generalized multiple kernel learning with data dependent priors multiple kernel learning mkl and classifier ensemble are two mainstream methods for solving learning problems in which some sets of features views are more informative than others or the features views within a given set are inconsistent in this paper we first present a novel probabilistic interpretation of mkl such that maximum entropy discrimination with a noninformative prior over multiple views is equivalent to the formulation of mkl instead of using the noninformative prior we introduce a novel data dependent prior based on an ensemble of kernel predictors which enhances the prediction performance of mkl by leveraging the merits of the classifier ensemble with the proposed probabilistic framework of mkl we propose a hierarchical bayesian model to learn the proposed data dependent prior and classification model simultaneously the resultant problem is convex and other information e g instances with either missing views or missing labels can be seamlessly incorporated into the data dependent priors furthermore a variety of existing mkl models can be recovered under the proposed mkl framework and can be readily extended to incorporate these priors extensive experiments demonstrate the benefits of our proposed framework in supervised and semisupervised settings as well as in tasks with partial correspondence among multiple views

q deformation of lie superalgebras b m n b 0 n c 1 n and d m n in their boson fermion representations a systematic approach is proposed to give the q deformation of basic lie superalgebras b m n b 0 n c 1 n and d m n in their boson fermion oscillator representation with special attention paid to the b m n series

equivalence of q bosons using the exponential phase operator various forms of the q boson are explained and their hidden symmetry revealed by transformations using the exponential phase operator both the one component and the multicomponent q bosons are discussed as a byproduct we obtain a new boson algebra having a shifted vacuum structure and define a global operator u 1 gauge transformation

a p q oscillator realization of two parameter quantum algebras it is noted that the study of a quantum algebra sup q 2 with two independent deformation parameters p q leads to a p q oscillator realization for it the analysis is extended to the p q analogues of su 1 1 osp 2 1 and the centreless virasoro algebra the standard single parameter q deformations are obtained in the limit p q

information theoretic subspace clustering this paper addresses the problem of grouping the data points sampled from a union of multiple subspaces in the presence of outliers information theoretic objective functions are proposed to combine structured low rank representations lrrs to capture the global structure of data and information theoretic measures to handle outliers in theoretical part we point out that group sparsity induced measures ell 2 1 norm ell alpha norm and correntropy can be justified from the viewpoint of half quadratic hq optimization which facilitates both convergence study and algorithmic development in particular a general formulation is accordingly proposed to unify hq based group sparsity methods into a common framework in algorithmic part we develop information theoretic subspace clustering methods via correntropy with the help of parzen window estimation correntropy is used to handle either outliers under any distributions or sample specific errors in data pairwise link constraints are further treated as a prior structure of lrrs based on the hq framework iterative algorithms are developed to solve the nonconvex information theoretic loss functions experimental results on three benchmark databases show that our methods can further improve the robustness of lrr subspace clustering and outperform other state of the art subspace clustering methods

multiview hessian regularization for image annotation the rapid development of computer hardware and internet technology makes large scale data dependent models computationally tractable and opens a bright avenue for annotating images through innovative machine learning algorithms semisupervised learning ssl therefore received intensive attention in recent years and was successfully deployed in image annotation one representative work in ssl is laplacian regularization lr which smoothes the conditional distribution for classification along the manifold encoded in the graph laplacian however it is observed that lr biases the classification function toward a constant function that possibly results in poor generalization in addition lr is developed to handle uniformly distributed data or single view data although instances or objects such as images and videos are usually represented by multiview features such as color shape and texture in this paper we present multiview hessian regularization mhr to address the above two problems in lr based image annotation in particular mhr optimally combines multiple hr each of which is obtained from a particular view of instances and steers the classification function that varies linearly along the data manifold we apply mhr to kernel least squares and support vector machines as two examples for image annotation extensive experiments on the pascal voc 07 dataset validate the effectiveness of mhr by comparing it with baseline algorithms including lr and hr

consensus and complementarity based maximum entropy discrimination for multi view classification maximum entropy discrimination med is a general framework for discriminative estimation based on the maximum entropy and large margin principles but it just uses only one view of the data not all the views of the data although multi view maximum entropy discrimination considered the multi view information of the data it just respects the consensus principle there are two common principles named consensus and complementarity in multi view learning we aim to take the full advantage of the multi view information of the data for classification and respect the two common principles consensus and complementarity simultaneously in this paper we propose a new method called consensus and complementarity based med med 2c for multi view classification which well utilizes the two principles consensus and complementarity for multi view learning mvl we first transform data from two views into a common subspace and make the transformed data in the new subspace identical to respect the consensus principle then we augment the transformed data with their original features to take into account the complementarity principle built on the augmented features and meanwhile by relaxing the consensus principle the objective function of med 2c is naturally formed whose inner optimization recovers the traditional med framework we provide an instantiation of the med 2c method and derive the corresponding solution experimental results on synthetic data and real world data show the effectiveness of the proposed med 2c it not only performs better than three single view classification methods but also generally outperforms three multi view classification methods canonical correlation analysis cca ensemble med emed and the multi view variant svm 2k of the classical support vector machine svm algorithm in addition med 2c performs better than or as well as state of the art mvmed on all the data sets

