eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

generalizing discriminant analysis using the generalized singular value decomposition discriminant analysis has been used for decades to extract features that preserve class separability it is commonly defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters the requirement that one of these matrices be nonsingular limits its application to data sets with certain relative dimensions we examine a number of optimization criteria and extend their applicability by using the generalized singular value decomposition to circumvent the nonsingularity requirement the result is a generalization of discriminant analysis that can be applied even when the sample size is smaller than the dimension of the sample data we use classification results from the reduced representation to compare the effectiveness of this approach with some alternatives and conclude with a discussion of their relative merits

adaptive interference canceler for narrowband and wideband interferences using higher order statistics a new higher order statistics based adaptive interference canceler is introduced to mitigate narrowband and wideband interferences in environments where the interference is non gaussian and a reference signal which is highly correlated with the interference is available the new scheme uses higher order statistics hos of the primary and reference inputs and employs a gradient type algorithm for updating the adaptive filter coefficients the update equation of the hos based adaptive filter is independent of uncorrelated gaussian noises and can mitigate the interference more effectively than adaptive filters based on second order statistics the performance of the hos based adaptive filter is much less sensitive to the choice of the step size parameter than the adaptive filters based on the lms algorithm it is demonstrated by means of extensive simulations that the hos based filter can mitigate both narrowband and wideband interferences effectively comparisons with adaptive filters based on the lms algorithm and second order statistics are also presented in the paper

estimation of frequency delay of arrival fdoa using fourth order statistics in unknown correlated gaussian noise sources a new family of nonparametric and parametric methods based on fourth order statistics for the estimation of the frequency delay of arrival fdoa between two sensor signal measurements corrupted by correlated gaussian noise sources in an unknown way is presented the new family of fdoa estimation methods utilizes the fourth order cumulants or 1 d fourier transforms of sliced fourth order cumulants of the two signal measurements it is demonstrated that the new family of fdoa estimation methods suppresses the effect due to correlated gaussian measurement noises and outperforms existing second order statistics based fdoa estimation methods using either cross ambiguity function or music algorithm various simulation results are presented for different types of signals different lengths of data and different signal to noise ratios

a computationally efficient scheme for feature extraction with kernel discriminant analysis the kernel discriminant analysis kda an extension of the linear discriminant analysis lda and null space based lda into the kernel space generally provides good pattern recognition pr performance for both small sample size sss and non sss pr problems due to the eigen decomposition technique adopted however the original scheme for the feature extraction with the kda suffers from a high complexity burden in this paper we derive a transformation of the kda into a linear equation problem and propose a novel scheme for the feature extraction with the kda the proposed scheme is shown to provide us with a reduction of complexity without degradation of pr performance in addition to enhance the pr performance further we address the incorporation of regularization into the proposed scheme highlightswe propose a complexity reduced scheme for the kernel discriminant analysis the proposed scheme does not cause degradation of recognition accuracy performance the core is the transformation of the original problem into a linear equation problem we further address the incorporation of regularization into the proposed scheme

complexity reduced scheme for feature extraction with linear discriminant analysis owing to the singularity of the within class scatter linear discriminant analysis lda becomes ill posed for small sample size sss problems null space based lda nlda which is an extension of lda provides good discriminant performances for sss problems yet as the original scheme for the feature extractor fe of nlda suffers from a complexity burden a few modified schemes have since been proposed for complexity reduction in this brief by transforming the problem of finding the fe of nlda into a linear equation problem a novel scheme is derived offering a further reduction of the complexity

a preference structure on aspiration levels in a goal programming problem a fuzzy approach abstract a method is proposed for comparing different sets of aspiration levels assigned to goals in a goal programming problem this is based on the relative flexibilities that are realised under different sets of aspiration levels the relative flexibility depends upon the relative degree of choosing an objective in presence of other objectives a pair wise comparison method in the sense of shimura has been proposed for measuring the degree of choosing an objective in presence of other objectives this methodology affords to compare different sets of assigned aspiration levels and thereby choosing the best set as the one with least relative flexibility

the overdetermined recursive instrumental variable method a recursive instrumental variable algorithm is derived for the overdetermined case in which the number of instruments is greater than the number of estimated parameters in some applications the algorithm provides improved parameter estimation accuracy compared to the standard recursive instrumental variable method the performance of the algorithm is illustrated by simulation results

