fault recognition method for speed up and speed down process of rotating machinery based on independent component analysis and factorial hidden markov model abstract the behavior characteristics of the speed up and speed down process of rotating machinery possess the distinct diagnostic value the abundant information non stationarity poor repeatability and reproducibility in this process lead to the necessity to find the corresponding method of feature extraction and fault recognition in this paper combining independent component analysis ica and factorial hidden markov model fhmm a new method of the fault recognition named ica fhmm is proposed in the proposed method ica is used for the redundancy reduction and feature extraction of the multi channel detection and fhmm as a classifier to recognize the faults of the speed up and speed down process in rotating machinery this method is compared with another recognition method named ica hmm in which ica is similarly used for the feature extraction however hidden markov model hmm as a classifier experimental results show that the proposed method is very effective and the ica fhmm recognition method is superior to the ica hmm recognition method

nonlinear extraction of independent components of natural images using radial gaussianization we consider the problem of efficiently encoding a signal by transforming it to a new representation whose components are statistically independent a widely studied linear solution known as independent component analysis ica exists for the case when the signal is generated as a linear transformation of independent nongaussian sources here we examine a complementary case in which the source is nongaussian and elliptically symmetric in this case no invertible linear transform suffices to decompose the signal into independent components but we show that a simple nonlinear transformation which we call radial gaussianization rg is able to remove all dependencies we then examine this methodology in the context of natural image statistics we first show that distributions of spatially proximal bandpass filter responses are better described as elliptical than as linearly transformed independent sources consistent with this we demonstrate that the reduction in dependency achieved by applying rg to either nearby pairs or blocks of bandpass filter responses is significantly greater than that achieved by ica finally we show that the rg transformation may be closely approximated by divisive normalization which has been used to model the nonlinear response properties of visual neurons

on the haar measure of the quantumsu n group we prove that the haar state associated to the compact matrix quantum groupsu n is faithful for 1 1 0 and anyn 2

blow ups and infinitesimal automorphisms of cr manifolds for a real analytic connected cr hypersurface m of cr dimension n geqslant 1 having a point of levi nondegeneracy the following alternative is demonstrated for its symmetry algebra mathfrak s mathfrak s m i either dim mathfrak s n 2 4n 3 and m is spherical everywhere ii or dim mathfrak s leqslant n 2 2n 2 delta 2 n and in the case of equality m is spherical and has fixed signature of the levi form in the complement to its levi degeneracy locus a version of this result is proved for the lie group of global automorphisms of m explicit examples of cr hypersurfaces and their infinitesimal and global automorphisms realizing the bound in ii are constructed we provide many other models with large symmetry using the technique of blow up in particular we realize all maximal parabolic subalgebras of the pseudo unitary algebras as a symmetry

on the analysis and interpretation of inhomogeneous quadratic forms as receptive fields in this letter we introduce some mathematical and numerical tools to analyze and interpret inhomogeneous quadratic forms the resulting characterization is in some aspects similar to that given by experimental studies of cortical cells making it particularly suitable for application to second order approximations and theoretical models of physiological receptive fields we first discuss two ways of analyzing a quadratic form by visualizing the coefficients of its quadratic and linear term directly and by considering the eigenvectors of its quadratic term we then present an algorithm to compute the optimal excitatory and inhibitory stimuli those that maximize and minimize the considered quadratic form respectively given a fixed energy constraint the analysis of the optimal stimuli is completed by considering their invariances which are the transformations to which the quadratic form is most insensitive and by introducing a test to determine which of these are statistically significant next we propose a way to measure the relative contribution of the quadratic and linear term to the total output of the quadratic form furthermore we derive simpler versions of the above techniques in the special case of a quadratic form without linear term in the final part of the letter we show that for each quadratic form it is possible to build an equivalent two layer neural network which is compatible with but more general than related networks used in some recent articles and with the energy model of complex cells we show that the neural network is unique only up to an arbitrary orthogonal transformation of the excitatory and inhibitory subunits in the first layer

a class of bounded component analysis algorithms for the separation of both independent and dependent sources bounded component analysis bca is a recent approach which enables the separation of both dependent and independent signals from their mixtures in this approach under the practical source boundedness assumption the widely used statistical independence assumption is replaced by a more generic domain separability assumption this article introduces a geometric framework for the development of bounded component analysis algorithms two main geometric objects related to the separator output samples namely principal hyper ellipsoid and bounding hyper rectangle are introduced the maximization of the volume ratio of these objects and its extensions are introduced as relevant optimization problems for bounded component analysis the article also provides corresponding iterative algorithms for both real and complex sources the numerical examples illustrate the potential advantage of the proposed bca framework in terms of correlated source separation capability as well as performance improvement for short data records

emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces olshausen and field 1996 applied the principle of independence maximization by sparse coding to extract features from natural images this leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency thus resembling gabor functions and simple cell receptive fields in this article we show that the same principle of independence maximization can explain the emergence of phase and shift invariant features similar to those found in complex cells this new kind of emergence is obtained by maximizing the independence between norms of projections on linear subspaces instead of the independence of simple linear filter outputs the norms of the projections on such independent feature subspaces then indicate the values of invariant features

