fast dimension reduction for document classification based on imprecise spectrum analysis latent semantic indexing lsi with singular value decomposition svd is an effective dimension reduction method for document classification and other information analysis tasks the computational overhead of svd is known to be a bottleneck in dealing with large data sets and faster dimension reduction with competitive accuracy is desired in such a setting this paper presents imprecise spectrum analysis isa to carry out fast dimension reduction for document classification isa follows the one sided jacobi method for computing svd and simplifies its intensive orthogonality computation it uses a representative matrix composed of top k column vectors derived from the original feature vector space and reduces the dimension of a feature vector by computing its product with this representative matrix the paper provides an analysis to show the approximation error and the rationale behind such a dimension reduction method to further improve classification accuracy this paper also presents a feature selection method in building the initial feature matrix and augments the representative matrix by including centroid vectors our extensive experimental results show that isa is fast in handling large term document feature matrices while delivering better or competitive classification accuracy for the tested benchmarks compared to lsi with svd

the spectrum of operators elliptic along the orbits of ℝ n actions it is shown that a periodic elliptic operator on n has no eigenvalues off of the set of discontinuities of its spectral density function the methods involve operator algebras and are based on a spectral duality principal first introduced by j bellisard and d testard a version of the spectral duality theorem is proved which relates the point spectrum of a certain family of operators to the continuous spectrum of an associated family

dimensionality reduction by feature clustering for regression problems one of the issues encountered in classification and regression is the processing inefficiency caused by a large number of input dimensions involved in the given training data set many dimensionality reduction approaches have been proposed to address this issue by reducing the number of input dimensions and maintaining the generalization capability of the original data set however less attention has been paid to regression than to classification besides the computation with covariance matrices involved results in an inefficient reduction process in most existing methods in this paper we propose a machine learning based dimensionality reduction approach for regression problems for a given set of training instances a group of clusters are formed such that the instances included in the same cluster are similar to each other then one new feature is extracted from each cluster through a certain weighted combination of the training instances consequently the dimensionality of the original data set is reduced the clusters are created incrementally and automatically without the need of specifying the number of clusters in advance by the user the characteristics of the original data set are substantially retained since all the original features are involved in the derivation of the extracted features also the computation with covariance matrices is avoided and thus efficiency is maintained a number of experiments on real world data sets are conducted to demonstrate the effectiveness of the proposed approach

feature selection using structural similarity a new method of feature selection is developed based on structural similarity the topological neighborhood information about pairs of objects or patterns to partition s is taken into consideration while computing a measure of structural similarity this is termed proximity and is defined in terms of membership values multi objective evolutionary optimization is employed to arrive at a consensus solution in terms of the contradictory criteria pair involving fuzzy proximity and feature set cardinality results for real and synthetic datasets of low medium and high dimensionality show that the method led to a correct selection of the reduced feature subset comparative study is also provided and quantified in terms of accuracy of classification and clustering validity indices

the floquet theory and the state density of quasi periodic schrodinger operators abstract we study the floquet solutions of quasi periodic schrodinger operators on flows which satisfy a diophantine condition using these solutions we show that the resolvent of such an operator is smooth with respect to certain derivations in the c algebra associated with the flow and that every projection corresponding to a spectral gap has a finite localization length based on these results we derive a formula which quantizes the integral components of the integrated density of states for the operator on each spectral gap

on the approximability of minimizing nonzero variables or unsatisfied relations in linear systems we investigate the computational complexity of two closely related classes of combinatorial optimization problems for linear systems which arise in various fields such as machine learning operations research and pattern recognition in the first class min ulr one wishes given a possibly infeasible system of linear relations to find a solution that violates as few relations as possible while satisfying all the others in the second class min rvls the linear system is supposed to be feasible and one looks for a solution with as few nonzero variables as possible for both min ulr and min rvls the four basic types of relational operators and are considered while min rvls with equations was mentioned to be np hard in garey and johnson 1979 we established in amaldi 1992 amaldi and kann 1995 that min ulr with equalities and inequalities are np hard even when restricted to homogeneous systems with bipolar coefficients the latter problems have been shown hard to approximate in arora et al 1993 in this paper we determine strong bounds on the approximability of various variants of min rvls and min ulr including constrained ones where the variables are restricted to take binary values or where some relations are mandatory while others are optional the various np hard versions turn out to have different approximability properties depending on the type of relations and the additional constraints but none of them can be approximated within any constant factor unless p np particular attention is devoted to two interesting special cases that occur in discriminant analysis and machine learning in particular we disprove a conjecture of van horn and martinez 1992 regarding the existence of a polynomial time algorithm to design linear classifiers or perceptrons that involve a close to minimum number of features

