contact models leading to variational hemivariational inequalities abstract a frictional contact model under the small deformations hypothesis for static processes is considered we model the behavior of the material by a constitutive law using the subdifferential of a proper convex and lower semicontinuous function the contact is described with a boundary condition involving clarke s generalized gradient our study focuses on the weak solvability of the model based on a fixed point theorem for set valued mappings we prove the existence of at least one weak solution the uniqueness the boundedness and the stability of the weak solution are also discussed the investigation is based on arguments in the theory of variational hemivariational inequalities finally we present several examples of constitutive laws and friction laws for which our theoretical results are valid

chains of darboux transformations for the matrix schrodinger equation chains of darboux transformations for the matrix schr odinger equation are considered a matrix generalization of the well known for the scalar equation crum krein formulae for the resulting action of such chains is given

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

comments on globally maximizing locally minimizing unsupervised discriminant projection with application to face and palm biometrics this paper develops an unsupervised discriminant projection udp technique for dimensionality reduction of high dimensional data in small sample size cases udp can be seen as a linear approximation of a multimanifolds based learning framework which takes into account both the local and nonlocal quantities udp characterizes the local scatter as well as the nonlocal scatter seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter this characteristic makes udp more intuitive and more powerful than the most up to date method locality preserving projection lpp which considers only the local scatter for clustering or classification tasks the proposed method is applied to face and palm biometrics and is examined using the yale feret and ar face image databases and the polyu palmprint database the experimental results show that udp consistently outperforms lpp and pca and outperforms lda when the training sample size per class is small this demonstrates that udp is a good choice for real world biometrics applications

adaptive manifold learning manifold learning algorithms seek to find a low dimensional parameterization of high dimensional data they heavily rely on the notion of what can be considered as local how accurately the manifold can be approximated locally and last but not least how the local structures can be patched together to produce the global parameterization in this paper we develop algorithms that address two key issues in manifold learning 1 the adaptive selection of the local neighborhood sizes when imposing a connectivity structure on the given set of high dimensional data points and 2 the adaptive bias reduction in the local low dimensional embedding by accounting for the variations in the curvature of the manifold as well as its interplay with the sampling density of the data set we demonstrate the effectiveness of our methods for improving the performance of manifold learning algorithms using both synthetic and real world data sets

eigenphase preserving two channel susy transformations we propose a new kind of supersymmetric susy transformation in the case of the two channel scattering problem with equal thresholds for partial waves of the same parity this two fold transformation is based on two imaginary factorization energies with opposite signs and with mutually conjugated factorization solutions we call it an eigenphase preserving susy transformation as it relates two hamiltonians the scattering matrices of which have identical eigenphase shifts in contrast to known phase equivalent transformations the mixing parameter is modified by the eigenphase preserving transformation

weyl titchmarsh functions of vector valued sturm liouville operators on the unit interval the matrix valued weyl titchmarsh functions m of vector valued sturm liouville operators on the unit interval with the dirichlet boundary conditions are considered the collection of the eigenvalues i e poles of m and the residues of m is called the spectral data of the operator the complete characterization of spectral data or equivalently n n weyl titchmarsh functions corresponding to n n self adjoint square integrable matrix valued potentials is given if all n eigenvalues of the averaged potential are distinct

solvability of dynamic antiplane frictional contact problems for viscoelastic cylinders abstract we study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation the process is dynamic the material behavior is described with a linearly viscoelastic constitutive law and friction is modeled with a general subdifferential boundary condition we derive a variational formulation of the model which is in a form of an evolutionary hemivariational inequality for the displacement field then we prove the existence of a weak solution to the model the proof is based on an abstract result for second order evolutionary inclusions in banach spaces also we prove that under additional assumptions the weak solution to the model is unique we complete our results with concrete examples of friction laws for which our results are valid

differential equations in the spectral parameter we determine all the potentialsv x for the schrodinger equation 2 v x k2 such that some family of eigenfunctions satisfies a differential equation in the spectral parameterk of the formb k k o x o for each suchv x we determine the algebra of all possible operatorsb and the corresponding functions x

singular matrix darboux transformations in the inverse scattering method singular darboux transformations in contrast to the conventional ones have a singular matrix as a coefficient before the derivative we incorporated such transformations into a chain of conventional transformations and presented determinant formulas for the resulting action of the chain a determinant representation of the kohlhoff von geramb solution to the marchenko equation is given

