analysis of input output clustering for determining centers of rbfn the key point in design of radial basis function networks is to specify the number and the locations of the centers several heuristic hybrid learning methods which apply a clustering algorithm for locating the centers and subsequently a linear least squares method for the linear weights have been previously suggested these hybrid methods can be put into two groups which will be called as input clustering ic and input output clustering ioc depending on whether the output vector is also involved in the clustering process the idea of concatenating the output vector to the input vector in the clustering process has independently been proposed by several papers in the literature although none of them presented a theoretical analysis on such procedures but rather demonstrated their effectiveness in several applications the main contribution of this paper is to present an approach for investigating the relationship between clustering process on input output training samples and the mean squared output error in the context of a radial basis function network rbfn we may summarize our investigations in that matter as follows 1 a weighted mean squared input output quantization error which is to be minimized by ioc yields an upper bound to the mean squared output error 2 this upper bound and consequently the output error can be made arbitrarily small zero in the limit case by decreasing the quantization error which can be accomplished through increasing the number of hidden units

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

pattern recognition with ordered labels abstract we consider a multi class pattern recognition problem with linearly ordered labels and a loss function which is a sum of squared deviations of decisions from true classes it is proved that the optimal in the bayesian sense decision rule is the a posteriori mean which is then rounded to the nearest integer then the plug in type estimator of the optimal decision rule is proposed we also investigate its asymptotic properties finally we discuss briefly the structure of a neural net which approximates the optimal decision rule

optical flow estimation and moving object segmentation based on median radial basis function network various approaches have been proposed for simultaneous optical flow estimation and segmentation in image sequences in this study the moving scene is decomposed into different regions with respect to their motion by means of a pattern recognition scheme the inputs of the proposed scheme are the feature vectors representing still image and motion information each class corresponds to a moving object the classifier employed is the median radial basis function mrbf neural network an error criterion function derived from the probability estimation theory and expressed as a function of the moving scene model is used as the cost function each basis function is activated by a certain image region marginal median and median of the absolute deviations from the median mad estimators are employed for estimating the basis function parameters the image regions associated with the basis functions are merged by the output units in order to identify moving objects

generalizations of steel s treatments versus control multivariate sign test abstract steel 1959 introduced a nonparametric multivariate sign test to allow one to compare p 2 test treatments simultaneously with a control or standard treatment in a randomized block setting steel proposed using blocks of size p 1 composed of one observation from each treatment intuitively it seems that the control should be observed more often that a test treatment because the control is involved in all treatment control comparisons and an individual test treatment is involved in only one studies in the corresponding parametric analyses bear out this intuition in this article steel s multivariate sign test is generalized to allow the control to appear more than once in each block and to allow the test treatments to appear an unequal number of times in each block a class of block designs known as sign treatment control balanced designs is proposed this class is a counterpart of the classes of supplemented balance designs and balanced treatment incomplete block designs that have been pop

analysis of augmented input layer rbfnn in this paper we present and analyze a new structure for designing a radial basis function neural network rbfnn in the training phase input layer of rbfnn is augmented with desired output vector generalization phase involves the following steps 1 identify the cluster to which a previously unseen input vector belongs 2 augment the input layer with an average of the targets of the input vectors in the identified cluster and 3 use the augmented network to estimate the unknown target it is shown that under some reasonable assumptions the generalization error function admits an upper bound in terms of the quantization errors minimized when determining the centers of the proposed method over the training set and the difference between training samples and generalization samples in a deterministic setting when the difference between the training and generalization samples goes to zero the upper bound can be made arbitrarily small by increasing the number of hidden neurons computer simulations verified the effectiveness of the proposed method

factorization of completely bounded bilinear operators and injectivity a completely bounded bilinear operator m m m on a von neumann algebra m is said to have a factorization in m if there exist completely bounded linear operators j j m m such that x y sum j j x j y x y m where convergence of the sum is made precise below the main result of the paper is that all completely bounded bilinear operators m m m have factorizations in m if and only if m is injective