nonnegative matrix factorization for spectral data analysis data analysis is pervasive throughout business engineering and science very often the data to be analyzed is nonnegative and it is often preferable to take this constraint into account in the analysis process here we are concerned with the application of analyzing data obtained using astronomical spectrometers which provide spectral data which is inherently nonnegative the identification and classification of space objects that cannot be imaged in the normal way with telescopes is an important but difficult problem for tracking thousands of objects including satellites rocket bodies debris and asteroids in orbit around the earth in this paper we develop an effective nonnegative matrix factorization algorithm with novel smoothness constraints for unmixing spectral reflectance data for space object identification and classification purposes promising numerical results are presented using laboratory and simulated datasets

joint independent subspace analysis using second order statistics this paper deals with a novel generalization of classical blind source separation bss in two directions first relaxing the constraint that the latent sources must be statistically independent this generalization is well known and sometimes termed independent subspace analysis isa second jointly analyzing several isa problems where the link is due to statistical dependence among corresponding sources in different mixtures when the data are one dimensional i e multiple classical bss problems this model known as independent vector analysis iva has already been studied in this paper we combine iva with isa and term this new model joint independent subspace analysis jisa we provide full performance analysis of jisa including closed form expressions for minimal mean square error mse fisher information and cramer rao lower bound in the separation of gaussian data the derived mse applies also for non gaussian data when only second order statistics are used we generalize previously known results on iva including its ability to uniquely resolve instantaneous mixtures of real gaussian stationary data and having the same arbitrary permutation at all mixtures numerical experiments validate our theoretical results and show the gain with respect to two competing approaches that either use a finer block partition or a different norm

convergence of formal cr mappings into strongly pseudoconvex cauchy riemann manifolds it is shown that any formal holomorphic mapping sending a real analytic generic submanifold m subset mathbb c n of finite type into a real analytic strongly pseudoconvex cr submanifold m subset mathbb c n is necessarily convergent as a consequence we obtain a positive answer to the long standing open question of whether formal holomorphic maps sending real analytic strongly pseudoconvex hypersurfaces into each other are convergent

learning visual spatial pooling by strong pca dimension reduction in visual modeling invariance properties of visual cells are often explained by a pooling mechanism in which outputs of neurons with similar selectivities to some stimulus parameters are integrated so as to gain some extent of invariance to other parameters for example the classical energy model of phase invariant v1 complex cells pools model simple cells preferring similar orientation but different phases prior studies such as independent subspace analysis have shown that phase invariance properties of v1 complex cells can be learned from spatial statistics of natural inputs however those previous approaches assumed a squaring nonlinearity on the neural outputs to capture energy correlation such nonlinearity is arguably unnatural from a neurobiological viewpoint but hard to change due to its tight integration into their formalisms moreover they used somewhat complicated objective functions requiring expensive computations for optimization in this study we show that visual spatial pooling can be learned in a much simpler way using strong dimension reduction based on principal component analysis this approach learns to ignore a large part of detailed spatial structure of the input and thereby estimates a linear pooling matrix using this framework we demonstrate that pooling of model v1 simple cells learned in this way even with nonlinearities other than squaring can reproduce standard tuning properties of v1 complex cells for further understanding we analyze several variants of the pooling model and argue that a reasonable pooling can generally be obtained from any kind of linear transformation that retains several of the first principal components and suppresses the remaining ones in particular we show how the classic wiener filtering theory leads to one such variant

algebraicity of holomorphic mappings between real algebraic sets in cn 0 introduction 1 holomorphic nondegenera y of real analytic manifolds 1 1 preliminaries on real submanifolds of c n 1 2 holomorphic nondegeneracy and its propagation 1 3 the levi number and essential finiteness 1 4 holomorphic nondegeneracy of real algebraic sets 2 the segre sets of a real analytic cr submanifold 2 1 complexification of m involution and projections 2 2 definition of the segre sets of m at p0 2 3 homogeneous submanifolds of cr dimension 1 2 4 homogeneous submanifolds of arbitrary cr dimension 2 5 proof of theorem 2 2 1 3 algebraic properties of holomorphic mappings between real algebraic sets 3 1 a generalization of theorems 1 and 4 3 2 propagation of algebralcity 3 3 proof of theorem 3 1 2 3 4 proof of theorem 3 1 8 3 5 an example 3 6 proofs of theorems 1 through 4

c algebras of multiplication operators on bergman spaces soit un domaine borne dans c soit a 2 l espace de bergman de toutes les fonctions analytiques sur qui sont de carre integrable par rapport a la mesure volumetrique et soit c la c algebre engendree par les operateurs de multiplication par les fonctions coordonnee sur on etudie les proprietes de c

learning nonlinear statistical regularities in natural images by modeling the outer product of image intensities it is well known that there exist nonlinear statistical regularities in natural images existing approaches for capturing such regularities always model the image intensities by assuming a parameterized distribution for the intensities and learn the parameters in the letter we propose to model the outer product of image intensities by assuming a gaussian distribution for it a two layer structure is presented where the first layer is nonlinear and the second layer is linear trained on natural images the first layer bases resemble the receptive fields of simple cells in the primary visual cortex v1 while the second layer units exhibit some properties of the complex cells in v1 including phase invariance and masking effect the model can be seen as an approximation of the covariance model proposed in karklin and lewicki 2009 but has more robust and efficient learning algorithms