learning graphs with monotone topology properties and multiple connected components recent papers have formulated the problem of learning graphs from data as an inverse covariance estimation problem with graph laplacian constraints while such problems are convex existing methods cannot guarantee that solutions will have specific graph topology properties e g being a tree which are desirable for some applications the problem of learning a graph with topology properties is in general non convex in this paper we propose an approach to solve these problems by decomposing them into two sub problems for which efficient solutions are known specifically a graph topology inference gti step is employed to select a feasible graph topology then a graph weight estimation gwe step is performed by solving a generalized graph laplacian estimation problem where edges are constrained by the topology found in the gti step our main result is a bound on the error of the gwe step as a function of the error in the gti step this error bound indicates that the gti step should be solved using an algorithm that approximates the data similarity matrix by another matrix whose entries have been thresholded to zero to have the desired type of graph topology the gti stage can leverage existing methods which are typically based on minimizing the total weight of removed edges since the gwe stage is an inverse covariance estimation problem with linear constraints it can be solved using existing convex optimization methods we demonstrate that our approach can achieve good results for both synthetic and texture image data

consistency of spectral clustering consistency is a key property of all statistical procedures analyzing randomly sampled data surprisingly despite decades of work little is known about consistency of most clustering algorithms in this paper we investigate consistency of the popular family of spectral clustering algorithms which clusters the data with the help of eigenvectors of graph laplacian matrices we develop new methods to establish that for increasing sample size those eigenvectors converge to the eigenvectors of certain limit operators as a result we can prove that one of the two major classes of spectral clustering normalized clustering converges under very general conditions while the other unnormalized clustering is only consistent under strong additional assumptions which are not always satisfied in real data we conclude that our analysis provides strong evidence for the superiority of normalized spectral clustering

application of complex network method to spatiotemporal patterns in a neuronal network abstract spiral waves have been found to appear alternatively with plane waves in the brain cerebral cortex which has a significant effect on neuron firing behaviors in this paper we propose a functional firing network based on the correlated firing behaviors among neuronal populations and use the complex network method to investigate the effects of spiral waves and plane waves on the structure and function of the network we first analyze the correlation coefficient and the largest eigenvalue of the functional firing network we find a larger range distribution of correlation coefficients and greater largest eigenvalue of the functional firing network for spiral waves than those for plane waves which indicates that spiral waves induce higher network synchronization in addition we explore the topological structure of the functional firing network using the complex network method we find that the functional firing network for spiral waves has a larger degree and global efficiency and a lower modularity and characteristic path length than that for plane waves revealing that spiral waves contribute to neural information transmission and strengthen the functional integration our work not only provides new insights for studying spatiotemporal patterns but is also helpful for explaining the modulation of spiral waves on brain function

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

q oscillator realizations of the quantum superalgebras slq m n andospq m 2n realizations of the quantum superalgebras corresponding to thea m n b m n c n 1 andd m n series are given in terms of the creation and annihilation operators ofq deformed bose and fermi oscillators

on a general framework for q particles paraparticles and q paraparticles through deformations the authors propose a unification of deformations associated with the descriptions of q para and q para bosons and fermions for complex values of q

on quantization of simple harmonic oscillators a general framework is presented of quantizing the system of a simple harmonic oscillator various methods of quantization so far proposed are accommodated here in a unified form some remarks are also made on quantization for the case of more than one oscillator

q analogues of the parabose and parafermi oscillators and representations of quantum algebras deformations of the one dimensional parabose oscillators are presented they are shown to provide fock representations of the quantum sp q 2 algebra and ospq 1 2 superalgebra the representations of suq 2 are used to define the q analogues of the parafermi oscillators

semisupervised support vector machines with tangent space intrinsic manifold regularization semisupervised learning has been an active research topic in machine learning and data mining one main reason is that labeling examples is expensive and time consuming while there are large numbers of unlabeled examples available in many practical problems so far laplacian regularization has been widely used in semisupervised learning in this paper we propose a new regularization method called tangent space intrinsic manifold regularization it is intrinsic to data manifold and favors linear functions on the manifold fundamental elements involved in the formulation of the regularization are local tangent space representations which are estimated by local principal component analysis and the connections that relate adjacent tangent spaces simultaneously we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines tisvms and tangent space intrinsic manifold regularized twin svms titsvms they effectively integrate the tangent space intrinsic manifold regularization consideration the optimization of tisvms can be solved by a standard quadratic programming while the optimization of titsvms can be solved by a pair of standard quadratic programmings the experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms

q oscillator realizations of the metaplectic representation of quantum osp 3 2 q oscillator representations of the quantum superalgebra ospq 3 2 are discussed it is pointed out that the metaplectic representation of ospq 3 2 can be equivalently realized either in terms of one q boson and one q fermion or with one q boson and two q fermions

