjoint convex hulls has two classical solutions the gilbert schlesinger kozinec gsk and mitchell dem yanov malozemov mdm algorithms when the convex hulls do intersect npp has to be stated in terms of reduced convex hulls rchs made up of convex pattern combinations whose coefficients are bound by a m 1 value and that are disjoint for suitable m the gsk and mdm methods have recently been extended to solve npp for rchs using the particular structure of the extreme points of a rch while effective their reliance on extreme points may make them computationally costly particularly when applied in a kernel setting in this work we propose an alternative clipped extension of classical mdm that results in a simpler algorithm with the same classification accuracy than that of the extensions already mentioned but also with a much faster numerical convergence

a geometric approach to support vector machine svm classification the geometric framework for the support vector machine svm classification problem provides an intuitive ground for the understanding and the application of geometric optimization algorithms leading to practical solutions of real world classification problems in this work the notion of reduced convex hull is employed and supported by a set of new theoretical results these results allow existing geometric algorithms to be directly and practically applied to solve not only separable but also nonseparable classification problems both accurately and efficiently as a practical application of the new theoretical results a known geometric algorithm has been employed and transformed accordingly to solve nonseparable problems successfully

dual unification of bi class support vector machine formulations support vector machine svm theory was originally developed on the basis of a linearly separable binary classification problem and other approaches have been later introduced for this problem in this paper it is demonstrated that all these approaches admit the same dual problem formulation in the linearly separable case and that all the solutions are equivalent for the non linearly separable case all the approaches can also be formulated as a unique dual optimization problem however their solutions are not equivalent discussions and remarks in the article point to an in depth comparison between svm formulations and associated parameters

a general soft method for learning svm classifiers with l 1 norm penalty based on the geometric interpretation of support vector machines svms this paper presents a general technique that allows almost all the existing l 2 norm penalty based geometric algorithms including gilbert s algorithm schlesinger kozinec s sk algorithm and mitchell dem yanov malozemov s mdm algorithm to be softened to achieve the corresponding learning l 1 svm classifiers intrinsically the resulting soft algorithms are to find e optimal nearest points between two soft convex hulls theoretical analysis has indicated that our proposed soft algorithms are essentially generalizations of the corresponding existing hard algorithms and consequently they have the same properties of convergence and almost the identical cost of computation as a specific example the problem of solving n svms by the proposed soft mdm algorithm is investigated and the corresponding solution procedure is specified and analyzed to validate the general soft technique several real classification experiments are conducted with the proposed l 1 norm based mdm algorithms and numerical results have demonstrated that their performance is competitive to that of the corresponding l 2 norm based algorithms such as sk and mdm algorithms

inference for the kumaraswamy distribution under k record values based on the k record values inference is considered for the parameters of the kumaraswamy distribution the maximum likelihood estimates and alternative point estimates based on proposed pivotal quantities are provided for the unknown model parameters and series of exact confidence intervals and exact confidence regions are constructed as well for the confidence intervals and regions the corresponding smallest size confidence sets and their optimization procedures are presented based on minimizing the lagrangian functions under given significance level two illustrative examples based on real and simulated data are provided to assess the performance of the proposed results maximum likelihood and pivotal based point estimates were proposed for kumaraswamy model exact confidence intervals and regions are constructed for kumaraswamy parameter pivotal based estimation methods can be extend to other model and failure samples cases the smallest sets are provided through constrained optimization problems monthly water capacity and simulated data examples are investigated

a further look at newmark houbolt etc time stepping formulae this paper looks at some well known methods for the numerical integration of the vibration equation from the point of view of various groupings of the independent equations involved new forms are given of the general three parameter method introduced by zienkiewicz 1 some new one step methods are introduced these are of great practical importance because of the ease with which the size of time step can be changed

online support vector machine based on convex hull vertices selection the support vector machine svm method as a promising classification technique has been widely used in various fields due to its high efficiency however svm cannot effectively solve online classification problems since when a new sample is misclassified the classifier has to be retrained with all training samples plus the new sample which is time consuming according to the geometric characteristics of svm in this paper we propose an online svm classifier called vs osvm which is based on convex hull vertices selection within each class the vs osvm algorithm has two steps 1 the samples selection process in which a small number of skeleton samples constituting an approximate convex hull in each class of the current training samples are selected and 2 the online updating process in which the classifier is updated with newly arriving samples and the selected skeleton samples from the theoretical point of view the first d 1 d is the dimension of the input samples selected samples are proved to be vertices of the convex hull this guarantees that the selected samples in our approach keep the greatest amount of information of the convex hull from the application point of view the new algorithm can update the classifier without reducing its classification performance experimental results on benchmark data sets have shown the validity and effectiveness of the vs osvm algorithm

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

simple proof of convergence of the smo algorithm for different svm variants in this brief we give a new proof of the asymptotic convergence of the sequential minimum optimization smo algorithm for both the most violating pair and second order rules to select the pair of coefficients to be updated the proof is more self contained shorter and simpler than previous ones and has a different flavor partially building upon gilbert s original convergence proof of its algorithm to solve the minimum norm problem for convex hulls it is valid for both support vector classification svc and support vector regression which are formulated under a general problem that encompasses them moreover this general problem can be further extended to also cover other support vector machines svm related problems such as svc or one class svms while the convergence proof of the slight variant of smo needed for them remains basically unchanged