separation theorem for independent subspace analysis and its consequences independent component analysis ica the theory of mixed independent non gaussian sources has a central role in signal processing computer vision and pattern recognition one of the most fundamental conjectures of this research field is that independent subspace analysis isa the extension of the ica problem where groups of sources are independent can be solved by traditional ica followed by grouping the ica components the conjecture called isa separation principle i has been rigorously proven for some distribution types recently ii forms the basis of the state of the art isa solvers iii enables one to estimate the unknown number and the dimensions of the sources efficiently and iv can be extended to generalizations of the isa task such as different linear controlled post nonlinear complex valued partially observed problems as well as to problems dealing with nonparametric source dynamics here we shall review the advances on this field

a general reflection principle in c2 abstract a real analytic hypersurface m through 0 in cn is said to have the reflection property if any holomorphic mapping defined on one side of m not totally degenerate at 0 and mapping m into another real analytic hypersurface in cn extends holomorphically to a full neighborhood of 0 in cn the main result of this paper is that a real analytic hypersurface in c2 has the reflection property if and only if it is not levi flat

l p nested symmetric distributions in this paper we introduce a new family of probability densities called lp nested symmetric distributions the common property shared by all members of the new class is the same functional form x f x where f is a nested cascade of lp norms x p xi p 1 p lp nested symmetric distributions thereby are a special case of spherical distributions for which f is only required to be positively homogeneous of degree one while both spherical and lp nested symmetric distributions contain many widely used families of probability models such as the gaussian spherically and elliptically symmetric distributions lp spherically symmetric distributions and certain types of independent component analysis ica and independent subspace analysis isa models spherical distributions are usually computationally intractable here we demonstrate that lp nested symmetric distributions are still computationally feasible by deriving an analytic expression for its normalization constant gradients for maximum likelihood estimation analytic expressions for certain types of marginals as well as an exact and efficient sampling algorithm we discuss the tight links of lp nested symmetric distributions to well known machine learning methods such as ica isa and mixed norm regularizers and introduce the nested radial factorization algorithm nrf which is a form of non linear ica that transforms any linearly mixed non factorial lp nested symmetric source into statistically independent signals as a corollary we also introduce the uniform distribution on the lp nested unit sphere

cr structures with group action and extendability of cr functions part i presents results on local embedding of cr structures we consider an abstract cr manifold whose structure is invariant under a transversal lie group action we show that such a manifold can always be locally embedded in complex space as a generic submanifold the proof is based on selection of canonical coordinates and repeated use of the newlander nirenberg theorem 13 when the lie group is abelian the embedding can be given a particularly simple form let l 1 be the codimension of our submanifold called m throughout the paper it is then convenient to denote by n i the dimension of the ambient complex space and by zl z w 1 w t the complex coordinates we shall systematically write

compact quantum groups and groupoidc algebras abstract we study simple compact matrix quantum groups in the context of groupoid c algebras and obtain explicit descriptions of the structure of the c algebra of quantum su n and a concrete formula for its haar functional

undercomplete blind subspace deconvolution we introduce the blind subspace deconvolution bssd problem which is the extension of both the blind source deconvolution bsd and the independent subspace analysis isa tasks we examine the case of the undercomplete bssd ubssd applying temporal concatenation we reduce this problem to isa the associated high dimensional isa problem can be handled by a recent technique called joint f decorrelation jfd similar decorrelation methods have been used previously for kernel independent component analysis kernel ica more precisely the kernel canonical correlation kcca technique is a member of this family and as is shown in this paper the kernel generalized variance kgv method can also be seen as a decorrelation method in the feature space these kernel based algorithms will be adapted to the isa task in the numerical examples we i examine how efficiently the emerging higher dimensional isa tasks can be tackled and ii explore the working and advantages of the derived kernel isa methods

nonalgebraizable real analytic tubes in ℂ n we give necessary conditions for certain real analytic tube generic submanifolds in n to be locally algebraizable as an application we exhibit families of real analytic non locally algebraizable tube generic submanifolds in n during the proof we show that the local cr automorphism group of a minimal finitely nondegenerate real algebraic generic submanifold is a real algebraic local lie group we may state one of the main results as follows let m be a real analytic hypersurface tube in n passing through the origin having a defining equation of the form v y where z w x iy u iv open image in new windown 1 open image in new window assume that m is levi nondegenerate at the origin and that the real lie algebra of local infinitesimal cr automorphisms of m is of minimal possible dimension n i e generated by the real parts of the holomorphic vector fields z1 z n 1 w then m is locally algebraizable only if every second derivative 2yky l is an algebraic function of the collection of first derivatives y1 ym

quantization of the poisson su 2 and its poisson homogeneous space the 2 sphere we show that deformation quantizations of the poisson structures on the poisson lie groupsu 2 and its homogeneous space the 2 sphere are compatible with woronowicz s deformation quantization ofsu 2 s group structure and podles deformation quantization of 2 sphere s homogeneous structure respectively so in a certain sense the multiplicativity of the lie poisson structure onsu 2 at the classical level is preserved under quantization

