a novel validity index with dynamic cut off for determining true clusters in a multi surveillance environment voluminous data is generated over a period of time data analysis for summarization and conclusion has paved a way for the need of an efficient clusterization clustering an unsupervised way of learning about data aims at defining clusters validation of clusters formed indicates the trueness of the clusters in this paper a novel validation technique with dynamic termination of clustering process has been proposed to obtain true clusters in the validation process the validity index is based on both global cluster proximity relationship and local proximity relationship the validity index is computed for validating the available clusters using within cluster sum of squares between cluster sum of squares total sum of squares intra cluster distances and inter cluster distances the ratio between two consecutive validity indices is the extent of variation which specifies the cut off point cut off terminates the clustering process dynamically indicating the number of clusters and validates the obtained clusters the proposed method is tested on several real and synthetic data sets comparisons with the existing methods demonstrate the efficiency of the proposed method in detecting true clusters a novel validation technique has been proposed to obtain true clusters the method dynamically terminates the clustering at true conception of clusters global and local proximity relationship of clusters are considered for validation

a particle swarm optimization based simultaneous learning framework for clustering and classification a particle swarm optimization based simultaneous learning framework for clustering and classification psoslcc is proposed in this paper firstly an improved particle swarm optimization pso is used to partition the training samples the number of clusters must be given in advance an automatic clustering algorithm rather than the trial and error is adopted to find the proper number of clusters and a set of clustering centers is obtained to form classification mechanism secondly in order to exploit more useful local information and get a better optimizing result a global factor is introduced to the update strategy update strategy of particle in pso psoslcc has been extensively compared with fuzzy relational classifier frc vector quantization and learning vector quantization vq lvq3 and radial basis function neural network rbfnn a simultaneous learning framework for clustering and classification scc over several real life datasets the experimental results indicate that the proposed algorithm not only greatly reduces the time complexity but also obtains better classification accuracy for most datasets used in this paper moreover psoslcc is applied to a real world application namely texture image segmentation with a good performance obtained which shows that the proposed algorithm has a potential of classifying the problems with large scale a particle swarm optimization based simultaneous learning framework for clustering and classification psoslcc is proposed the simultaneous frame consists of two parts clustering section and classification section an automatic clustering algorithm is used to find the proper number of clusters an improved particle swarm optimization with a global factor is used in the training phase the performance of psoslcc has been extensively compared with four state of the art classification algorithms over a test suit of datasets and texture image segmentation

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

on principal hessian directions for data visualization and dimension reduction another application of stein s lemma abstract modern graphical tools have enhanced our ability to learn many things from data directly with much user friendly graphical software available we are encouraged to plot a lot more often than before the benefits from direct interaction with graphics have been enormous but trailing behind these high tech advances is the issue of appropriate guidance on what to plot there are too many directions to project a high dimensional data set and unguided plotting can be time consuming and fruitless in a recent article li set up a statistical framework for study on this issue based on a notion of effective dimension reduction edr directions they are the directions to project a high dimensional input variable for the purpose of effectively viewing and studying its relationship with an output variable a methodology sliced inverse regression was introduced and shown to be useful in finding edr directions this article introduces another method for finding edr directions it begins with the observat

extremal solutions of φ laplacian diffusion scalar problems with nonlinear functional boundary conditions in a unified way abstract the aim of this paper is to ensure the existence of extremal solutions lying between a pair of lower and upper solutions for a second order differential equation that includes both the laplacian and some classes diffusion equations the results hold from a suitable change of variables an example is given to expose the applicability of the obtained results

gain scheduled and nonlinear systems dynamic analysis by velocity based linearization families a family of velocity based linearizations is proposed for a nonlinear system in contrast to the conventional series expansion linearization a member of the family of velocity based linearizations is valid in the vicinity of any operating point not just an equilibrium operating point the velocity based linearizations facilitate dynamic analysis far from the equilibrium operating points and enable the transient behaviour of the nonlinear system to be investigated using velocity based linearizations stability conditions are derived for both smooth and non smooth nonlinear systems which avoid the restrictions to trajectories lying within an unnecessarily perhaps excessively small neighbourhood about the equilibrium operating points inherent in existing frozen input theory for systems where there is no restriction on the rate of variation the velocity based linearization analysis is global in nature the analysis techniques developed although quite general are motivated by the gain scheduling design