silhouettes a graphical aid to the interpretation and validation of cluster analysis a new graphical display is proposed for partitioning techniques each cluster is represented by a so called silhouette which is based on the comparison of its tightness and separation this silhouette shows which objects lie well within their cluster and which ones are merely somewhere in between clusters the entire clustering is displayed by combining the silhouettes into a single plot allowing an appreciation of the relative quality of the clusters and an overview of the data configuration the average silhouette width provides an evaluation of clustering validity and might be used to select an appropriate number of clusters

the rotation number for almost periodic potentials we define and analyze the rotation number for the almost periodic schrodinger operatorl d2 dx2 q x we use the rotation number to discuss i the spectrum ofl ii its relation to the korteweg de vries equation

combining dissimilarity spaces for text categorization text categorization systems are designed to classify documents into a fixed number of predefined categories bag of words is one of the most used approaches to represent a document however it generates high dimensional sparse data matrix with a high feature to instance ratio an aggressive feature selection can alleviate these drawbacks but such selection degrades the classifiers performance in this paper we propose an approach for text categorization based on dissimilarity representation and multiple classifier systems the proposed system combined dissimilarity spaces codis is composed of multiple classifiers trained on data from different dissimilarity spaces each dissimilarity space is a transformation of the original space that reduces the dimensionality feature to instance ratio and sparseness experiments using forty seven text categorization databases show that codis presents a better performance in comparison to literature systems

nested structure in parameterized rough reduction abstract in this paper by strict mathematical reasoning we discover the relationship between the parameters and the reducts in parameterized rough reduction this relationship named the nested reduction shows that the reducts act as a nested structure with the monotonically increasing parameter we present a systematic theoretical framework that provides some basic principles for constructing the nested structure in parameterized rough reduction some specific parameterized rough set models in which the nested reduction can be constructed are pointed out by strict mathematical reasoning based on the nested reduction we design several quick algorithms to find a different reduct when one reduct is already given here different refers to the reducts obtained on the different parameters all these algorithms are helpful for quickly finding a proper reduct in the parameterized rough set models the numerical experiments demonstrate the feasibility and the effectiveness of the nested reduction approach

a fast feature weighting algorithm of data gravitation classification the data gravitation classification dgc model is a new classification method that has gained great research interest in recent years feature weights are the key parameters in dgc models because the classification performances of these models are very sensitive to such feature weights the available dgc models use wrapper like algorithms to obtain their optimised feature weights although such algorithms produce high classification accuracies but they contribute to the high computational complexities of the dgc models in this study we propose a fast feature weight algorithm for dgc models called ffw dgc we use the concepts of feature discrimination and redundancy to measure the importance of a feature after which two fuzzy subsets are constructed to respectively represent these concepts next we combine the two fuzzy subsets to compute the feature weights used in gravitational computing we conduct our experiments on 25 standard data sets and 22 imbalance data sets and compare ffw dgc with 11 kinds of classifiers including the swarm intelligence based dgc pso dgc model competitive results of ffw dgc demonstrate that it can obtain high classification accuracies but also hundreds of times of speedup ratios compared with pso dgc

how to tune the system parameters to realize stochastic resonance the paper presents a numerical method of realizing stochastic resonance sr by tuning system parameters firstly a simple and effective method of evaluating the system response speed 1 is introduced then the parameter induced sr problem can be reduced to the parameter optimization problem under the condition 1 const to solve this optimization problem we put forward the following techniques i compensate the deviation from the prescribed system response speed 1 at each step ii take the curve length increment on the parameter plane as the step size in searching the maximal signal to noise ratio snr gain finally a numerical simulation confirms the effectiveness of this method

unsupervised clustering and feature weighting based on generalized dirichlet mixture modeling abstract we propose a possibilistic approach for generalized dirichlet mixture parameter estimation data clustering and feature weighting the proposed algorithm called robust and unsupervised learning of finite generalized dirichlet mixture models rule gdm exploits a property of the generalized dirichlet distributions that transforms the data to make the features independent and follow beta distributions then it learns optimal relevance weights for each feature within each cluster this property makes rule gdm suitable for noisy and high dimensional feature spaces in addition rule gdm associates two types of memberships with each data sample the first one is the posterior probability and indicates how well a sample fits each estimated distribution the second membership represents the degree of typicality and is used to identify and discard noise points and outliers rule gdm minimizes one objective function which combines learning the two membership functions distribution parameters and the relevance weights for each feature within each distribution we also extend our algorithm to find the optimal number of clusters in an unsupervised and efficient way by exploiting some properties of the possibilistic membership function the performance of rule gdm is illustrated and compared to similar algorithms we use synthetic data to illustrate its robustness to noisy and high dimensional features we also compare our approach to other relevant algorithms using several standard data sets