a nonnegative pca algorithm for independent component analysis we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded so that they have a nonzero probability density function pdf in the region of zero we propose the use of a nonnegative principal component analysis nonnegative pca algorithm which is a special case of the nonlinear pca algorithm but with a rectification nonlinearity and we conjecture that this algorithm will find such nonnegative well grounded independent sources under reasonable initial conditions while the algorithm has proved difficult to analyze in the general case we give some analytical results that are consistent with this conjecture and some numerical simulations that illustrate its operation

projections over quantum homogeneous odd dimensional spheres abstract we give a complete classification of isomorphism classes of finitely generated projective modules or equivalently unitary equivalence classes of projections over the c algebra c s q 2 n 1 of the quantum homogeneous sphere s q 2 n 1 then we explicitly identify as concrete elementary projections the quantum line bundles l k over the quantum complex projective space c p q n associated with the quantum hopf principal u 1 bundle s q 2 n 1 c p q n

on the c version of the reflection principle for mappings between cr manifolds we prove a smooth version of the classical schwarz reflection principle for cr mappings between an abstract cr manifold m and a generic cr manifold embedded in euclidean complex space as a consequence of our results we settle a conjecture of x huang formulated in 1994

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

infinitesimal cr automorphisms of real hypersurfaces let m be an analytic real hypersurface through the origin in c n 1 and let hol m denote the space of vector fields x re z m tangent to m in a neighborhood of the origin where z is a holomorphic vector field defined in a neighborhood of the origin the hypersurface m is holomorphically nondegenerate at the origin if there is no holomorphic vector field tangent to m in a neighborhood of the origin the main result of the paper is that hol m is finite dimensional if and only if m is holomorphically nondegenerate at the origin

blind separation of multi dimensional components via subspace decomposition performance analysis a prevalent approach to blind separation of multi dimensional data is a two step procedure in the first step the data are assigned a one dimensional model a separating algorithm is applied according to this model this step corresponds to classical blind source separation bss in the second step the output is assigned into groups representing the multi dimensional components in this paper we consider an even more general case in which the subpartition of the components in the first step may be into elements of any dimension not necessarily one we consider a piecewise stationary model and assume that the number and dimensions of the underlying multi dimensional components are known we obtain a closed form analytical expression for the mean square error mse in the estimation of the multi dimensional components using this two step procedure as expected this approach is suboptimal in the presence of finite data size errors therefore we can predict the expected gain from using the correct model of the components over any finer decomposition thereof in addition we demonstrate the dependence of this gain on the model parameters

second order multidimensional ica performance analysis independent component analysis ica and blind source separation bss deal with extracting a number of mutually independent elements from a set of observed linear mixtures motivated by various applications this paper considers a more general and more flexible model the sources can be partitioned into groups exhibiting dependence within a given group but independence between two different groups we argue that this is tantamount to considering multidimensional components as opposed to the standard ica case which is restricted to one dimensional components the core of the paper is devoted to the statistical analysis of the blind separation of multidimensional components based on second order statistics in a piecewise stationary model we develop the likelihood and the associated estimating equations for the gaussian case we obtain closed form expressions for the fisher information matrix and the cramer rao bound of the de mixing parameters as well as the mean square error mse of the component estimates the derived mse is valid also for non gaussian data our analysis is verified through numerical experiments and its performance is compared to classical ica in various dependence scenarios quantifying the gain in the accuracy of component recovery in presence of multidimensional components

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

defining equations for real analytic real hypersurfaces in ⁿ a defining function for a real analytic real hypersurface can be utliquely written as 2 re h e where h is holomorphic and e contains no pure terms we study how h and e change when we perform a local biholomorphic change of coordinates or multiply by a unit one of the main results is necesary and sufficient conditions on the first nonvanishing homogeneous part of e expanded in terms of h beyond eoo that serve as obstructions to writing a defining equation as 2 re h e where e is independent of h we also find necessary pluriharmonic obstructions to doing this which arise from the easier case of attempting to straighten the hypersurface

a unifying view of wiener and volterra theory and polynomial kernel regression volterra and wiener series are perhaps the best understood nonlinear system representations in signal processing although both approaches have enjoyed a certain popularity in the past their application has been limited to rather low dimensional and weakly nonlinear systems due to the exponential growth of the number of terms that have to be estimated we show that volterra and wiener series can be represented implicitly as elements of a reproducing kernel hilbert space by using polynomial kernels the estimation complexity of the implicit representation is linear in the input dimensionality and independent of the degree of nonlinearity experiments show performance advantages in terms of convergence interpretability and system sizes that can be handled

linear multilayer ica generating hierarchical edge detectors in this letter a new ica algorithm linear multilayer ica lmica is proposed there are two phases in each layer of lmica one is the mapping phase where a two dimensional mapping is formed by moving more highly correlated nonindependent signals closer with the stochastic multidimensional scaling network another is the local ica phase where each neighbor namely highly correlated pair of signals in the mapping is separated by maxkurt algorithm because in lmica only a small number of highly correlated pairs have to be separated it can extract edge detectors efficiently from natural scenes we conducted numerical experiments and verified that lmica generates hierarchical edge detectors from large size natural scenes