slow feature analysis unsupervised learning of invariances invariant features of temporally varying signals are useful for analysis and classification slow feature analysis sfa is a new method for learning invariant or slowly varying features from a vectorial input signal it is based on a nonlinear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative it is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decorrelated features which are ordered by their degree of invariance sfa can be applied hierarchically to process high dimensional input signals and extract complex features sfa is applied first to complex cell tuning properties based on simple cell output including disparity and motion then more complicated input output functions are learned by repeated application of sfa finally a hierarchical network of sfa modules is presented as a simple model of the visual system the same unstructured network can learn translation size rotation contrast or to a lesser degree illumination invariance for one dimensional objects depending on only the training stimulus surprisingly only a few training objects suffice to achieve good generalization to new objects the generated representation is suitable for object recognition performance degrades if the network is trained to learn multiple invariances simultaneously

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

a unified framework for semi supervised dimensionality reduction in practice many applications require a dimensionality reduction method to deal with the partially labeled problem in this paper we propose a semi supervised dimensionality reduction framework which can efficiently handle the unlabeled data under the framework several classical methods such as principal component analysis pca linear discriminant analysis lda maximum margin criterion mmc locality preserving projections lpp and their corresponding kernel versions can be seen as special cases for high dimensional data we can give a low dimensional embedding result for both discriminating multi class sub manifolds and preserving local manifold structure experiments show that our algorithms can significantly improve the accuracy rates of the corresponding supervised and unsupervised approaches

curvilinear component analysis a self organizing neural network for nonlinear mapping of data sets we present a new strategy called curvilinear component analysis cca for dimensionality reduction and representation of multidimensional data sets the principle of cca is a self organized neural network performing two tasks vector quantization vq of the submanifold in the data set input space and nonlinear projection p of these quantizing vectors toward an output space providing a revealing unfolding of the submanifold after learning the network has the ability to continuously map any new point from one space into another forward mapping of new points in the input space or backward mapping of an arbitrary position in the output space

darboux transformations of the jaynes cummings hamiltonian a detailed analysis of matrix darboux transformations under the condition that the derivative of the superpotential be self adjoint is given as a consequence a class of symmetries associated with schrodinger matrix hamiltonians is characterized the applications are oriented towards the jaynes cummings eigenvalue problem so that exactly solvable 2 2 matrix hamiltonians of the jaynes cummings type are obtained as supersymmetric partners it is also established that due to nontrivial symmetries the jaynes cummings hamiltonian is a quadratic function of a dirac type hamiltonian

local and global mappings of topology representing networks as data analysis tasks often have to deal with complex data structures the nonlinear dimensionality reduction methods play an important role in exploratory data analysis in the literature a number of nonlinear dimensionality reduction techniques have been proposed e g sammon mapping locally linear embedding these techniques attempt to preserve either the local or the global geometry of the original data and they perform metric or non metric dimensionality reduction nevertheless it is difficult to apply most of them to large data sets there is a need for new algorithms that are able to combine vector quantisation and mapping methods in order to visualise the data structure in a low dimensional vector space in this paper we define a new class of algorithms to quantify and disclose the data structure that are based on the topology representing networks and apply different mapping methods to the low dimensional visualisation not only existing methods are combined for that purpose but also a novel group of mapping methods topology representing network map are introduced as a part of this class topology representing network maps utilise the main benefits of the topology representing networks and of the multidimensional scaling methods to disclose the real structure of the data set under study to determine the main properties of the topology representing network based mapping methods a detailed analysis of classical benchmark examples wine and optical recognition of handwritten digits data set is presented

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

monodromy of the matrix schrodinger equations and darboux transformations a schrodinger operator with a matrix valued rational potential u z is said to have trivial monodromy if all the solutions of the corresponding schrodinger equations are single valued in the complex plane for any a local criterion of this property in terms of the laurent coefficients of the potential u near its singularities which are assumed to be regular is found it is proved that any such operator with a potential vanishing at infinity can be obtained by a matrix analogue of the darboux transformation from the schrodinger operator this generalizes the well known duistermaat grunbaum result to the matrix case and gives the explicit description of the schrodinger operators with trivial monodromy in this case