an effective method to determine whether a point is within a convex hull and its generalized convex polyhedron classifier abstract a convex polyhedron classifier that encloses the minority class using a combination of hyperplanes is potentially effective in imbalanced classification to construct an easy to use convex polyhedron classifier this paper first presents a theoretical foundation for determining whether a point is within the convex hull of a finite point set this foundation corresponds to a geometric method in which the result is expressed as a separating hyperplane if the given point and the given convex hull are located on either side of the learned hyperplane this indicates that the point is outside of the convex hull otherwise the conclusion that the point is within the convex hull can be obtained as a generalization of the geometric method a convex polyhedron classifier is further proposed for binary classification if two finite point sets are polyhedrally separable a series of hyperplanes can be learned as a combined piecewise linear classifier which surrounds a point set that is inside using a convex polyhedron and excludes the other point set that is outside experimental results on twelve real world datasets show that the proposed classifier is generally better than the other two piecewise linear classifiers moreover a comparison with several types of support vector machines confirms its competitiveness

unconditionally convergent partitioned solution procedure for dynamic coupled mechanical systems a new partitioned solution procedure for the direct time integration of second order coupled field systems is presented and it is applied to the problem of soil pore fluid interaction the necessary convergence analysis for the iterative method is carried out and the fulfilment of the convergence condition is achieved with the introduction of two suitable auxiliary matrices in the basic equations governing the dynamic phenomena numerical examples are presented to demonstrate the effectiveness and the versatility of the proposed solution procedure

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

interval estimation of parameters of life from progressively censored data a conditional method of inference is used to derive exact confidence intervals for several life characteristics such as location scale quantiles and reliability when the data are type ii progressively censored the method is shown to be feasible and practical although a computer program may be required for its implementation the method is applied for the purpose of illustration to the extreme value and the one and two parameter exponential models prediction limits for the lifelength of future units are also discussed an example consisting of data from an accelerated test on insulating fluid reported by nelson is used for illustration and comparison

statistical inference for the burr model based on progressively censored data abstract maximum likelihood and bayes estimates for the two parameters and the reliability function of the burr type xii distribution are obtained based on progressive type ii censored samples an approximation based on the laplace approximation method developed by tierney and kadane 1 and a bivariate prior density for the two unknown parameters suggested by al hussaini and jaheen 2 are used for obtaining the bayes estimates these estimates are compared via monte carlo simulation study

a geometric nearest point algorithm for the efficient solution of the svm classification task geometric methods are very intuitive and provide a theoretically solid approach to many optimization problems one such optimization task is the support vector machine svm classification which has been the focus of intense theoretical as well as application oriented research in machine learning in this letter the incorporation of recent results in reduced convex hulls rchs to a nearest point algorithm npa leads to an elegant and efficient solution to the svm classification task with encouraging practical results to real world classification problems i e linear or nonlinear and separable or nonseparable

geometric algorithms to large margin classifier based on affine hulls the geometric framework for binary data classification problems provides an intuitive foundation for the comprehension and application of geometric optimization algorithms leading to practical solutions of real world classification problems in this paper some theoretical results on the candidate extreme points of the notion of reduced affine hull rah are introduced these results allow the existing nearest point algorithms to be directly applied to solve both separable and inseparable classification problems based on rahs successfully and efficiently as the practical applications of the new theoretical results the popular gilbert schlesinger kozinec and mitchell dem yanov malozemov algorithms are presented to solve binary classification problems in the context of the rah framework the theoretical analysis and some experiments show that the proposed methods successfully achieve significant performance

linear convergence rate for the mdm algorithm for the nearest point problem in this paper we will prove a linear convergence rate for the extension of the mitchell dem yanov and malozemov mdm algorithm for solving the nearest point problem npp while linear convergence proofs for the related but different smo method intended for svm training require that the kernel matrix be positive definite no such assumption is needed in npp for mdm moreover we will also show linear convergence for the sequence of mdm vectors to the unique solution vector w of npp and for a quantity that measures the gap in the karush kuhn tucker conditions furthermore even if there might be several multiplier representations for w we will show that any mdm generated multiplier sequence converges linearly to an optimal multiplier this linear convergence is shown to be optimal and it is also numerically illustrated over six datasets we will follow an approach that relies on a geometric point of view that yields a simple path to the proofs highlightslinear convergence rate for the mdm algorithm is proved no particular assumption is needed for the proof a geometric and simple approach is followed this may pave the way for proving similar results for the smo algorithm used to train svms

l1 norm loss based twin support vector machine for data recognition this paper proposes a novel l1 norm loss based twin support vector machine l1ltsvm classifier for binary recognition in this l1ltsvm each optimization problem simultaneously minimizes the l1 norm based losses for the two classes of points which results in a different dual problem compared with twin support vector machine twsvm compared with twsvm the main advantages of this l1ltsvm classifier are first the dual problems of l1ltsvm do not need to inverse the kernel matrices during the learning process indicating l1ltsvm not only has a partly sparse decision function but also can be solved efficiently by some svm type learning algorithms and then is suitable for large scale problems second this l1ltsvm has more perfect and practical geometric interpretation experimental results on several synthetic as well as benchmark datasets indicate the significant advantage of l1ltsvm in the generalization performance

multiconlitron a general piecewise linear classifier based on the convexly separable concept we present a solid geometric theory and a new general framework to design piecewise linear classifiers for two arbitrarily complicated nonintersecting classes by using a multiconlitron which is a union of multiple conlitrons that comprise a set of hyperplanes or linear functions surrounding a convex region for separating two convexly separable datasets we propose a new iterative algorithm called the cross distance minimization algorithm cdma to compute hard margin non kernel support vector machines svms via the nearest point pair between two convex polytopes using cdma we derive two new algorithms i e the support conlitron algorithm sca and the support multiconlitron algorithm sma to construct support conlitrons and support multiconlitrons respectively which are unique and can separate two classes by a maximum margin as in an svm comparative experiments show that sma can outperform linear svm on many of the selected databases and provide similar results to radial basis function svm on some of them while sca performs better than linear svm on three out of four applicable databases other experiments show that sma and sca may be further improved to draw more potential in the new research direction of piecewise linear learning