dimension and stable rank in the k theory of c algebras in topological k theory which can be viewed as the algebraic side of the theory of vector bundles some of the interesting properties which one investigates are for example the conditions under which bundles must possess trivial direct summands or the extent to which the cancellation property for direct whitney sums of bundles holds such properties turn out to be controlled in part by the dimension of the base space and results describing the nature of this control are among what are frequently called stability results 17 during the past few years there has been a sudden flowering of a theory for c algebras see surveys 35 36 37 since c algebras are profitably thought of as non commutative locally compact spaces with the finitely generated projective modules being the appropriate generalization of vector bundles according to swan s theorem 40 it would be natural to look for stability results for c algebras but until now the theory has been focussed on the c groups of c algebras and there has been little discussion of stability properties presumably in part for lack of an appropriate concept of dimension for c algebras one of the main objectives of this paper is to introduce a concept of dimension for c algebras which directly generalizes the classical concept of dimension for compact spaces 16 20 22 and to develop some techniques for calculating it notably for c algebras which are obtained as crossed product algebras for an action of the group of integers in algebraic k theory which is the generalization of topological c theory to rings a substantial number of stability properties have been discovered 2 39 42 48 within that theory the concept which has played a role most analogous to that of dimension is the bass stable rank but despite its many successes the bass stable rank has often been difficult to calculate even for relatively uncomplicated rings another main objective of the present paper is to make accessible for application to c algebras some of the stability results from algebraic c theory this comes about from the fact that the concept of dimension which we introduce dominates the bass stable rank i was led to seek stability results for c algebras by my desire to determine whether the cancellation property for projective modules holds for the irrational rotation c algebras discussed in 30 which as elliott 11 has suggested can appropriately be called 2 dimensional non commutative tori in more concrete terms the question is whether two projections in such an algebra which have the same trace must be unitarily equivalent the present paper provides the general theory which is needed for the affirmative answer which i obtained in a subsequent paper i will derive the

independent component analysis involving autocorrelated sources with an application to functional magnetic resonance imaging independent component analysis ica is an effective data driven method for blind source separation it has been successfully applied to separate source signals of interest from their mixtures most existing ica procedures are carried out by relying solely on the estimation of the marginal density functions either parametrically or nonparametrically in many applications correlation structures within each source also play an important role besides the marginal distributions one important example is functional magnetic resonance imaging fmri analysis where the brain function related signals are temporally correlated in this article we consider a novel approach to ica that fully exploits the correlation structures within the source signals specifically we propose to estimate the spectral density functions of the source signals instead of their marginal density functions this is made possible by virtue of the intrinsic relationship between the unobserved sources and the observed mixed signals

building blocks for variational bayesian learning of latent variable models we introduce standardised building blocks designed to be used with variational bayesian learning the blocks include gaussian variables summation multiplication nonlinearity and delay a large variety of latent variable models can be constructed from these blocks including nonlinear and variance models which are lacking from most existing variational systems the introduced blocks are designed to fit together and to yield efficient update rules practical implementation of various models is easy thanks to an associated software package which derives the learning formulas automatically once a specific model structure has been fixed variational bayesian learning provides a cost function which is used both for updating the variables of the model and for optimising the model structure all the computations can be carried out locally resulting in linear computational complexity we present experimental results on several structures including a new hierarchical nonlinear model for variances and means the test results demonstrate the good performance and usefulness of the introduced method

an algebraic characterization of holomorphic nondegeneracy for real algebraic hypersurfaces and its application to cr mappings we give a new algebraic characterization of holomorphic nondegeneracy for embedded real algebraic hypersurfaces in mathcal c n 1 n geq 1 we then use this criterion to prove the following result about real analyticity of smooth cr mappings any smooth cr mapping h between a real analytic hypersurface and a rigid polynomial holomorphically nondegenerate hypersurface is real analytic provided the map h is not totally degenerate in the sense of baouendi and rothschild

soft mixer assignment in a hierarchical generative model of natural scene statistics gaussian scale mixture models offer a top down description of signal generation that captures key bottom up statistical characteristics of filter responses to images however the pattern of dependence among the filters for this class of models is prespecified we propose a novel extension to the gaussian scale mixturemodel that learns the pattern of dependence from observed inputs and thereby induces a hierarchical representation of these inputs specifically we propose that inputs are generated by gaussian variables modeling local filter structure multiplied by a mixer variable that is assigned probabilistically to each input from a set of possible mixers we demonstrate inference of both components of the generative model for synthesized data and for different classes of natural images such as a generic ensemble and faces for natural images the mixer variable assignments show invariances resembling those of complex cells in visual cortex the statistics of the gaussian components of the model are in accord with the outputs of divisive normalization models we also show how our model helps interrelate a wide range of models of image statistics and cortical processing