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

learning invariance from transformation sequences the visual system can reliably identify objects even when the retinal image is transformed considerably by commonly occurring changes in the environment a local learning rule is proposed which allows a network to learn to generalize across such transformations during the learning phase the network is exposed to temporal sequences of patterns undergoing the transformation an application of the algorithm is presented in which the network learns invariance to shift in retinal position such a principle may be involved in the development of the characteristic shift invariance property of complex cells in the primary visual cortex and also in the development of more complicated invariance properties of neurons in higher visual areas

hartman stampacchia results for stably pseudomonotone operators and non linear hemivariational inequalities we are concerned with two classes of non standard hemivariational inequalities in the first case we establish a hartman stampacchia type existence result in the framework of stably pseudomonotone operators next we prove an existence result for a class of non linear perturbations of canonical hemivariational inequalities our analysis includes both the cases of compact sets and of closed convex sets in banach spaces applications to non coercive hemivariational and variational hemivariational inequalities illustrate the abstract results of this article

on the equivalence of the integral and the differential exact solution generation methods for the one dimensional schrodinger equation it is demonstrated that the integral exact solution generation methods for the one dimensional schrodinger equation based on the gelfand levitan formalism are in some cases equivalent to the differential ones based on the n order darboux transformation some new exact solvable potentials are generated from the effective coulomb potential and the harmonic oscillator potential a new form of n soliton potential i e reflectionless potential with n discrete energy levels disposed in a desirable manner based on an explicit expression for an n order wronski determinant constructed from hyperbolic functions and its orthonormal discrete spectrum eigenfunctions are given

feature extraction using a fast null space based linear discriminant analysis algorithm the small sample size problem is often encountered in pattern recognition several algorithms for null space based linear discriminant analysis nlda have been developed to solve the problem however these algorithms for nlda have high computational cost in this paper we simplify the recently proposed algorithm for nlda in chu and thye 2010 5 with the assumption that all the training data vectors are linearly independent and propose a new and fast algorithm for nlda our main observation is that two steps of economic qr decomposition with column pivoting can be replaced by one step of economic qr decomposition without column pivoting if the related matrix is of full column rank the main features of our algorithm for nlda include i our nlda algorithm is carried out by only one step of economic qr decomposition and does not compute any singular value decomposition svd when all the training data vectors are linearly independent ii the main cost of our method is the cost of an economic qr decomposition of an mx n 1 matrix here m is the dimension of the training data and n is the number of samples our method is a fast one experimental studies on orl feret and pie face databases demonstrate the effectiveness of our new algorithm for nlda

pt symmetry cartan decompositions lie triple systems and krein space related clifford algebras gauged quantum mechanics ptqm and corresponding krein space setups are studied for models with constant non abelian gauge potentials and extended parity inversions compact and noncompact lie group components are analyzed via cartan decompositions a lie triple structure is found and an interpretation as symmetrically generalized jaynes cummings model is possible with close relation to recently studied cavity qed setups with transmon states in multilevel artificial atoms for models with abelian gauge potentials a hidden clifford algebra structure is found and used to obtain the fundamental symmetry of krein space related j self adjoint extensions for ptqm setups with ultra localized potentials

spectral design for matrix hamiltonians different methods of constructing of a matrix intertwining operator we study relations describing the intertwining of n n matrix in general non hermitian one dimensional hamiltonians by matrix linear differential operators with nondegenerate coefficients of in the highest degree some methods for constructing matrix intertwining operators of the first order of general form are proposed and their interrelations are examined we construct as an example a 2 2 matrix hamiltonian of general form intertwined by an operator of the first order with the hamiltonian with zero matrix potential it is shown that one can add for the final 2 2 matrix hamiltonian with respect to the initial matrix hamiltonian with the help of an intertwining operator of first order up to two bound states for different energy values or up to two bound states described by vector eigenfunctions for the same energy value or up to two bound states described by a vector eigenfunction and an associated vector function for the same energy value

parametrization of the isospectral set for the vector valued sturm liouville problem abstract we obtain a parametrization of the isospectral set of matrix valued potentials for the vector valued sturm liouville problem on a finite interval

weak solutions for nonlinear antiplane problems leading to hemivariational inequalities abstract we analyze the antiplane shear deformation of an elastic cylinder in frictional contact with a rigid foundation for static processes under the small deformation hypothesis based on the knaster kuratowski mazurkiewicz technique in the theory of the hemivariational inequalities we prove that the model has at least one weak solution moreover we present several examples of constitutive laws and friction laws for which our theoretical results are valid finally we comment on the conditions which guarantee the uniqueness of the solution