spectral embedded clustering a framework for in sample and out of sample spectral clustering spectral clustering sc methods have been successfully applied to many real world applications the success of these sc methods is largely based on the manifold assumption namely that two nearby data points in the high density region of a low dimensional data manifold have the same cluster label however such an assumption might not always hold on high dimensional data when the data do not exhibit a clear low dimensional manifold structure e g high dimensional and sparse data the clustering performance of sc will be degraded and become even worse than k means clustering in this paper motivated by the observation that the true cluster assignment matrix for high dimensional data can be always embedded in a linear space spanned by the data we propose the spectral embedded clustering sec framework in which a linearity regularization is explicitly added into the objective function of sc methods more importantly the proposed sec framework can naturally deal with out of sample data we also present a new laplacian matrix constructed from a local regression of each pattern and incorporate it into our sec framework to capture both local and global discriminative information for clustering comprehensive experiments on eight real world high dimensional datasets demonstrate the effectiveness and advantages of our sec framework over existing sc methods and k means based clustering methods our sec framework significantly outperforms sc using the nystrom algorithm on unseen data

white noise induced spiral waves and multiple spatial coherence resonances in a neuronal network with type i excitability abstract white noise induced pattern formation is studied in a network composed of morris lecar neuronal models with type i excitability and with initial values higher than that of the resting potential the appearance and disappearance of spiral waves as well as the transitions between spiral wave patterns with different kinds of complexity characterized by the normalized spatial autocorrelation function enable changes in the order of the network so as to exhibit a scenario with two or more locally maximal peaks as can be clearly seen in the signal to noise ratio curves as the noise intensity is adjusted from small to large in a wide range a possible physical mechanism of the multiple resonances based on the dynamics of type i excitability and initial values is provided the potential biological significance of the noise induced spiral waves is discussed

a completeness relation for the q analogue coherent states by q integration q integration is defined for the q oscillator realization of quantum groups this is used to prove a completeness relation for the q analogue of the usual coherent states these states are overcomplete

random matrix approach to cross correlations in financial data we analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory rmt using two large databases we calculate cross correlation matrices c of returns constructed from i 30 min returns of 1000 us stocks for the 2 yr period 1994 1995 ii 30 min returns of 881 us stocks for the 2 yr period 1996 1997 and iii 1 day returns of 422 us stocks for the 35 yr period 1962 1996 we test the statistics of the eigenvalues lambda i of c against a null hypothesis a random correlation matrix constructed from mutually uncorrelated time series we find that a majority of the eigenvalues of c fall within the rmt bounds lambda lambda for the eigenvalues of random correlation matrices we test the eigenvalues of c within the rmt bound for universal properties of random matrices and find good agreement with the results for the gaussian orthogonal ensemble of random matrices implying a large degree of randomness in the measured cross correlation coefficients further we find that the distribution of eigenvector components for the eigenvectors corresponding to the eigenvalues outside the rmt bound display systematic deviations from the rmt prediction in addition we find that these deviating eigenvectors are stable in time we analyze the components of the deviating eigenvectors and find that the largest eigenvalue corresponds to an influence common to all stocks our analysis of the remaining deviating eigenvectors shows distinct groups whose identities correspond to conventionally identified business sectors finally we discuss applications to the construction of portfolios of stocks that have a stable ratio of risk to return less

quantum groups and lie admissible time evolution the time evolution of operators for q oscillators is derived for the first time by exploiting the connection between q deformation algebras and lie admissible algebras

discriminative semi supervised feature selection via manifold regularization feature selection has attracted a huge amount of interest in both research and application communities of data mining we consider the problem of semi supervised feature selection where we are given a small amount of labeled examples and a large amount of unlabeled examples since a small number of labeled samples are usually insufficient for identifying the relevant features the critical problem arising from semi supervised feature selection is how to take advantage of the information underneath the unlabeled data to address this problem we propose a novel discriminative semi supervised feature selection method based on the idea of manifold regularization the proposed approach selects features through maximizing the classification margin between different classes and simultaneously exploiting the geometry of the probability distribution that generates both labeled and unlabeled data in comparison with previous semi supervised feature selection algorithms our proposed semi supervised feature selection method is an embedded feature selection method and is able to find more discriminative features we formulate the proposed feature selection method into a convex concave optimization problem where the saddle point corresponds to the optimal solution to find the optimal solution the level method a fairly recent optimization method is employed we also present a theoretic proof of the convergence rate for the application of the level method to our problem empirical evaluation on several benchmark data sets demonstrates the effectiveness of the proposed semi supervised feature selection method

a quasi parafermionic realization of g2 and uq g2 the authors present a construction of the exceptional lie algebra g2 and of corresponding quantum algebra uq g2 using quasi parafermionic creation and annihilation operators and their quantum analogue as a by product a new realization of uq a2 is found

on the combinatorics of normal ordering bosonic operators and deformations of it recently some combinatorial aspects for the normal ordering of powers of arbitrary monomials of boson operators were discussed in particular it was shown that the resulting formulae lead to generalizations of the usual bell and stirling numbers in this paper these considerations are generalized to the q deformed case in particular it is shown that the simplest example of this generalization leads to q deformed lah numbers the connection between generalized stirling and bell numbers and matrix elements of the above mentioned operators with respect to the usual fock space basis and coherent states is discussed

a realization of generalized deformed oscillators with cyclic symmetry the algebra of generalized deformed oscillators that possess cyclic symmetry is studied the general set of multilinear operator relations is presented which characterizes the multilinear part of the algebra of cyclic extended deformed oscillators the realization scheme of generalized deformed oscillators with cyclic symmetry in terms of those without cyclic symmetry is established it is shown that all generalized deformed oscillators with cyclic symmetry constructed by the scheme are actually equivalent in the viewpoint of mathematics though each generalized deformed oscillator admits its own particular cyclic extended counterpart examples are given to illustrate this peculiar realization scheme