multipath clustering and cluster tracking for geometry based stochastic channel modeling this paper presents a clustering and tracking method that exploits the geometry of the scattering points sps obtained from the measurement based ray tracer the multipath components mpcs were categorized into clusters by applying the kpowermeans kpm framework to those sps the clusters were tracked by comparing the cluster centroid sps of the adjacent snapshots the clusters were estimated based on the indoor environment geometry at 11 ghz and their physical mechanisms were interpreted the complexity and performance of this method was assessed and compared with that of conventional kpm by comparing the number of floating point operations flops and the channel eigenvalues obtained from the reconstructed channel matrices which were calculated by superposing the mpcs randomly generated from intracluster parameters the verification of this method showed that most clusters were estimated and tracked according to the physical location of the scatterers in the environment with acceptable error moreover the eigenvalues reconstructed from the proposed method were closer to the measured ones with less number of flops which indicates both accuracy and complexity improvement the results also imply that multiple input multiple output performance is highly dependent on the radio propagation channel therefore it is imperative that clusters in the channel be determined accurately

solving the small sample size problem in face recognition using generalized discriminant analysis the goal of face recognition is to distinguish persons via their facial images each person s images form a cluster and a new image is recognized by assigning it to the correct cluster since the images are very high dimensional it is necessary to reduce their dimension linear discriminant analysis lda has been shown to be effective at dimension reduction while preserving the cluster structure of the data it is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters the requirement that one of these matrices be nonsingular restricts its application to datasets in which the dimension of the data does not exceed the sample size for face recognition however the dimension typically exceeds the number of images in the database resulting in what is referred to as the small sample size problem recently the applicability of lda has been extended by using the generalized singular value decomposition gsvd to circumvent the nonsingularity requirement thus making lda directly applicable to face recognition data our experiments confirm that lda gsvd solves the small sample size problem very effectively as compared with other current methods

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

implicit nonlinear discontinuous functional boundary value φ laplacian problems extremality results this paper is devoted to the study of the following implicit nonlinear discontinuous functional boundary value problem ip l 0u t f t u l 0u fora e t i a b l 1 u b 1 u l 1 u 0 l 2 u a u b wherel 0u t ddt f t u t u t g t u u t u t andl 1 u l 1 u a u b u a u b u supposing that there is a lower solution a and an upper solution b such that a b the existence of extremal solutions lying between both functions is proved

a new point symmetry based fuzzy genetic clustering technique for automatic evolution of clusters in this paper a fuzzy point symmetry based genetic clustering technique fuzzy vgaps is proposed which can automatically determine the number of clusters present in a data set as well as a good fuzzy partitioning of the data the clusters can be of any size shape or convexity as long as they possess the property of symmetry here the membership values of points to different clusters are computed using the newly proposed point symmetry based distance a variable number of cluster centers are encoded in the chromosomes a new fuzzy symmetry based cluster validity index fsym index is first proposed here and thereafter it is utilized to measure the fitness of the chromosomes the proposed index can detect non convex as well as convex non hyperspherical partitioning with variable number of clusters it is mathematically justified via its relationship to a well defined hard cluster validity function the dunn s index for which the condition of uniqueness has already been established the results of the fuzzy vgaps are compared with those obtained by seven other algorithms including both fuzzy and crisp methods on four artificial and four real life data sets some real life applications of fuzzy vgaps to automatically cluster the gene expression data as well as segmenting the magnetic resonance brain image with multiple sclerosis lesions are also demonstrated

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

automatic clustering using genetic algorithms abstract in face of the clustering problem many clustering methods usually require the designer to provide the number of clusters as input unfortunately the designer has no idea in general about this information beforehand in this article we develop a genetic algorithm based clustering method called automatic genetic clustering for unknown k agcuk in the agcuk algorithm noising selection and division absorption mutation are designed to keep a balance between selection pressure and population diversity in addition the davies bouldin index is employed to measure the validity of clusters experimental results on artificial and real life data sets are given to illustrate the effectiveness of the agcuk algorithm in automatically evolving the number of clusters and providing the clustering partition

maximum relevance minimum common redundancy feature selection for nonlinear data abstract in recent years feature selection based on relevance redundancy trade off criteria has become a very promising and popular approach in the field of machine learning however the existing algorithmic frameworks of mutual information feature selection have certain limitations for the common feature selection problems in practice to overcome these limitations the idea of a new framework is developed by introducing a novel maximum relevance and minimum common redundancy criterion and a minimax nonlinear optimization approach in particular a novel mutual information feature selection method based on the normalization of the maximum relevance and minimum common redundancy n mrmcr mi is presented which produces a normalized value in the range 0 1 and results in a regression problem we perform extensive experimental comparisons over numerous state of art algorithms using different forecasts bayesian additive regression tree treed gaussian process k nn and svm and different data sets two simulated and five real datasets the results show that the proposed algorithm outperforms the others in terms of feature selection and forecasting accuracy