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

shape classification by manifold learning in multiple observation spaces manifold learning is a non linear method with the aim of finding a constructive way to embed the data from a high dimensional space into a low dimensional one the improvement of shape classification is the major approach in this paper which is based on the continuity in feature space in accordance with the continuity in semantic one in this regard a non linear approach is employed to map the shape feature vectors to a new space while their semantics become similar with human opinion the euclidean distance between two feature vectors would be closed shapes are described by four contour based and region based techniques by the proposed method in other word they are described in four observation spaces furthermore a parameter space is learnt from multiple observation spaces based on fusion of dissimilarities in a supervised manner experimental results show the validity and efficiency of the proposed approach for shape classification over a variety of standard shape datasets

backlund transformations and the atiyah ward ansatz for non commutative anti self dual yang mills equations we present backlund transformations for the non commutative anti self dual yang mills equation where the gauge group is g gl 2 and use it to generate a series of exact solutions from a simple seed solution the solutions generated by this approach are represented in terms of quasi determinants we also explain the origins of all the ingredients of the backlund transformations within the framework of non commutative twistor theory in particular we show that the generated solutions belong to a non commutative version of the atiyah ward ansatz

single and coupled channel radial inverse scattering with supersymmetric transformations the present status of the three dimensional inverse scattering method with supersymmetric transformations is reviewed for the coupled channel case we first revisit in a pedagogical way the single channel case where the supersymmetric approach is shown to provide a complete efficient and elegant solution to the inverse scattering problem for the radial schrodinger equation with short range interactions a special emphasis is put on the differences between conservative and non conservative transformations i e transformations that do or do not conserve the behaviour of solutions of the radial schrodinger equation at the origin in particular we show that for the zero initial potential a non conservative transformation is always equivalent to a pair of conservative transformations these single channel results are illustrated on the inversion of the neutron proton triplet eigenphase shifts for the s and d waves we then summarize and extend our previous works on the coupled channel case i e on systems of coupled radial schrodinger equations and stress remaining difficulties and open questions of this problem by putting it in perspective with the single channel case we mostly concentrate on two channel examples to illustrate general principles while keeping mathematics as simple as possible in particular we discuss the important difference between the equal threshold and different threshold problems for equal thresholds conservative transformations can provide non diagonal jost and scattering matrices iterations of such transformations in the two channel case are studied and shown to lead to practical algorithms for inversion a convenient particular technique where the mixing parameter can be fitted without modifying the eigenphases is developed with iterations of pairs of conjugate transformations this technique is applied to the neutron proton triplet s d scattering matrix for which exactly solvable matrix potential models are constructed for different thresholds conservative transformations do not seem to be able to provide a non trivial coupling between channels in contrast a single non conservative transformation can generate coupled channel potentials starting from the zero potential and is a promising first step towards a full solution to the coupled channel inverse problem with threshold differences

generalized jaynes cummings hamiltonians by shape invariant hierarchies and their susy partners a generalization of the matrix jaynes cummings model in the rotating wave approximation is proposed by means of the shape invariant hierarchies of scalar factorized hamiltonians a class of darboux transformations sometimes called susy transformations in this context suitable for these generalized jaynes cummings models is constructed finally one example is worked out using the methods developed

adaptive nonlinear manifolds and their applications to pattern recognition dimensionality reduction has long been associated with retinotopic mapping for understanding cortical maps multisensory information is processed fused and mapped to an essentially 2 d cortex in an information preserving manner data processing and projection techniques inspired by this biological mechanism are playing an increasingly important role in pattern recognition computational intelligence data mining information retrieval and image recognition dimensionality reduction involves reduction of features or volume of data and has become an essential step of information processing in many fields the topic of manifold learning has recently attracted a great deal of attention and a number of advanced techniques for extracting nonlinear manifolds and reducing data dimensions have been proposed from statistics geometry theory and adaptive neural networks this paper provides an overview of this challenging and emerging topic and discusses various recent methods such as self organizing map som kernel pca principal manifold isomap local linear embedding and laplacian eigenmap many of them can be considered in a learning manifold framework the paper further elaborates on the biologically inspired som model and its metric preserving variant visom under the framework of adaptive manifold and their applications in dimensionality reduction with face recognition are investigated the experiments demonstrate that adaptive visom based methods produce markedly improved performance over the others due to their metric scaling and preserving properties along the nonlinear manifold