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

fisher regularized support vector machine this paper proposes fisher regularized support vector machine fishersvm fishersvm is a graph based supervised learning method fishersvm has two regularization terms maximum margin and fisher regularizations fishersvm aims to maximize the margin and minimize the within class scatter support vector machine svm and fisher discriminant analysis fda are two commonly used methods in machine learning and pattern recognition a combined method of the linear svm and fda called svm lda linear discriminant analysis has been proposed only for the linear case this paper generalizes this combined method to the nonlinear case from the view of regularization a fisher regularization is defined and incorporated into svm to obtain a fisher regularized support vector machine fishersvm in fishersvm there are two regularization terms the maximum margin regularization and fisher regularization which allow fishersvm to maximize the classification margin and minimize the within class scatter roughly speaking fishersvm can approximatively fulfill the fisher criterion and obtain good statistical separability this paper also discusses the connections of fishersvm to graph based regularization methods and the mathematical programming method to kernel fisher discriminant analysis kfda it shows that fishersvm can be thought of as a graph based supervised learning method or a robust kfda experimental results on artificial and real world data show that fishersvm has a promising generalization performance

covariant differential calculus on the quantum superplane and generalization of the wess zumino formalism it is shown that the construction of covariant differential calculus on quantum planes developed by wess and zumino 1990 for arbitrary quadratic algebras can generalize to the quantum superplane if one accounts for the differences due to the graduation of the superplane

comment on the q deformed fermionic oscillator the q deformed fermionic oscillator is identified with the usual fermionic oscillator by virtue of a simple transformation so the realization of quantum algebra suq 2 can also be constructed from the usual fermionic oscillator

local linear regression on manifolds and its geometric interpretation high dimensional data analysis has been an active area and the main focus areas have been variable selection and dimension reduction in practice it occurs often that the variables are located on an unknown lower dimensional nonlinear manifold under this manifold assumption one purpose of this article is regression and gradient estimation on the manifold and another is developing a new tool for manifold learning as regards the first aim we suggest directly reducing the dimensionality to the intrinsic dimension d of the manifold and performing the popular local linear regression llr on a tangent plane estimate an immediate consequence is a dramatic reduction in the computational time when the ambient space dimension p d we provide rigorous theoretical justification of the convergence of the proposed regression and gradient estimators by carefully analyzing the curvature boundary and nonuniform sampling effects we propose a bandwidth selector that can handle heteroscedastic errors with re

flexible manifold embedding a framework for semi supervised and unsupervised dimension reduction we propose a unified manifold learning framework for semi supervised and unsupervised dimension reduction by employing a simple but effective linear regression function to map the new data points for semi supervised dimension reduction we aim to find the optimal prediction labels f for all the training samples x the linear regression function h x and the regression residue f0 f h x simultaneously our new objective function integrates two terms related to label fitness and manifold smoothness as well as a flexible penalty term defined on the residue f0 our semi supervised learning framework referred to as flexible manifold embedding fme can effectively utilize label information from labeled data as well as a manifold structure from both labeled and unlabeled data by modeling the mismatch between h x and f we show that fme relaxes the hard linear constraint f h x in manifold regularization mr making it better cope with the data sampled from a nonlinear manifold in addition we propose a simplified version referred to as fme u for unsupervised dimension reduction we also show that our proposed framework provides a unified view to explain and understand many semi supervised supervised and unsupervised dimension reduction techniques comprehensive experiments on several benchmark databases demonstrate the significant improvement over existing dimension reduction algorithms

generalized deformed oscillator corresponding to the modified poschl teller energy spectrum a generalized deformed oscillator with eigenvalues equal to the eigenvalues of the schrodinger equation with the modified poschl teller potential is constructed for special values of the potential depth the deformed oscillator algebra has a finite dimensional irreducible representation the polynomial representation and the associate deformed operations of integration and differentiation are studied the results of this study are general and they can be applied directly to the case of the q deformed oscillator with q being a root of unity

deformed algebras from the inverse schwinger method we consider a problem which may be viewed as inverse to the schwinger realization of lie algebra and suggest a procedure for deforming the algebra so obtained we illustrate the method through a few simple examples extending schwinger s su 1 1 construction as results various q deformed algebras are re produced as well as their undeformed counterparts some extensions of the method are briefly pointed out