a note on a class of problems for a higher order fully nonlinear equation under one sided nagumo type condition abstract the purpose of this work is to establish existence and location results for the higher order fully nonlinear differential equation u n t f t u t u t u n 1 t n 2 with the boundary conditions u i a a i for i 0 n 3 u n 1 a b u n 1 b c or u i a a i for i 0 n 3 c 1 u n 2 a c 2 u n 1 a b c 3 u n 2 b c 4 u n 1 b c with a i b c r for i 0 n 3 and c 1 c 2 c 3 c 4 real positive constants it is assumed that f a b r n 1 r is a continuous function satisfying one sided nagumo type conditions which allows an asymmetric unbounded behaviour on the nonlinearity the arguments are based on the leray schauder topological degree and lower and upper solutions method

fuzzy bayesian validation for cluster analysis of yeast cell cycle data clustering for the analysis of the genes organizes the patterns into groups by the similarity of the dataset and has been used for identifying the functions of the genes in the cluster and analyzing the functions of unknown genes since the genes usually belong to multiple functional families fuzzy clustering methods are more appropriate than the conventional hard clustering methods which assign a sample to only one group in this paper a bayesian like validation method selecting a fuzzy partition is proposed to evaluate the fuzzy partitions effectively the theoretical interpretation of the obtained memberships is beyond the scope of this paper and an empirical evaluation of the proposed method is conducted by comparing to the four representative conventional fuzzy cluster validity measures in four well known datasets analysis of yeast cell cycle data follows to evaluate the proposed method

a cluster validity index for fuzzy clustering in this paper a cluster validity index proposed by kim et al 15 is analyzed and a problem is discussed that the validity index faces in situations when there are well separated clusters that themselves include subclusters based on this analysis a new validity index is proposed the new validity index employs a compactness measure and a separation measure the compactness measure combines the fuzziness in the membership matrix u with the geometrical compactness of the representation of the data set x via the prototypes v the separation measure is defined as the average value of the degrees of overlap of all possible pairs of fuzzy clusters in the system the proposed index is tested and validated using several data sets the results of the comparison show the superior effectiveness and reliability of the proposed index in comparison to other indices

interval type 2 credibilistic clustering for pattern recognition this paper presents a new approach to interval type 2 fuzzy clustering in order to consider compactness within the clusters and separation of them simultaneously the objective function of this paper is designed such that it generates both degrees of membership and non membership of each data in each cluster and integrates them using credibility concept also a new approach to separation of clusters is proposed and utilized in designing the objective function in this approach the borders of clusters and therefore their compactness contribute in attaining their separation so the separation of clusters is not assessed only by the distance of their centers the credibility degrees are transformed to interval type 2 form to handle different sources of uncertainty finally a new validity index to characterize the number of clusters based on proposed approach to separation of clusters and choquet integrals are proposed the advantages of paper contributions are illustrated using several examples a new objective function based fuzzy clustering is introduced using credibility concept a new approach to separation of clusters is presented a new validity index is designed by proposed approach to separation and choquet integral the obtained results show that proposed model can handle different types of clusters

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

nonlinear second order equations with functional implicit impulses and nonlinear functional boundary conditions abstract in this paper we present existence results for solutions of nonlinear second order boundary value problems with impulses our impulses are applied at p points in the interval and given implicitly by nonlinear functions of the solution moreover we allow functional dependence on the solution our existence results follow from the existence of a pair of well ordered lower and upper solutions we generalize earlier results of cabada and tomec ek allowing more general compatible boundary conditions impulses and laplacian equations

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

nonlinear black box models in system identification mathematical foundations we discuss several aspects of the mathematical foundations of the nonlinear black box identification problem we shall see that the quality of the identification procedure is always a result of a certain trade off between the expressive power of the model we try to identify the larger the number of parameters used to describe the model the more flexible is the approximation and the stochastic error which is proportional to the number of parameters a consequence of this trade off is the simple fact that a good approximation technique can be the basis of a good identification algorithm from this point of view we consider different approximation methods and pay special attention to spatially adaptive approximants we introduce wavelet and neuron approximations and show that they are spatially adaptive then we apply the acquired approximation experience to estimation problems finally we consider some implications of these theoretical developments for the practically implemented versions of the spatially adaptive algorithms

a cluster validity index combining an overlap measure and a separation measure based on fuzzy aggregation operators since a clustering algorithm can produce as many partitions as desired one needs to assess their quality in order to select the partition that most represents the structure in the data if there is any this is the rationale for the cluster validity cv problem and indices this paper presents a cv index that helps to find the optimal number of clusters of data from partitions generated by a fuzzy clustering algorithm such as the fuzzy c means fcm or its derivatives given a fuzzy partition this new index uses a measure of multiple cluster overlap and a separation measure for each data point both based on an aggregation operation of membership degrees experimental results on artificial and benchmark datasets are given to demonstrate the performance of the proposed index as compared with traditional and recent indices