time delay estimation in unknown gaussian spatially correlated noise a novel class of methods that estimate the difference in arrival time between signals corrupted by spatially correlated gaussian noise sources of unknown cross correlation is presented the methods are based on the idea of comparing the similarities between the two sensor measurements in higher order spectrum domains bispectrum rather than in the cross correlation domain it is demonstrated that estimation techniques based on higher order cumulants suppress the effect of correlated gaussian noise sources and therefore exhibit improved performance over generalized cross correlation methods results are reported for different types of signals lengths of data records and signal to noise ratios

adaptive eigensubspace algorithms for direction or frequency estimation and tracking the authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator s practical implementations the general formulation of the proposed estimator results from an asymptotic argument which shows the signal or noise subspace computation to be equivalent to a constrained gradient search procedure a highly parallel algorithm denoted the inflation method is introduced for the estimation of the noise subspace the simulation results of these adaptive estimators show that the adaptive subspace algorithms perform substantially better than p a thompson s 1980 adaptive version of v f pisarenko s technique 1973 in estimating frequencies or directions of arrival doa of plane waves for tracking nonstationary parameters the simulation results also show that the adaptive subspace algorithms are better than direct eigendecomposition methods for which computational complexity is much higher than the adaptive versions

a new and fast implementation for null space based linear discriminant analysis in this paper we present a new implementation for the null space based linear discriminant analysis the main features of our implementation include i the optimal transformation matrix is obtained easily by only orthogonal transformations without computing any eigendecomposition and singular value decomposition svd consequently our new implementation is eigendecomposition free and svd free ii its main computational complexity is from a economic qr factorization of the data matrix and a economic qr factorization of a nxn matrix with column pivoting here n is the sample size thus our new implementation is a fast one the effectiveness of our new implementation is demonstrated by some real world data sets

the cumulant theory of cyclostationary time series ii development and applications for pt i see ibid vol 42 no 12 p 3387 3408 1994 the development of the theory of nonlinear processing of cyclostationary time series that is initiated in part i is continued a new type of cumulant for complex valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time series from real valued to complex valued time series the relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined formulas for the temporal and spectral cumulants of complex valued pulse amplitude modulated time series are derived estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed the performance of these estimators is illustrated by several computer simulation examples for pulse amplitude modulated time series the theory is applied to the problems of weak signal detection and interference tolerant time delay estimation

a fuzzy goal programming approach to multi objective optimization problem with priorities abstract in goal programming problem the general equilibrium and optimization are often two conflicting factors this paper proposes a generalized varying domain optimization method for fuzzy goal programming fgp incorporating multiple priorities according to the three possible styles of the objective function the varying domain optimization method and its generalization are proposed this method can generate the results consistent with the decision maker dm s expectation that the goal with higher priority may have higher level of satisfaction using this new method it is a simple process to balance between the equilibrium and optimization and the result is the consequence of a synthetic decision between them in contrast to the previous method the proposed method can make that the higher priority achieving the higher satisfactory degree to get the global solution of the nonlinear nonconvex programming problem resulting from the original problem and the varying domain optimization method the co evolutionary genetic algorithms gas called genocopiii is used instead of the sqp method in this way the dm can get the optimum of the optimization problem we demonstrate the power of this proposed method by illustrative examples

in defense of one vs all classification we consider the problem of multiclass classification our main thesis is that a simple one vs all scheme is as accurate as any other approach assuming that the underlying binary classifiers are well tuned regularized classifiers such as support vector machines this thesis is interesting in that it disagrees with a large body of recent published work on multiclass classification we support our position by means of a critical review of the existing literature a substantial collection of carefully controlled experimental work and theoretical arguments

bearing estimation in the bispectrum domain a new array processing method is presented for bearing estimation based on the cross bispectrum of the array output data the method is based on the asymptotic distribution of cross bispectrum estimates and uses maximum likelihood theory it is demonstrated that when the noise additive sources are spatially correlated gaussian with unknown cross spectral matrix csm the cross bispectrum method provides better bearing estimates than the stochastic maximum likelihood method with known csm analytical studies and simulations are given to document the performance of the new method