a new image representation algorithm inspired by image submodality models redundancy reduction and learning in biological vision we develop a new biologically motivated algorithm for representing natural images using successive projections into complementary subspaces an image is first projected into an edge subspace spanned using an ica basis adapted to natural images which captures the sharp features of an image like edges and curves the residual image obtained after extraction of the sharp image features is approximated using a mixture of probabilistic principal component analyzers mppca model the model is consistent with cellular functional information theoretic and learning paradigms in visual pathway modeling we demonstrate the efficiency of our model for representing different attributes of natural images like color and luminance we compare the performance of our model in terms of quality of representation against commonly used basis like the discrete cosine transform dct independent component analysts ica and principal components analysis pca based on their entropies chrominance and luminance components of images are represented using codes having lower entropy than dct ica or pca for similar visual quality the model attains considerable simplification for learning from images by using a sparse independent code for representing edges and explicitly evaluating probabilities in the residual subspace

a hierarchical bayesian model for learning nonlinear statistical regularities in nonstationary natural signals capturing statistical regularities in complex high dimensional data is an important problem in machine learning and signal processing models such as principal component analysis pca and independent component analysis ica make few assumptions about the structure in the data and have good scaling properties but they are limited to representing linear statistical regularities and assume that the distribution of the data is stationary for many natural complex signals the latent variables often exhibit residual dependencies as well as nonstationary statistics here we present a hierarchical bayesian model that is able to capture higher order nonlinear structure and represent nonstationary data distributions the model is a generalization of ica in which the basis function coefficients are no longer assumed to be independent instead the dependencies in their magnitudes are captured by a set of density components each density component describes a common pattern of deviation from the marginal density of the pattern ensemble in different combinations they can describe nonstationary distributions adapting the model to image or audio data yields a nonlinear distributed code for higher order statistical regularities that reflect more abstract invariant properties of the signal

explicit bounds for the finite jet determination problem we introduce biholomorphic invariants for germs of rigid holomorphically nondegenerate real hypersurfaces in complex space and show how they can be used to compute explicit bounds on the order of jets for which biholomorphisms of the hypersurface are determined uniquely by their jets the main result which allows us to derive these bounds is a theorem which shows that solutions of certain singular analytic equations are uniquely determined by their 1 jet

the two dimensional gabor function adapted to natural image statistics a model of simple cell receptive fields and sparse structure in images the two dimensional gabor function is adapted to natural image statistics leading to a tractable probabilistic generative model that can be used to model simple cell receptive field profiles or generate basis functions for sparse coding applications learning is found to be most pronounced in three gabor function parameters representing the size and spatial frequency of the two dimensional gabor function and characterized by a nonuniform probability distribution with heavy tails all three parameters are found to be strongly correlated resulting in a basis of multiscale gabor functions with similar aspect ratios and size dependent spatial frequencies a key finding is that the distribution of receptive field sizes is scale invariant over a wide range of values so there is no characteristic receptive field size selected by natural image statistics the gabor function aspect ratio is found to be approximately conserved by the learning rules and is therefore not well determined by natural image statistics this allows for three distinct solutions a basis of gabor functions with sharp orientation resolution at the expense of spatial frequency resolution a basis of gabor functions with sharp spatial frequency resolution at the expense of orientation resolution or a basis with unit aspect ratio arbitrary mixtures of all three cases are also possible two parameters controlling the shape of the marginal distributions in a probabilistic generative model fully account for all three solutions the best performing probabilistic generative model for sparse coding applications is found to be a gaussian copula with pareto marginal probability density functions

simple modification of oja rule limits l1 norm of weight vector and leads to sparse connectivity this letter describes a simple modification of the oja learning rule which asymptotically constrains the l1 norm of an input weight vector instead of the l2 norm as in the original rule this constraining is local as opposed to commonly used instant normalizations which require the knowledge of all input weights of a neuron to update each one of them individually the proposed rule converges to a weight vector that is sparser has more zero weights than the vector learned by the original oja rule with or without the zero bound which could explain the developmental synaptic pruning

learning slowness in a sparse model of invariant feature detection primary visual cortical complex cells are thought to serve as invariant feature detectors and to provide input to higher cortical areas we propose a single model for learning the connectivity required by complex cells that integrates two factors that have been hypothesized to play a role in the development of invariant feature detectors temporal slowness and sparsity this model the generative adaptive subspace self organizing map gassom extends kohonen s adaptive subspace self organizing map assom with a generative model of the input each observation is assumed to be generated by one among many nodes in the network each being associated with a different subspace in the space of all observations the generating nodes evolve according to a first order markov chain and generate inputs that lie close to the associated subspace this model differs from prior approaches in that temporal slowness is not an externally imposed criterion to be maximized during learning but rather an emergent property of the model structure as it seeks a good model of the input statistics unlike the assom the gassom does not require an explicit segmentation of the input training vectors into separate episodes this enables us to apply this model to an unlabeled naturalistic image sequence generated by a realistic eye movement model we show that the emergence of temporal slowness within the model improves the invariance of feature detectors trained on this input