alternative multiview maximum entropy discrimination maximum entropy discrimination med is a general framework for discriminative estimation based on maximum entropy and maximum margin principles and can produce hard margin support vector machines under some assumptions recently the multiview version of med multiview med mvmed was proposed in this paper we try to explore a more natural mvmed framework by assuming two separate distributions p 1 theta 1 over the first view classifier parameter theta 1 and p 2 theta 2 over the second view classifier parameter theta 2 we name the new mvmed framework as alternative mvmed amvmed which enforces the posteriors of two view margins to be equal the proposed amvmed is more flexible than the existing mvmed because compared with mvmed which optimizes one relative entropy amvmed assigns one relative entropy term to each of the two views thus incorporating a tradeoff between the two views we give the detailed solving procedure which can be divided into two steps the first step is solving our optimization problem without considering the equal margin posteriors from two views and then in the second step we consider the equal posteriors experimental results on multiple real world data sets verify the effectiveness of the amvmed and comparisons with mvmed are also reported

q fermionic operators and quantum exceptional algebras using a q deformation of the usual clifford algebra one constructs a realization of the quantum exceptional algebras e6 e7 e8 and f4 in terms of q fermionic operators

noise robust semi supervised learning via fast sparse coding this paper presents a novel noise robust graph based semi supervised learning algorithm to deal with the challenging problem of semi supervised learning with noisy initial labels inspired by the successful use of sparse coding for noise reduction we choose to give new l1 norm formulation of laplacian regularization for graph based semi supervised learning since our l1 norm laplacian regularization is explicitly defined over the eigenvectors of the normalized laplacian matrix we formulate graph based semi supervised learning as an l1 norm linear reconstruction problem which can be efficiently solved by sparse coding furthermore by working with only a small subset of eigenvectors we develop a fast sparse coding algorithm for our l1 norm semi supervised learning finally we evaluate the proposed algorithm in noise robust image classification the experimental results on several benchmark datasets demonstrate the promising performance of the proposed algorithm highlightswe propose novel semi supervised learning based on fast sparse coding our algorithm achieves promising results in noise robust image classification our algorithm can readily be extended to many other challenging problems

image interpolation via graph based bayesian label propagation in this paper we propose a novel image interpolation algorithm via graph based bayesian label propagation the basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones this process can be posed as a bayesian inference in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation specially our algorithm first constructs a set of local interpolation models which predict the intensity labels of all image samples and a loss term will be minimized to keep the predicted labels of the available low resolution lr samples sufficiently close to the original ones then all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples moreover a graph laplacian based manifold regularization term is incorporated to penalize the global smoothness of intensity labels such smoothing can alleviate the insufficient training of the local models and make them more robust finally we construct a unified objective function to combine together the global loss of the locally linear regression square error of prediction bias on the available lr samples and the manifold regularization term it can be solved with a closed form solution as a convex optimization problem experimental results demonstrate that the proposed method achieves competitive performance with the state of the art image interpolation algorithms

on p 2 generalized deformed parafermions and exotic statistics generalized deformed parafermions of order two are analysed according to the lie super algebras they generate a classification of the subtended exotic statistics is then given and for each of them remarkable embedded lie structures are pointed out

network unfolding map by vertex edge dynamics modeling the emergence of collective dynamics in neural networks is a mechanism of the animal and human brain for information processing in this paper we develop a computational technique using distributed processing elements in a complex network which are called particles to solve semisupervised learning problems three actions govern the particles dynamics generation walking and absorption labeled vertices generate new particles that compete against rival particles for edge domination active particles randomly walk in the network until they are absorbed by either a rival vertex or an edge currently dominated by rival particles the result from the model evolution consists of sets of edges arranged by the label dominance each set tends to form a connected subnetwork to represent a data class although the intrinsic dynamics of the model is a stochastic one we prove that there exists a deterministic version with largely reduced computational complexity specifically with linear growth furthermore the edge domination process corresponds to an unfolding map in such way that edges stretch and shrink according to the vertex edge dynamics consequently the unfolding effect summarizes the relevant relationships between vertices and the uncovered data classes the proposed model captures important details of connectivity patterns over the vertex edge dynamics evolution in contrast to the previous approaches which focused on only vertex or only edge dynamics computer simulations reveal that the new model can identify nonlinear features in both real and artificial data including boundaries between distinct classes and overlapping structures of data

conjugate relation between loss functions and uncertainty sets in classification problems there are two main approaches to binary classification problems the loss function approach and the uncertainty set approach the loss function approach is widely used in real world data analysis statistical decision theory has been used to elucidate its properties such as statistical consistency conditional probabilities can also be estimated by using the minimum solution of the loss function in the uncertainty set approach an uncertainty set is defined for each binary label from training samples the best separating hyperplane between the two uncertainty sets is used as the decision function although the uncertainty set approach provides an intuitive understanding of learning algorithms its statistical properties have not been sufficiently studied in this paper we show that the uncertainty set is deeply connected with the convex conjugate of a loss function on the basis of the conjugate relation we propose a way of revising the uncertainty set approach so that it will have good statistical properties such as statistical consistency we also introduce statistical models corresponding to uncertainty sets in order to estimate conditional probabilities finally we present numerical experiments verifying that the learning with revised uncertainty sets improves the prediction accuracy

approximating the largest eigenvalue of network adjacency matrices the largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes e g synchronization of oscillators percolation on directed networks and linear stability of equilibria of network coupled systems in this paper we develop approximations to the largest eigenvalue of adjacency matrices and discuss the relationships between these approximations numerical experiments on simulated networks are used to test our results

q integrals on the quantum complex plane q integration is defined for the complex quantum plane the existence of classical and grassmanian limits of q integration is proved quantum versions of cauchy s and stokes theorems are formulated