fuzzy goal programming with different importance and priorities abstract this paper formulates fuzzy goal programming fgp incorporating different importance and preemptive priorities by using an additive model to maximize the sum of achievement degrees of all fuzzy goals in contrast to previous works the proposed approach allows the decision maker to determine a desirable achievement degree for each fuzzy goal to reflect explicitly the relative importance of these goals this approach can generate a set of achievement degrees consistent with the decision maker s expectations even though the relative importance of the goals may change furthermore in this paper we incorporate the decision maker s preemptive priority structure into a single formulation the resulting solutions satisfy both the preemptive priority structure and have the maximum achievement degrees in sum the proposed approaches effectiveness and computational superiority over the existing approaches are demonstrated and compared with examples from the literature

priority structure in fuzzy goal programming abstract this paper introduces priority structure in fuzzy goal programming fgp this approach utilizes the lexicographic order of goal programming gp and yields an efficient computational algorithm for solving fgp fuzzy priorities are also discussed a numerical example is given to highlight the procedure concluding remarks are also made

arma bispectrum approach to nonminimum phase system identification an identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase fir finite impulse response system the method is based on parametric modeling of the third moments of the output sequence and uses causal and anticausal autoregressive moving average arma models the magnitude and phase response of the system are expressed in terms of the ar parameters of the arma models in particular the ar part of the causal arma model captures the minimum phase component of the system and the ar part of the anticausal arma captures the maximum phase component both sets of parameters are obtained by solving overdetermined linear systems of equations a model order selection criterion based on third order moments is proposed the arma bispectrum approach is compared to more conventional approaches for magnitude and phase reconstruction it is demonstrated that the proposed identification procedure exhibits improved modeling performance the method does not require knowledge of the non gaussian noise distribution

complete large margin linear discriminant analysis using mathematical programming approach in this paper we develop a novel dimensionality reduction dr framework coined complete large margin linear discriminant analysis clmlda inspired by several recently proposed dr methods clmlda constructs two mathematical programming models by maximizing the minimum distance between each class center and the total class center respectively in the null space of within class scatter matrix and its orthogonal complementary space in this way clmlda not only makes full use of the discriminative information contained in the whole feature space but also overcome the weakness of linear discriminant analysis lda in dealing with the class separation problem the solutions of clmlda follow from solving two nonconvex optimization problems each of which is transformed to a series of convex quadratic programming problems by using the constrained concave convex procedure first and then solved by off the shelf optimization toolbox experiments on both toy and several publicly available databases demonstrate its feasibility and effectiveness

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

a comparison of generalized linear discriminant analysis algorithms linear discriminant analysis lda is a dimension reduction method which finds an optimal linear transformation that maximizes the class separability however in undersampled problems where the number of data samples is smaller than the dimension of data space it is difficult to apply lda due to the singularity of scatter matrices caused by high dimensionality in order to make lda applicable several generalizations of lda have been proposed recently in this paper we present theoretical and algorithmic relationships among several generalized lda algorithms and compare their computational complexities and performances in text classification and face recognition towards a practical dimension reduction method for high dimensional data an efficient algorithm is proposed which reduces the computational complexity greatly while achieving competitive prediction accuracies we also present nonlinear extensions of these lda algorithms based on kernel methods it is shown that a generalized eigenvalue problem can be formulated in the kernel based feature space and generalized lda algorithms are applied to solve the generalized eigenvalue problem resulting in nonlinear discriminant analysis performances of these linear and nonlinear discriminant analysis algorithms are compared extensively

modeling of time delay and its application to estimation of nonstationary delays a method to model a time delay by a finite impulse response filter is presented it is useful in simulation work that involves time delays and transforms the time delay estimation problem into one of parameter estimation the benefits of this approach are the elimination of spectral estimation a choice of many parameter estimation algorithms and the capability to track time varying delays two examples of estimating nonstationary time delays are also given

the cross bicepstrum definition properties and application for simultaneous reconstruction of three nonminimum phase signals the recovery of three signals from their cross bispectrum or the identification of the impulse responses of three parallel linear time invariant lti systems from the cross bispectrum of their system outputs by computing the complex cepstrum of the cross bispectrum as long as the signals or impulse responses have no zeros on the unit circle is discussed it is shown that the three signals can be separated completely and approximately recovered in the cross bicepstrum domain except for their magnitude and linear phase factors the computation of the cross bicepstrum can be seen as a method for the simultaneous computation of the ordinary complex cepstra of three nonminimum phase signals without the need for phase unwrapping both least squares and fast fourier transform fft based methods for computing the bicepstral coefficients are presented simulation examples of signal reconstruction in gaussian white and nongaussian colored noise and of system identification are included the results are extended to nth order cross spectra and the factorization problem for these spectra is discussed