median radial basis function neural network radial basis functions rbfs consist of a two layer neural network where each hidden unit implements a kernel function each kernel is associated with an activation region from the input space and its output is fed to an output unit in order to find the parameters of a neural network which embeds this structure we take into consideration two different statistical approaches the first approach uses classical estimation in the learning stage and it is based on the learning vector quantization algorithm and its second order statistics extension after the presentation of this approach we introduce the median radial basis function mrbf algorithm based on robust estimation of the hidden unit parameters the proposed algorithm employs the marginal median for kernel location estimation and the median of the absolute deviations for the scale parameter estimation a histogram based fast implementation is provided for the mrbf algorithm the theoretical performance of the two training algorithms is comparatively evaluated when estimating the network weights the network is applied in pattern classification problems and in optical flow segmentation

layered neural networks with gaussian hidden units as universal approximations a neural network with a single layer of hidden units of gaussian type is proved to be a universal approximator for real valued maps defined on convex compact sets of rn

self organized fuzzy system generation from training examples in the synthesis of a fuzzy system two steps are generally employed the identification of a structure and the optimization of the parameters defining it the paper presents a methodology to automatically perform these two steps in conjunction using a three phase approach to construct a fuzzy system from numerical data phase 1 outlines the membership functions and system rules for a specific structure starting from a very simple initial topology phase 2 decides a new and more suitable topology with the information received from the previous step it determines for which variable the number of fuzzy sets used to discretize the domain must be increased and where these new fuzzy sets should be located this in turn decides in a dynamic way in which part of the input space the number of fuzzy rules should be increased phase 3 selects from the different structures obtained to construct a fuzzy system the one providing the best compromise between the accuracy of the approximation and the complexity of the rule set the accuracy and complexity of the fuzzy system derived by the proposed self organized fuzzy rule generation procedure sofrg are studied for the problem of function approximation simulation results are compared with other methodologies such as artificial neural networks neuro fuzzy systems and genetic algorithms

tensor products of operator spaces abstract in this paper we lay the foundations for a systematic study of tensor products of subspaces of c algebras to accomplish this various notions of duality are introduced and employed elementary proofs of the complete injectivity of the haagerup norm and of the extension theorem for completely bounded maps are given pisier s gamma norms are examined and found to be special cases of the haagerup norm we identify the greatest operator space cross norm and show that the spatial tensor norm is the least operator space cross norm in an appropriate sense indeed most of the elementary theory of banach space tensor norms generalizes to the category of operator spaces

an asymptotically optimal subclass of balanced treatment incomplete block designs for comparisons with a control summary incomplete block designs for estimation of treatment control differences are studied a class of designs for this purpose called balanced treatment incomplete block designs has recently been proposed and studied by several authors here a relatively small subclass of these designs is shown to contain the asymptotically optimal design under the criterion of minimizing the length of simultaneous confidence intervals for treatmentcontrol differences these results can be used to easily construct good large designs some specific finite cases are considered

representations of completely bounded multilinear operators a deli ion of a completely bounded multilinear operator from one c algebra into another is introduced each completely bounded multilinear operator from a algebra into the algebra of bounded linear operators on a hilbert space is shown to be representable in terms of representations of the c algebra and interlacing operators this result extends wittstock s theorem that decomposes a completely bounded linear operator from a c algebra into an injective c algebra into completely positive linear operators 0 1987 academic press inc stinespring s theorem gives a useful representation for a completely positive linear operator from a c algebra into the algebra bl h for continuous linear operators on a hilbert space h 12 11 using this representation with wittstock s theorem that decomposes a completely bounded linear operator as a finite linear combination of completely positive linear operators 14 lo one obtains a representation of a completely bounded linear operator from a c algebra into bl h our main result is a representation theorem for completely bounded multilinear operators from a c algebra into bl h which generalizes this representation of completely bounded linear operators corollaries give multilinear generalizations of several results known for completely bounded linear operators we shall briefly describe the type of representations to be 151

prediction and tracking of moving objects in image sequences we employ a prediction model for moving object velocity and location estimation derived from bayesian theory the optical flow of a certain moving object depends on the history of its previous values a joint optical flow estimation and moving object segmentation algorithm is used for the initialization of the tracking algorithm the segmentation of the moving objects is determined by appropriately classifying the unlabeled and the occluding regions segmentation and optical flow tracking is used for predicting future frames