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

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

value regularization and fenchel duality regularization is an approach to function learning that balances fit and smoothness in practice we search for a function f with a finite representation f i ci i in most treatments the ci are the primary objects of study we consider value regularization constructing optimization problems in which the predicted values at the training points are the primary variables and therefore the central objects of study although this is a simple change it has profound consequences from convex conjugacy and the theory of fenchel duality we derive separate optimality conditions for the regularization and loss portions of the learning problem this technique yields clean and short derivations of standard algorithms this framework is ideally suited to studying many other phenomena at the intersection of learning theory and optimization we obtain a value based variant of the representer theorem which underscores the transductive nature of regularization in reproducing kernel hilbert spaces we unify and extend previous results on learning kernel functions with very simple proofs we analyze the use of unregularized bias terms in optimization problems and low rank approximations to kernel matrices obtaining new results in these areas in summary the combination of value regularization and fenchel duality are valuable tools for studying the optimization problems in machine learning

new semi supervised classification method based on modified cluster assumption the cluster assumption which assumes that similar instances should share the same label is a basic assumption in semi supervised classification learning and has been found very useful in many successful semi supervised classification methods it is rarely noticed that when the cluster assumption is adopted there is an implicit assumption that every instance should have a crisp class label assignment in real applications however there are cases where it is difficult to tell that an instance definitely belongs to one class and does not belong to other neighboring classes in such cases it is more adequate to assume that similar instances should share similar label memberships rather than sharing a crisp label assignment here label memberships can be represented as a vector where each element corresponds to a class and the value at the element expresses the likelihood of the concerned instance belonging to the class by adopting this modified cluster assumption in this paper we propose a new semi supervised classification method that is semi supervised classification based on class membership ssccm specifically we try to solve the decision function and adequate label memberships for instances simultaneously and constrain that an instance and its local weighted mean lwm share the same label membership vector where the lwm is a robust image of the instance constructed by calculating the weighted mean of its neighboring instances we formulate the problem in a unified objective function for the labeled unlabeled data and their lwms based on the square loss function and take an alternating iterative strategy to solve it in which each step generates a closed form solution and the convergence is guaranteed the solution will provide both the decision function and the label membership function for classification their classification results can verify each other and the reliability of semi supervised classification learning might be enhanced by checking the consistency between those two predictions experiments show that ssccm obtains encouraging results compared to state of the art semi supervised classification methods

multiple spatial coherence resonance induced by the stochastic signal in neuronal networks near a saddle node bifurcation abstract this paper reported multiple induction of spiral waves with a stochastic signal in a square lattice network model composed of type i morris lecar ml neurons where each neuron is coupled to its four nearest neighbors the induction occurs in two or three distinct regions of noise intensity and thus enables emergence of multiple spatial coherence in the network demonstrating a novel evidence of multiple coherence resonance emergence of this multiple spatial coherence resonance was evidenced by calculating the degree of spatial complexity spatial correlation length spatial structure function circular symmetry and signal to noise ratio curves the network was further characterized by spatial frequency and inherent spatial scale reflecting its inherent ability to manifest ordered pattern formation under the driven of noisy signals

deformation of lie algebras in a non chevalley basis and embedding of q algebras a deformation scheme for lie algebras in a basis which manifestly exhibits for q 1 the content of a singular subalgebra is presented this scheme allows to build up embedding chains of q algebras which can be physically interesting the case when the rank of the subalgebra is one unit less than the rank of the algebra is studied and explicit constructions of the algebras are given in terms of q bosonic and or q fermionic oscillators

non standard covariant deformed oscillator algebras it is shown that deformed oscillator algebras with a non standard behaviour similar to that observed for the quon algebra arise quite naturally when imposing covariance properties under the transformations of some quantum group by non standard behaviour we mean that there may not be enough rules available to order creation operators and that some fock states with positive squared norm for generic q values disappear for q to 1 two examples are given for the quantum groups oq 3 r and suq 2 suq 2 approximately oq 4 r respectively

generalized q fermion oscillators and q coherent states the algebra of q fermion operators developed earlier by two of the present authors is re examined it is shown that these operators represent particles that are distinct from usual spacetime fermions except in the limit q 1 it is shown that it is possible to introduce generalized q oscillators defined for infinity q or 1 in the range infinity q 0 these coincide with the q boson operators and for 0 q or 1 they coincide with q fermions the ordinary bosons and fermions may be identified with the limits q 1 and 1 respectively generalized q fermion coherent states are constructed by utilizing a nonlinear shift automorphism of the algebra of q fermion operators these are compared with the coherent states defined as eigenstates of annihilation operator matrix elements of the shift operator in the fock space basis are evaluated