an interactive fuzzy satisficing method for large scale multiobjective 0 1 programming problems with fuzzy parameters through genetic algorithms abstract in this paper by considering the experts imprecise or fuzzy understanding of the nature of the parameters in the problem formulation process multiobjective block angular 0 1 programming problems involving fuzzy numbers are formulated using the level sets of fuzzy numbers the corresponding nonfuzzy multiobjective 0 1 programming problem is introduced and an extended pareto optimality concept is defined for the multiobjective 0 1 programming problem the fuzzy goal of the decision maker for each objective function quantified by eliciting the corresponding membership function is considered since the decision maker must select a compromise or satisficing solution from the extended pareto optimal solution set including an infinite number of elements in general an interactive fuzzy satisficing method through genetic algorithms for deriving a satisficing solution for the decision maker from an extended pareto optimal solution set is presented then for fixed and reference membership levels the corresponding extended pareto optimal solution can be obtained by solving a minimax problem with block angular structure in order to solve the minimax problem efficiently we adopt a genetic algorithm with decomposition procedures finally both feasibility and effectiveness of the proposed method is discussed on the basis of results of simple numerical experiments

generalized discriminant analysis using a kernel approach we present a new method that we call generalized discriminant analysis gda to deal with nonlinear discriminant analysis using kernel function operator the underlying theory is close to the support vector machines svm insofar as the gda method provides a mapping of the input vectors into high dimensional feature space in the transformed space linear properties make it easy to extend and generalize the classical linear discriminant analysis lda to nonlinear discriminant analysis the formulation is expressed as an eigenvalue problem resolution using a different kernel one can cover a wide class of nonlinearities for both simulated data and alternate kernels we give classification results as well as the shape of the decision function the results are confirmed using real data to perform seed classification

adaptive iir algorithms based on high order statistics recursive estimation algorithms are derived for moving average and autoregressive moving average processes these algorithms can be used for adaptive infinite impulse response iir filtering of non gaussian processes the behavior of these algorithms is illustrated by extensive numerical examples

complex ambiguity functions using nonstationary higher order cumulant estimates the complex ambiguity function based on second order statistics caf sos has been used to simultaneously estimate the frequency delay of arrival fdoa and time delay of arrival tdoa between two signal measurements its performance however is sensitive to the correlation between two additive noise sources when the noise sources are assumed to be gaussian we develop a new complex ambiguity function based on higher order statistics caf hos that reduces the unknown noise correlation effect the new caf hos algorithm utilizes nonstationary higher order cross cumulant estimates and their fourier transform in fact we suggest a nonstationary estimate of fourth order cross cumulants and obtain the analytical expressions for its mean value and variance we compare the analytical expressions with results obtained by monte carlo runs also we compare the performance of the new complex ambiguity function based on fourth order statistics caf fos against the caf sos algorithm using different gaussian noise sources different signals of interest different signal to noise ratios and different lengths of data

fuzzy goal programming an additive model abstract an additive model to solve fuzzy goal programming fgp is formulated the method uses arithmetic addition to aggregate the fuzzy goals to construct the relevant decision function cardinal and ordinal weights for nonequivalent fuzzy goals are also incorporated in the method the solution procedure is illustrated with a numerical example

a new method for adaptive time delay estimation for non gaussian signals a novel adaptive scheme for time delay estimation is introduced for signal environments where the signal is non gaussian and the additive noise sources are spatially correlated gaussian with unknown power spectrum characteristics this scheme is based on parametric modeling between two sensor measurements and employs higher order statistics third or fourth order of the data it is demonstrated by means of extensive simulations that this scheme works well for both stationary and nonstationary cases as expected it outperforms the cross correlation based gradient method for time delay adaptation in spatially correlated gaussian noises the proposed scheme is compared to the overdetermined recursive instrumental variable method and is shown to exhibit substantially less computational complexity