learning intermediate level representations of form and motion from natural movies we present a model of intermediate level visual representation that is based on learning invariances from movies of the natural environment the model is composed of two stages of processing an early feature representation layer and a second layer in which invariances are explicitly represented invariances are learned as the result of factoring apart the temporally stable and dynamic components embedded in the early feature representation the structure contained in these components is made explicit in the activities of second layer units that capture invariances in both form and motion when trained on natural movies the first layer produces a factorization or separation of image content into a temporally persistent part representing local edge structure and a dynamic part representing local motion structure consistent with known response properties in early visual cortex area v1 this factorization linearizes statistical dependencies among the first layer units making them learnable by the second layer the second layer units are split into two populations according to the factorization in the first layer the form selective units receive their input from the temporally persistent part local edge structure and after training result in a diverse set of higher order shape features consisting of extended contours multiscale edges textures and texture boundaries the motion selective units receive their input from the dynamic part local motion structure and after training result in a representation of image translation over different spatial scales and directions in addition to more complex deformations these representations provide a rich description of dynamic natural images and testable hypotheses regarding intermediate level representation in visual cortex

beyond independent components trees and clusters we present a generalization of independent component analysis ica where instead of looking for a linear transform that makes the data components independent we look for a transform that makes the data components well fit by a tree structured graphical model this tree dependent component analysis tca provides a tractable and flexible approach to weakening the assumption of independence in ica in particular tca allows the underlying graph to have multiple connected components and thus the method is able to find clusters of components such that components are dependent within a cluster and independent between clusters finally we make use of a notion of graphical models for time series due to brillinger 1996 to extend these ideas to the temporal setting in particular we are able to fit models that incorporate tree structured dependencies among multiple time series

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

mappings of real algebraic hypersurfaces a holomorphic function h z defined in a neighborhood of a point z0 e cn is algebraic if there are polynomials qj z j 0 k not all identically zero such that qk z h z k qo z 0 a holomorphic mapping is algebraic if all its components are algebraic a smooth real hypersurface m in cn is algebraic if it is contained in the zero set of a nontrivial real valued polynomial in z and z we assume throughout this paper that n 1 in wi webster proved the following celebrated result if m and m are algebraic hypersurfaces in cn with nondegenerate levi forms and if h is a biholomorphism defined in an open neighborhood of m and mapping m into m then h is algebraic previously it had long been known that if m and m are open subsets of spheres then the components of h are in fact rational functions poincare p tanaka t in this paper we go a step further and give a complete characterization of algebraic hypersurfaces in cn such that any holomorphic mapping with nonvanishing jacobian determinant between two such hypersurfaces must be algebraic our main result is stated in theorem 1 below n by a germ at p0 of a holomorphic vector field in c we shall mean a

suprathreshold stochastic resonance in neural processing tuned by correlation suprathreshold stochastic resonance ssr is examined in the context of integrate and fire neurons with an emphasis on the role of correlation in the neuronal firing we employed a model based on a network of spiking neurons which received synaptic inputs modeled by poisson processes stimulated by a stepped input signal the smoothed ensemble firing rate provided an output signal and the mutual information between this signal and the input was calculated for networks with different noise levels and different numbers of neurons it was found that an ssr effect was present in this context we then examined a more biophysically plausible scenario where the noise was not controlled directly but instead was tuned by the correlation between the inputs the ssr effect remained present in this scenario with nonzero noise providing improved information transmission and it was found that negative correlation between the inputs was optimal finally an examination of ssr in the context of this model revealed its connection with more traditional stochastic resonance and showed a trade off between supratheshold and subthreshold components we discuss these results in the context of existing empirical evidence concerning correlations in neuronal firing

parametrization of local cr automorphisms by finite jets and applications the goal of this work is to study the structure of the group of all local realanalytic cr automorphisms of a germ of a real analytic hypersurface m p in c or equivalently of all local biholomorphisms h c p c p mapping the germ m p into itself we also deal with the more general situation of a realanalytic cr manifold of arbitrary codimension see 2 for every fixed point p m we refer to this group of local biholomorphisms as the stability group of m p and denote it by aut m p endowed with the topology of uniform convergence on compact neighbourhoods of p it becomes a topological group this natural inductive limit topology can be described in the following way a sequence of germs of biholomorphisms hj aut m p converges to another such germ h aut m p if there exists a neighbourhood u of p in c to which all mappings hj extend holomorphically and such that hj h uniformly on u this group arises in a variety of different circumstances one of the most important ones where it naturally appears is the biholomorphic equivalence problem which consists in deciding whether two given germs of real analytic hypersurfaces are biholomorphically equivalent the biholomorphic equivalence problem has been studied since the beginning of the last century when poincare 37 observed probably for the first time that two real hypersurfaces in c for n 2 are not necessarily locally equivalent via a holomorphic transformation though they are via a c transformation today the biholomorphic equivalence problem for strongly pseudoconvex or levi nondegenerate hypersurfaces is pretty well understood based on the works of e cartan 14 15 in dimension two and the results of tanaka 42 and chern moser 17 in arbitrary dimension thanks to the works initiated in the 1970s a number of remarkable properties of the stability group of strongly pseudoconvex real analytic hypersurfaces have been discovered see e g the surveys by vitushkin 45 huang 30 and baouendi ebenfelt and rothschild 5 for complete discussions on this matter these properties depend on whether the germ m p can be biholomorphically mapped onto a piece of the unit sphere if there exists such a biholomorphism one says that m p is spherical for instance if m p is not spherical the group aut m p is