amenability and virtual diagonals for von neumann algebras abstract it is shown that a certain universal bimodule over a von neumann algebra is automatically normal this leads to a simple direct proof of haagerup s result that a von neumann algebra is amenable or equivalently injective if and only if it has a normal virtual diagonal haagerup has used this fact to prove that nuclear c algebras are amenable

object classification in 3 d images using alpha trimmed mean radial basis function network we propose a pattern classification based approach for simultaneous three dimensional 3 d object modeling and segmentation in image volumes the 3 d objects are described as a set of overlapping ellipsoids the segmentation relies on the geometrical model and graylevel statistics the characteristic parameters of the ellipsoids and of the graylevel statistics are embedded in a radial basis function rbf network and they are found by means of unsupervised training a new robust training algorithm for rbf networks based on spl alpha trimmed mean statistics is employed in this study the extension of the hough transform algorithm in the 3 d space by employing a spherical coordinate system is used for ellipsoidal center estimation we study the performance of the proposed algorithm and we present results when segmenting a stack of microscopy images

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

incomplete block designs for comparing treatments wth a control general theory in this paper we develop a theory of optimal incomplete block designs for comparing several treatments with a control this class of designs is appropriate for comparing simultaneously p 2 test treatments with a control treatment the so called multiple comparisons with a control mcc problem when the observations are taken in incomplete blocks of common size k p 1 for this problem we propose a new general class of incomplete block designs that are balanced with respect to wrt test treatments we shall use the abbreviation btib to refer to such designs we study their structure and give some methods of construction a procedure for making exact joint confidence statements for this multiple comparisons problem is described by using a new concept of admissibility of designs it is shown how inferior designs can be eliminated from consideration and attention limited to a small class of btib designs that can be constructed from so called generator designs in the minimal complete class of such d

minimum class variance support vector machines in this paper a modified class of support vector machines svms inspired from the optimization of fisher s discriminant ratio is presented the so called minimum class variance svms mcvsvms the mcvsvms optimization problem is solved in cases in which the training set contains less samples that the dimensionality of the training vectors using dimensionality reduction through principal component analysis pca afterward the mcvsvms are extended in order to find nonlinear decision surfaces by solving the optimization problem in arbitrary hilbert spaces defined by mercer s kernels in that case it is shown that under kernel pca the nonlinear optimization problem is transformed into an equivalent linear mcvsvms problem the effectiveness of the proposed approach is demonstrated by comparing it with the standard svms and other classifiers like kernel fisher discriminant analysis in facial image characterization problems like gender determination eyeglass and neutral facial expression detection

multilinear maps and tensor norms on operator systems abstract we extend work of christensen and sinclair on completely bounded multilinear forms to the case of subspaces of c algebras and obtain a representation theorem and a hahn banach extension theorem for such maps in the second part of the paper the haagerup norms on tensor products are investigated and we obtain new characterizations of these quantities

remarks on complemented subspaces of von neumann algebras in this note we include two remarks about bounded not necessarily contractive linear projections on a von neumann algebra we show that if m is a von neumann subalgebra of b h which is complemented in b h and isomorphic to m m then m is injective or equivalently m is contractively complemented we do not know how to get rid of the second assumption on m in the second part we show that any complemented reflexive subspace of a c algebra is necessarily linearly isomorphic to a hilbert space

variants of self organizing maps self organizing maps have a bearing on traditional vector quantization a characteristic that makes them more closely resemble certain biological brain maps however is the spatial order of their responses which is formed in the learning process a discussion is presented of the basic algorithms and two innovations dynamic weighting of the input signals at each input of each cell which improves the ordering when very different input signals are used and definition of neighborhoods in the learning algorithm by the minimal spanning tree which provides a far better and faster approximation of prominently structured density functions it is cautioned that if the maps are used for pattern recognition and decision process it is necessary to fine tune the reference vectors so that they directly define the decision borders