nearest neighbor classifier generalization through spatially constrained filters it is widely understood that the performance of the nearest neighbor nn rule is dependent on i the way distances are computed between different examples and ii the type of feature representation used linear filters are often used in computer vision as a pre processing step to extract useful feature representations in this paper we demonstrate an equivalence between i and ii for nn tasks involving weighted euclidean distances specifically we demonstrate how the application of a bank of linear filters can be re interpreted in the form of a symmetric weighting matrix as a manipulation of how distances are computed between different examples for nn classification further we argue that filters fulfill the role of encoding local spatial constraints into this weighting matrix we then demonstrate how these constraints can dramatically increase the generalization capability of canonical distance metric learning techniques in the presence of unseen illumination and viewpoint change

the cumulant theory of cyclostationary time series i foundation the problem of characterizing the sine wave components in the output of a polynomial nonlinear system with a cyclostationary random time series input is investigated the concept of a pure nth order sine wave is introduced and it is shown that pure nth order sine wave strengths in the output time series are given by scaled fourier coefficients of the polyperiodic temporal cumulant of the input time series the higher order moments and cumulants of narrowband spectral components of time series are defined and then idealized to the case of infinitesimal bandwidth such spectral moments and cumulants are shown to be characterized by the fourier transforms of the temporal moments and cumulants of the time series it is established that the temporal and spectral cumulants have certain mathematical and practical advantages over their moment counterparts to put the contributions of the paper in perspective a uniquely comprehensive historical survey that traces the development of the ideas of temporal and spectral cumulants from their inception is provided

discriminative common vector method with kernels in some pattern recognition tasks the dimension of the sample space is larger than the number of samples in the training set this is known as the small sample size problem linear discriminant analysis lda techniques cannot be applied directly to the small sample size case the small sample size problem is also encountered when kernel approaches are used for recognition in this paper we attempt to answer the question of how should one choose the optimal projection vectors for feature extraction in the small sample size case based on our findings we propose a new method called the kernel discriminative common vector method in this method we first nonlinearly map the original input space to an implicit higher dimensional feature space in which the data are hoped to be linearly separable then the optimal projection vectors are computed in this transformed space the proposed method yields an optimal solution for maximizing a modified fisher s linear discriminant criterion discussed in the paper thus under certain conditions a 100 recognition rate is guaranteed for the training set samples experiments on test data also show that in many situations the generalization performance of the proposed method compares favorably with other kernel approaches

an interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model abstract for decision making problems involving uncertainty both stochastic programming as an optimization method based on the theory of probability and fuzzy programming representing the ambiguity by fuzzy concept have been developing in various ways in this paper we focus on multiobjective linear programming problems with random variable coefficients in objective functions and or constraints for such problems as a fusion of these two approaches after incorporating fuzzy goals of the decision maker for the objective functions we propose an interactive fuzzy satisficing method for the expectation model to derive a satisficing solution for the decision maker an illustrative numerical example is provided to demonstrate the feasibility of the proposed method

image motion estimation algorithms using cumulants a class of algorithms is presented that estimates the displacement vector from two successive image frames consisting of signal plus noise in the model the signals are assumed to be either non gaussian or quasistationary deterministic and via a consistency result for cumulant estimators the authors unify the stochastic and deterministic signal viewpoints the noise sources are assumed to be gaussian perhaps spatially and temporally correlated and of unknown covariance viewing image motion estimation as a 2d time delay estimation problem the displacement vector of a moving object is estimated by solving linear equations involving third order auto cumulants and cross cumulants additionally a block matching algorithm is developed that follows from a cumulant error optimality criterion finally the displacement vector for each pel is estimated using a recursive algorithm that minimizes a mean 2d fourth order cumulant criterion simulation results are presented and discussed