infinite hidden markov models for unusual event detection in video we address the problem of unusual event detection in a video sequence invariant subspace analysis isa is used to extract features from the video and the time evolving properties of these features are modeled via an infinite hidden markov model ihmm which is trained using ldquonormalrdquo ldquotypicalrdquo video the ihmm retains a full posterior density function on all model parameters including the number of underlying hmm states anomalies unusual events are detected subsequently if a low likelihood is observed when associated sequential features are submitted to the trained ihmm a hierarchical dirichlet process framework is employed in the formulation of the ihmm the evaluation of posterior distributions for the ihmm is achieved in two ways via markov chain monte carlo and using a variational bayes formulation comparisons are made to modeling based on conventional maximum likelihood based hmms as well as to dirichlet process based gaussian mixture models

simultaneous estimation of nongaussian components and their correlation structure the statistical dependencies that independent component analysis ica cannot remove often provide rich information beyond the linear independent components it would thus be very useful to estimate the dependency structure from data while such models have been proposed they have usually concentrated on higher order correlations such as energy square correlations yet linear correlations are a fundamental and informative form of dependency in many real data sets linear correlations are usually completely removed by ica and related methods so they can only be analyzed by developing new methods that explicitly allow for linearly correlated components in this article we propose a probabilistic model of linear nongaussian components that are allowed to have both linear and energy correlations the precision matrix of the linear components is assumed to be randomly generated by a higher order process and explicitly parameterized by a parameter matrix the estimation of the parameter matrix is shown to be particularly simple because using score matching hyvarinen 2005 the objective function is a quadratic form using simulations with artificial data we demonstrate that the proposed method improves the identifiability of nongaussian components by simultaneously learning their correlation structure applications on simulated complex cells with natural image input as well as spectrograms of natural audio data show that the method finds new kinds of dependencies between the components

the cancellation theorem for projective modules over irrational rotation c algebras on montre que deux modules projectifs sur a qui sont isomorphes de facon stable sont en fait isomorphes

topographic independent component analysis in ordinary independent component analysis the components are assumed to be completely independent and they do not necessarily have any meaningful order relationships in practice however the estimated independent components are often not at all independent we propose that this residual dependence structure could be used to define a topographic order for the components in particular a distance between two components could be defined using their higher order correlations and this distance could be used to create a topographic representation thus we obtain a linear decomposition into approximately independent components where the dependence of two components is approximated by the proximity of the components in the topographic representation

recovery of sparse translation invariant signals with continuous basis pursuit we consider the problem of decomposing a signal into a linear combination of features each a continuously translated version of one of a small set of elementary features although these constituents are drawn from a continuous family most current signal decomposition methods rely on a finite dictionary of discrete examples selected from this family e g shifted copies of a set of basic waveforms and apply sparse optimization methods to select and solve for the relevant coefficients here we generate a dictionary that includes auxiliary interpolation functions that approximate translates of features via adjustment of their coefficients we formulate a constrained convex optimization problem in which the full set of dictionary coefficients represents a linear approximation of the signal the auxiliary coefficients are constrained so as to only represent translated features and sparsity is imposed on the primary coefficients using an l1 penalty the basis pursuit denoising bp method may be seen as a special case in which the auxiliary interpolation functions are omitted and we thus refer to our methodology as continuous basis pursuit cbp we develop two implementations of cbp for a one dimensional translation invariant source one using a first order taylor approximation and another using a form of trigonometric spline we examine the tradeoff between sparsity and signal reconstruction accuracy in these methods demonstrating empirically that trigonometric cbp substantially outperforms taylor cbp which in turn offers substantial gains over ordinary bp in addition the cbp bases can generally achieve equally good or better approximations with much coarser sampling than bp leading to a reduction in dictionary dimensionality

determination of formal cr mappings by a finite jet abstract we prove that if m is a connected real analytic holomorphically nondegenerate hypersurface in c n 1 then for any point p m there exists an integer k such that any two germs at p of local biholomorphic mappings h 1 h 2 c n 1 p c n 1 p that send m into itself and whose k jets agree at p are identical the above is a special case of a more general theorem stated for formal hypersurfaces that gives a finite jet determination result for the class of formal mappings whose jacobian determinant does not vanish identically

an adaptive method for subband decomposition ica subband decomposition ica sdica an extension of ica assumes that each source is represented as the sum of some independent subcomponents and dependent subcomponents which have different frequency bands in this article we first investigate the feasibility of separating the sdica mixture in an adaptive manner second we develop an adaptive method for sdica namely band selective ica bs ica which finds the mixing matrix and the estimate of the source independent subcomponents this method is based on the minimization of the mutual information between outputs some practical issues are discussed for better applicability a scheme to avoid the high dimensional score function difference is given third we investigate one form of the overcomplete ica problems with sources having specific frequency characteristics which bs ica can also be used to solve experimental results illustrate the success of the proposed method for solving both sdica and the overcomplete ica problems