the longitudinal cocycle and the index of toeplitz operators abstract let d be a self adjoint leafwise elliptic operator on a foliated manifold compressing multiplication operators to the range of the positive spectral projection for d yields the class of leafwise toeplitz operators the extension generated by these operators is constructed a topological formula for the index of a toeplitz operator with invertible symbol is given this index can also be obtained by pairing the k theory class of the symbol with a certain cyclic cocycle if one lifts an elliptic operator on a closed manifold to a leafwise elliptic operator on an associated flat foliated principal bundle then this cocycle can be used to obtain refined invariants of the original operator

nature of different types of absorbing states we present a comparison of three different types of langevin equations exhibiting absorbing states the langevin equation defining the reggeon field theory one with multiplicative noise and a third type in which the noise is complex each one is found to describe a different underlying physical mechanism in particular the nature of the different absorbing states depends on the type of noise considered by studying the stationary single site effective potential we analyze the impossibility of finding a reaction diffusion model in the multiplicative noise universality class we also discuss some theoretical questions related to the nature of complex noise as for example whether it is necessary or not to consider a complex equation in order to describe processes as the annihilation reaction a stackrel ensuremath rightarrow a 0

effects of signal spectrum varying on signal processing by parameter induced stochastic resonance abstract the effects of signal spectrum varying on signal processing by the method of parameter induced stochastic resonance psr are investigated for a binary signal with a smooth power spectral density psd when the psd curve becomes sharper and narrower the performance of the nonlinear system via psr is better for a multi frequency signal formed by sine waves with different frequencies the larger the signal spectral density is the lower the ability of the psr system processing signal is and the signal to noise ratio snr gain of the psr system is increased with the increasing height of the spectral line moreover with the method of psr the stochastic signal the combination of sine waves and noise improvement is obvious the results obtained via this method are superior to those with a linear filter

effective markovian approximation for non gaussian noises a path integral approach abstract we have analyzed diffusion in a double well potential driven by a colored non gaussian noise using a path integral approach we have obtained a consistent markovian approximation to the initially non markovian problem such an approximation allows us to get analytical expressions for the mean first passage time that has been tested against extensive numerical simulations

a method for comparing two hierarchical clusterings abstract this article concerns the derivation and use of a measure of similarity between two hierarchical clusterings the measure bk is derived from the matching matrix mij formed by cutting the two hierarchical trees and counting the number of matching entries in the k clusters in each tree the mean and variance of bk are determined under the assumption that the margins of mij are fixed thus bk represents a collection of measures for k 2 n 1 k bk plots are found to be useful in portraying the similarity of two clusterings bk is compared to other measures of similarity proposed respectively by baker 1974 and rand 1971 the use of k bk plots for studying clustering methods is explored by a series of monte carlo sampling experiments an example of the use of k bk on real data is given

a nonlinear oscillator with parametric coloured noise some analytical results the asymptotic behaviour of a nonlinear oscillator subject to a multiplicative ornstein uhlenbeck noise is investigated when the dynamics is expressed in terms of energy angle coordinates it is observed that the angle is a fast variable as compared to the energy thus an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out however the standard elimination procedure performed earlier for a gaussian white noise fails when the noise is coloured because of correlations between the noise and the fast angular variable we develop here a specific averaging scheme that retains these correlations this allows us to calculate the probability distribution function pdf of the system and to derive the behaviour of physical observables in the long time limit

geometric invariants of the quantum hall effect we study the two dimensional hall effect with a random potential the hall conductivity is identified as a geometric invariant associated with an algebra of observables using the pairing betweenk theory and cyclic cohomology theory we identify this geometric invariant with a topological index thereby giving the hall conductivity a new interpretation

feature selection for clustering using instance based learning by exploring the nearest and farthest neighbors feature selection for clustering is an active research topic and is used to identify salient features that are helpful for data clustering while partitioning a dataset into clusters a data instance and its nearest neighbors will belong to the same cluster and this instance and its farthest neighbors will belong to different clusters we propose a new feature selection method to identify salient features that are useful for maintaining the instance s nearest neighbors and farthest neighbors referred to here as fsnf in particular fsnf uses the mutual information criterion to estimate feature salience by considering maintainability experiments on benchmark datasets demonstrate the effectiveness of fsnf within the context of cluster analysis