three dimensional solutions of supersymmetrical intertwining relations and pairs of isospectral hamiltonians the general solution of supersymmetrical intertwining relations for three dimensional schrodinger operators is built using the class of second order supercharges with nondegenerate constant metric this solution includes several models with arbitrary parameters we are interested only in quantum systems which are not amenable to separation of variables i e cannot be reduced to lower dimensional problems all constructed hamiltonians are partially integrable each of them commutes with a symmetry operator of fourth order in momenta the same models can be considered also for complex values of parameters leading to a class of non hermitian isospectral hamiltonians

kernel class wise locality preserving projection in the recent years the pattern recognition community paid more attention to a new kind of feature extraction method the manifold learning methods which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure among them locality preserving projection lpp is one of the most promising feature extraction techniques however when lpp is applied to the classification tasks it shows some limitations such as the ignorance of the label information in this paper we propose a novel local structure based feature extraction method called class wise locality preserving projection clpp clpp utilizes class information to guide the procedure of feature extraction in clpp the local structure of the original data is constructed according to a certain kind of similarity between data points which takes special consideration of both the local information and the class information the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper moreover a kernel version of clpp namely kernel clpp kclpp is developed through applying the kernel trick to clpp to increase its performance on nonlinear feature extraction experiments on orl face database and yale face database are performed to test and evaluate the proposed algorithm

existence and uniqueness results for a class of quasi hemivariational inequalities abstract in this paper we are concerned with the study of a nonstandard quasi hemivariational inequality using a fixed point theorem for set valued mappings the existence of at least one solution in bounded closed and convex subsets is established we also provide sufficient conditions for which our inequality possesses solutions in the case of unbounded sets finally the uniqueness and the stability of the solution are analyzed in a particular case

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

removing time variation with the anti hebbian differential synapse i describe a local synaptic learning rule that can be used to remove the effects of certain types of systematic temporal variation in the inputs to a unit according to this rule changes in synaptic weight result from a conjunction of short term temporal changes in the inputs and the output formally this is like the differential rule proposed by klopf 1986 and kosko 1986 except for a change of sign which gives it an anti hebbian character by itself this rule is insufficient a weight conservation condition is needed to prevent the weights from collapsing to zero and some further constraint implemented here by a biasing term to select particular sets of weights from the subspace of those which give minimal variation as an example i show that this rule will generate center surround receptive fields that remove temporally varying linear gradients from the inputs

smooth orthogonal decomposition based vibration mode identification a new multivariate data analysis method called smooth orthogonal decomposition sod is proposed to extract linear normal modes and natural frequencies of multi degree of freedom and distributed parameter vibration systems it is demonstrated that for an undamped free vibration of a multi degree of freedom system the computed smooth orthogonal modes are in direct correspondence with the actual normal vibration modes and the smooth orthogonal values are related to the corresponding natural frequencies the same is also shown to be true for lightly damped free vibrations of both lumped and distributed parameter systems in contrast to the intrinsic limitations of the proper orthogonal decomposition pod analysis which requires the knowledge of system s mass matrix to extract normal modes and cannot uniquely identify modal subspaces that have similar proper orthogonal values the sod is shown to overcome both of these deficiencies numerical examples are provided to compare the performances of the pod and sod based modal identification in various types of vibration environment

nonlinear dimensionality reduction using a temporal coherence principle temporal coherence principle is an attractive biologically inspired learning rule to extract slowly varying features from quickly varying input data in this paper we develop a new nonlinear neighborhood preserving nnp technique by utilizing the temporal coherence principle to find an optimal low dimensional representation from the original high dimensional data nnp is based on a nonlinear expansion of the original input data such as polynomials of a given degree it can be solved by the eigenvalue problem without using gradient descent and is guaranteed to find the global optimum nnp can be viewed as a nonlinear dimensionality reduction framework which takes into consideration both time series and data sets without an obvious temporal structure according to different situations we introduce three algorithms of nnp named nnp 1 nnp 2 and nnp 3 the objective function of nnp 1 is equal to slow feature analysis sfa and it works well for time series such as image sequences nnp 2 artificially constructs time series consisting of neighboring points for data sets without a clear temporal structure such as image data nnp 3 is proposed for classification tasks which can minimize the distances of neighboring points in the embedding space and ensure that the remaining points are as far apart as possible simultaneously furthermore the kernel extension of nnp is also discussed in this paper the proposed algorithms work very well on some image sequences and image data sets compared to other methods meanwhile we perform the classification task on the mnist handwritten digit database using the supervised nnp algorithms the experimental results demonstrate that nnp is an effective technique for nonlinear dimensionality reduction tasks