fuzzy goal programming approach for structural optimization a fuzzy nonlinear goal programming approach is presented for solving multiobjective optimization problems involving vague and imprecise information several computational models including simple additive weighted additive and preemptive priority models are given for the numerical solution of the problem the methodolo gies are illustrated with the help of two structural optimization problems involving multiple goals the solution of the first example is obtained using a graphical procedure whereas the second example is solved using nonlinear programming techniques linear membership functions are used in the numerical work for simplicity the methodologies presented in this work aid in the preliminary design of structural systems involving imprecise and vague information about the goals and or constraints inear goal programming has been extensively used in solving decision making problems involving linear equa tions and multiple conflicting goals the goals can be rank ordered depending on their importance to the decision maker goal programming attempts to achieve as man 7 of these goals as possible by minimizing deviational variables from the goal levels depending on their relative weights linear goal pro gramming algorithms were developed by charnes et al 1 ig nizio 2 and zanakis and gupta 3 the extension of goal pro gramming to nonlinear optimization problems has also been considered by several authors 3 4 a fuzzy programming ap proach for linear programming problems with several objec tives was suggested by zimmerman 5 subsequently several authors proposed different fuzzy goal programming ap proaches for solving linear goal programming problems in volving imprecise statements and information 6 10 narasimhan6 suggested a method for solving fuzzy linear goal programming problems under the assumption of linear membership functions his method involves solving a set of 2k linear programming problems each containing 3k constraints where k denotes the number of goals in the original problem hannan7 indicated a procedure for formulating a fuzzy goal programming problem as an equivalent single linear program ming problem with 2k goal related constraints the problems associated with the definition of fuzzy priorities were dis cussed in ref 7 a brief review of the history and the state of the art in fuzzy multicriteria programming as of 1982 was presented by ignizio 8 the distinction between fuzzy goal pro gramming and fuzzy multicriteria formulations was given in ref 9 models are presented by hannan7 for the use of fuzzy goal programming with preemptive priorities with archime dian weights and with the maximization of the membership function corresponding to the minimum goal a methodology based on the use of a nested hierarchy of priorities for each goal was presented by rubin and narasimhan 10 the impor tance of multiple objectives in the design of practical engineer

fuzzy programming with nonlinear membership functions piecewise linear approximation one promising approach that has been proposed for dealing with multicriteria i e multiple objective programming models has been fuzzy linear programming flp in essence the flp approach involves the replacement of the multiple objectives with goals by means of assigning an aspiration level to each objective fuzzy membership functions are then introduced to represent the measure of the achievement of the actual solution for each goal relative to its aspired level it has been shown that if the flp problem is linear and if linear membership functions are employed to reflect goal achievement then the flp problem may be transformed into a conventional i e single objective linear programming model as such one may use any conventional linear programming algorithm to solve the transformed model however in the more general case of nonlinear membership functions the transformation process becomes considerably more involved and has in the past typically led to less desirable formulations in this paper we present what we believe to be a straightforward and computationally efficient procedure for dealing with the flp problem with any general class of nonlinear membership functions conversion of such a flp will result in either a regular linear programming model or a linear integer programming model depending upon the specific characteristics of the membership function in either case existing commercial software is readily available to solve such models

a generalized optimal set of discriminant vectors abstract a generalized optimal set of discriminant vectors for linear feature extraction is presented first the criteria of selecting the generalized optimal discriminant vectors are introduced and then a unified solving method is derived to solve the vectors of the generalized optimal set in both cases of a large number of samples and a small number of samples the experimental results show that the present method is superior to the foley sammon method foley and sammon ieee trans comput 24 281 289 1975 the positive pseudoinverse method tian et al opt engng 25 7 834 839 1986 the perturbation method hong and yang pattern recognition 24 317 324 1991 and the matrix rank decomposition method cheng et al pattern recognition 25 101 111 1992 in terms of correct classification rate

blind identification of simo systems and simultaneous estimation of multiple time delays from hos based inverse filter criteria higher order statistics based inverse filter criteria ifc have been effectively used for blind equalization of single input multiple output simo systems recently chi and chen reported a relationship between the unknown simo system and the optimum equalizer designed by the ifc for finite signal to noise ratio snr in this paper based on this relationship an iterative fast fourier transform fft based nonparametric blind system identification bsi algorithm and an fft based multiple time delay estimation mtde algorithm are proposed with a given set of non gaussian measurements the proposed bsi algorithm allows the unknown simo system to have common subchannel zeros and its performance estimation accuracy is superior to that of the conventional ifc based methods the proposed mtde algorithm can simultaneously estimate all the p 1 time delays with respect to a reference sensor with space diversity of sensors exploited therefore its performance estimation accuracy is robust to the nonuniform distribution of snrs of p spl ges 2 sensors due to channel fading some simulation results are presented to support the efficacy of the proposed bsi algorithm and mtde algorithm