feature subset selection and ranking for data dimensionality reduction a new unsupervised forward orthogonal search fos algorithm is introduced for feature selection and ranking in the new algorithm features are selected in a stepwise way one at a time by estimating the capability of each specified candidate feature subset to represent the overall features in the measurement space a squared correlation function is employed as the criterion to measure the dependency between features and this makes the new algorithm easy to implement the forward orthogonalization strategy which combines good effectiveness with high efficiency enables the new algorithm to produce efficient feature subsets with a clear physical interpretation

on the spectra of schrodinger operators we give two formulas for the lowest point open image in new window in the spectrum of the schrodinger operatorl d dt p d dt q where the coefficientsp andq are real valued bounded uniformly continuous functions on the real line we determine whether or not open image in new window is an eigenvalue forl in terms of a set of probability measures on the maximal ideal space of thec algebra generated by the translations ofp andq

phase diagram of the random frequency oscillator the case of ornstein uhlenbeck noise abstract we study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an ornstein uhlenbeck noise this system undergoes a noise induced bifurcation when the amplitude of the noise grows the critical curve that separates the absorbing phase from an extended non equilibrium steady state corresponds to the vanishing of the lyapunov exponent that measures the asymptotic logarithmic growth rate of the energy we derive various expressions for this lyapunov exponent by using different approximation schemes this allows us to study quantitatively the phase diagram of the random parametric oscillator

a generalized spectral duality theorem we establish a version of the spectral duality theorem relating the point spectrum of a family of representations of a certain covariance algebra to the continuous spectrum of an associated family of representations using that version we prove that almost all the images of any element of a certain space of fixed points of some automorphism of an irrational rotation algebra via standard representations of the algebra inl2 do not have pure point spectrum over any non empty open subset of the common spectrum of those images as another application of the spectral duality theorem we prove that if almost all the bloch operators associated with a real almost periodic function on have pure point spectrum over a borel subset of then almost all the schrodinger operators with potentials belonging to the compact hull of the translates of this function have over the same set purely continuous spectrum

path integral solution of the system with coloured multiplicative noise the behaviour of most probable values of the order parameter x and the amplitude of the conjugate force fluctuations is studied for a stochastic system with a coloured multiplicative noise and absorbing state the phase diagrams introduced as dependencies of the noise self correlation time vs temperature and noise growth velocity are defined it is shown that phase plane x is divided into isolated domains of large intermediate and small values of x the behaviour of the system in these domains is studied in terms of the path integral in the region x 1 the trajectories converge to the point x 0 at 0 a 12 and to x 0 at 12 a 1 in the former case the probability of realization of trajectories is finite while in the latter case it is vanishing small and an absorbing state can be formed

aperiodic stochastic resonance stochastic resonance sr is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular level of noise recently we presented a method and theory for characterizing sr type behavior in excitable systems with aperiodic i e broadband input signals phys rev e 52 r3321 1995 we coined the term aperiodic stochastic resonance asr to describe this general type of behavior in that earlier study we demonstrated asr in the fitzhugh nagumo neuronal model here we demonstrate asr in three additional systems a bistable well system an integrate and fire neuronal model and the hodgkin huxley hh neuronal model we present computational and theoretical results for each system in the context of the hh model we develop a general theory for asr in excitable membranes this work clearly shows that sr type behavior is not limited to systems with periodic inputs thus in general noise can serve to enhance the response of a nonlinear system to a weak input signal regardless of whether the signal is periodic or aperiodic textcopyright 1996 the american physical society

hybridising harmony search with a markov blanket for gene selection problems gene selection which is a well known np hard problem is a challenging task that has been the subject of a large amount of research especially in relation to classification tasks this problem addresses the identification of the smallest possible set of genes that could achieve good predictive performance many gene selection algorithms have been proposed however because the search space increases exponentially with the number of genes finding the best possible approach for a solution that would limit the search space is crucial metaheuristic approaches have the ability to discover a promising area without exploring the whole solution space hence we propose a new method that hybridises the harmony search algorithm hsa and the markov blanket mb called hsa mb for gene selection in classification problems in this proposed approach the hsa as a wrapper approach improvises a new harmony that is passed to the mb treated as a filter approach for further improvement the addition and deletion of operators based on gene ranking information is used in the mb algorithm to further improve the harmony and to fine tune the search space the hsa mb algorithm method works especially well on selected genes with higher correlation coefficients based on symmetrical uncertainty ten microarray datasets were experimented on and the results demonstrate that the hsa mb has a performance that is comparable to state of the art approaches hsa mb yields very small sets of genes while preserving the classification accuracy the results suggest that hsa mb has a high potential for being an alternative method of gene selection when applied to microarray data and can be of benefit in clinical practice