semi supervised learning with nuclear norm regularization integrating new knowledge sources into various learning tasks to improve their performance has recently become an interesting topic in this paper we propose a novel semi supervised learning ssl approach called semi supervised learning with nuclear norm regularization ssl nnr which can simultaneously handle both sparse labeled data and additional pairwise constraints together with unlabeled data specifically we first construct a unified ssl framework to combine the manifold assumption and the pairwise constraints assumption for classification tasks then we provide a modified fixed point continuous algorithm to learn a low rank kernel matrix that takes advantage of laplacian spectral regularization finally we develop a two stage optimization strategy and present a semi supervised classification algorithm with enhanced spectral kernel esk moreover we also present a theoretical analysis of the proposed esk algorithm and derive an easy approach to extend it to out of sample data experimental results on a variety of synthetic and real world data sets demonstrate the effectiveness of the proposed esk algorithm

data visualization and dimensionality reduction using kernel maps with a reference point in this paper a new kernel based method for data visualization and dimensionality reduction is proposed a reference point is considered corresponding to additional constraints taken in the problem formulation in contrast with the class of kernel eigenmap methods the solution coordinates in the low dimensional space is characterized by a linear system instead of an eigenvalue problem the kernel maps with a reference point are generated from a least squares support vector machine ls svm core part that is extended with an additional regularization term for preserving local mutual distances together with reference point constraints the kernel maps possess primal and dual model representations and provide out of sample extensions e g for validation based tuning the method is illustrated on toy problems and real life data sets

semi supervised domain adaptation on manifolds in real life problems the following semi supervised domain adaptation scenario is often encountered we have full access to some source data which is usually very large the target data distribution is under certain unknown transformation of the source data distribution meanwhile only a small fraction of the target instances come with labels the goal is to learn a prediction model by incorporating information from the source domain that is able to generalize well on the target test instances we consider an explicit form of transformation functions and especially linear transformations that maps examples from the source to the target domain and we argue that by proper preprocessing of the data from both source and target domains the feasible transformation functions can be characterized by a set of rotation matrices this naturally leads to an optimization formulation under the special orthogonal group constraints we present an iterative coordinate descent solver that is able to jointly learn the transformation as well as the model parameters while the geodesic update ensures the manifold constraints are always satisfied our framework is sufficiently general to work with a variety of loss functions and prediction problems empirical evaluations on synthetic and real world experiments demonstrate the competitive performance of our method with respect to the state of the art

equivalence of deformed fermionic algebras generalized deformations of the fermionic algebra are studied the polynomial representations of these algebras are constructed all the deformation schemes can be realized by the same polynomial basis using the bargmann representation thus proving that all deformed fermionic algebras are isomorphically equivalent to the non deformed fermionic algebra

a deformed oscillator with coulomb energy spectrum a deformed oscillator with eigenvalues equal to the eigenvalues of the schrodinger equation with the coulomb potential is constructed the deformed oscillator algebra has a polynomial realization and the associate deformed operations of integration and differentiation are studied

quantization of set theory and generalization of the fermion algebra the quantum states of a d dimensional fermion algebra are in one to one correspondence with the subsets of a d element universal set in this paper we use this set theoretical motivation to construct a one parameter deformation of the fermion algebra and extend it to a d dimensional generalization which is invariant under the group u d this discrete fermionic oscillator system is extended to the continuous case we also show that the q deformation of these systems is related to supercovariant q oscillators

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

generalized deformed oscillator and nonlinear algebras the harmonic oscillator is deformed arbitrarily and the properties of the deformed oscillator algebra are studied the eigenstates and eigenvalues of the deformed oscillator are calculated this generalized deformed oscillator algebra is used to create nonlinear deformation of the classical su 2 algebra the deformed boson realizations of an arbitrary nonlinear su 2 algebra are calculated the algebra of the q deformed oscillator is a special case of the generalized deformed oscillator algebra

a q analogue of bargmann space and its scalar product a q analogue of bargmann space is defined using the properties of coherent states associated with a pair of q deformed bosons the space consists of a class of entire functions of a complex variable z and has a reproducing kernel on this space the q boson creation and annihilation operators are represented as multiplication by z and q differentiation with respect to z respectively a q integral analogue of bargmann s scalar product is defined involving the q exponential as a weight function associated with this is a completeness relation for the q coherent states

from local similarities to global coding a framework for coding applications feature coding has received great attention in recent years as a building block of many image processing algorithms in particular the importance of the locality assumption in coding approaches has been studied in many previous works we review this assumption and claim that using the similarity of data points to a more global set of anchor points does not necessarily weaken the coding method as long as the underlying structure of the anchor points is considered we propose to capture the underlying structure by assuming a random walker over the anchor points we also show that our method is a fast approximation to the diffusion map kernel experiments on various data sets show that with a knowledge of the underlying structure of anchor points different state of the art coding algorithms may boost their performance in different learning tasks by utilizing the proposed method

q oscillators realization of fq 4 and gq 3 a realization of the quantum superalgebras corresponding to f 4 and g 3 is given in terms of q deformed bosonic and fermionic oscillators

algebraic shape invariant potentials as the generalized deformed oscillator within the framework of supersymmetric quantum mechanics we study the simplified version of the potential algebra of the shape invariance condition in k steps where k is an arbitrary positive integer the associated potential algebra is found to be equivalent to the generalized deformed oscillator algebra that has a built in zk grading structure the algebraic realization of the shape invariance condition in k steps is therefore formulated by the method of the zk graded deformed oscillator based on this formulation we explicitly construct the general algebraic properties for shape invariant potentials in k steps in which the parameters of partner potentials are related to each other by the translation a1 a0 the obtained results include the cyclic shape invariant potentials of period k as a special case

a q analogue of the supersymmetric oscillator and its q superalgebra a q analogue of the supersymmetric oscillator is constructed out of q boson and q fermion creation and annihilation operators for a fixed nb nf 2n where nb and nf are q boson and q fermion occupation numbers the irreducible representations of the q superalgebra generated by the q oscillator are 2n 1 dimensional particular cases when q is a root of or 1 are discussed a realization of the quantum group suq 2 is obtained using a pair of 1 fermion creation and annihilation operators

sparse semi supervised learning using conjugate functions in this paper we propose a general framework for sparse semi supervised learning which concerns using a small portion of unlabeled data and a few labeled data to represent target functions and thus has the merit of accelerating function evaluations when predicting the output of a new example this framework makes use of fenchel legendre conjugates to rewrite a convex insensitive loss involving a regularization with unlabeled data and is applicable to a family of semi supervised learning methods such as multi view co regularized least squares and single view laplacian support vector machines svms as an instantiation of this framework we propose sparse multi view svms which use a squared e insensitive loss the resultant optimization is an inf sup problem and the optimal solutions have arguably saddle point properties we present a globally optimal iterative algorithm to optimize the problem we give the margin bound on the generalization error of the sparse multi view svms and derive the empirical rademacher complexity for the induced function class experiments on artificial and real world data show their effectiveness we further give a sequential training approach to show their possibility and potential for uses in large scale problems and provide encouraging experimental results indicating the efficacy of the margin bound and empirical rademacher complexity on characterizing the roles of unlabeled data for semi supervised learning

manifold regularization and semi supervised learning some theoretical analyses manifold regularization belkin et al 2006 is a geometrically motivated framework for machine learning within which several semi supervised algorithms have been constructed here we try to provide some theoretical understanding of this approach our main result is to expose the natural structure of a class of problems on which manifold regularization methods are helpful we show that for such problems no supervised learner can learn effectively on the other hand a manifold based learner that knows the manifold or learns it from unlabeled examples can learn with relatively few labeled examples our analysis follows a minimax style with an emphasis on finite sample results in terms of n the number of labeled examples these results allow us to properly interpret manifold regularization and related spectral and geometric algorithms in terms of their potential use in semi supervised learning

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

constrained nonnegative matrix factorization for image representation nonnegative matrix factorization nmf is a popular technique for finding parts based linear representations of nonnegative data it has been successfully applied in a wide range of applications such as pattern recognition information retrieval and computer vision however nmf is essentially an unsupervised method and cannot make use of label information in this paper we propose a novel semi supervised matrix decomposition method called constrained nonnegative matrix factorization cnmf which incorporates the label information as additional constraints specifically we show how explicitly combining label information improves the discriminating power of the resulting matrix decomposition we explore the proposed cnmf method with two cost function formulations and provide the corresponding update solutions for the optimization problems empirical experiments demonstrate the effectiveness of our novel algorithm in comparison to the state of the art approaches through a set of evaluations based on real world applications

multiclass data segmentation using diffuse interface methods on graphs we present two graph based algorithms for multiclass segmentation of high dimensional data on graphs the algorithms use a diffuse interface model based on the ginzburg landau functional related to total variation and graph cuts a multiclass extension is introduced using the gibbs simplex with the functional s double well potential modified to handle the multiclass case the first algorithm minimizes the functional using a convex splitting numerical scheme the second algorithm uses a graph adaptation of the classical numerical merriman bence osher mbo scheme which alternates between diffusion and thresholding we demonstrate the performance of both algorithms experimentally on synthetic data image labeling and several benchmark data sets such as mnist coil and webkb we also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph laplacian and take advantage of the sparsity of the matrix experiments indicate that the results are competitive with or better than the current state of the art in multiclass graph based segmentation algorithms for high dimensional data

the q deformed differential operator algebra a new solution to the yang baxter equation and quantum plane the q deformed differential calculus is proposed and analysed in the framework of quantum plane the q deformed differential operator algebra is investigated and applied in the investigation of the quantum group suq 2 and its representations the generalization to n dimensional differential calculus is made and shown to be a new solution to quantum plane by providing a new solution of the yang baxter equation