a new and fast implementation for null space based linear discriminant analysis in this paper we present a new implementation for the null space based linear discriminant analysis the main features of our implementation include i the optimal transformation matrix is obtained easily by only orthogonal transformations without computing any eigendecomposition and singular value decomposition svd consequently our new implementation is eigendecomposition free and svd free ii its main computational complexity is from a economic qr factorization of the data matrix and a economic qr factorization of a nxn matrix with column pivoting here n is the sample size thus our new implementation is a fast one the effectiveness of our new implementation is demonstrated by some real world data sets

enhancement of the classification and reconstruction performance of fuzzy c means with refinements of prototypes abstract owning to their abilities to reveal structural relationships in data fuzzy clustering plays a pivotal role in fuzzy modeling pattern recognition and data analysis as supporting an unsupervised mode of learning fuzzy clustering brings about unique opportunities to build a structural backbone of numerous constructs in the areas identified above a follow up phase is required when the structural findings developed in the form of fuzzy clusters need some refinements usually when the clustering results are used afterwards in the model being developed in a supervised mode following this general line of thought in this study we propose a novel approach to optimize the clustering and classification performance of the fuzzy c means fcm algorithm proceeding with a collection of clusters information granules produced by the fcm we carry out the refinements of the results in order to improve the representation or classification capabilities of fuzzy clusters by adjusting a location of the prototypes so that a certain performance index becomes optimized at this phase the optimization is carried out in a supervised mode with the aid of differential evolution de we propose five different strategies to adjust a location of the prototypes experimental studies completed on synthetic data and publicly available real world data quantify the improvement of the representation and classification abilities of the clustering method

on singular functional nonsmooth and implicit phi laplacian initial and boundary value problems in this paper we apply fixed point results for mappings in partially ordered spaces to derive existence results for extremal solutions of phi laplacian initial and boundary value problems the considered problems can be singular functional discontinuous nonlocal and implicit concrete examples are also solved

a novel cluster validity index for fuzzy clustering based on bipartite modularity a novel cluster validity index whose implementation is based on the membership degrees and improved bipartite modularity of bipartite network is proposed for the validation of partitions produced by the fuzzy c means fcm algorithm fcm algorithm is employed to group the dataset in order to obtain the membership degree of samples then a weighted bipartite network is constructed by samples and centroids of each cluster this allows the introduction of a new measurement for optimizing the numbers of clusters for fuzzy partitions the proposed index utilizes the optimum membership as its global property and the modularity of bipartite network as its local independent property the proposed index is compared with a number of popular validation indices on fifteen datasets the experimental results show that the effectiveness and reliability of the proposal is superior to other indices

the generalized c index for internal fuzzy cluster validity the c index is an internal cluster validity index that was introduced in 1970 as a way to define and identify a best crisp partition on n objects represented by either unlabeled feature vectors or dissimilarity matrix data this index is often one of the better performers among the plethora of internal indices available for this task this paper develops a soft generalization of the c index that can be used to evaluate sets of candidate partitions found by either fuzzy or probabilistic clustering algorithms we define four generalizations based on relational transformations of the soft partition and then compare their performance to eight other popular internal fuzzy cluster indices using two methods of comparison internal best c and internal external i e best match six synthetic datasets and six real world labeled datasets our main conclusion is that the sum min generalization is the second best performer in the best c tests and the best performer in the i e tests on small data

a selection model for optimal fuzzy clustering algorithm and number of clusters based on competitive comprehensive fuzzy evaluation fuzzy c means fcm and its variants suffer from two problems local minima and cluster validity which have a direct impact on the formation of final clustering there are two strategies optimization and center initialization strategies that address the problem of local minima this paper proposes a center initialization approach based on a minimum spanning tree to keep fcm from local minima with regard to cluster validity various strategies have been proposed on the basis of the fuzzy cluster validity index this paper proposes a selection model that combines multiple pairs of a fuzzy clustering algorithm and cluster validity index to identify the number of clusters and simultaneously selects the optimal fuzzy clustering for a dataset the promising performance of the proposed center initialization method and selection model is demonstrated by experiments on real datasets

identification of non linear system structure and parameters using regime decomposition abstract an off line algorithm for empirical modeling and identification of non linear dynamic systems is presented the minimal input to the algorithm is a sequence of empirical data and the model order using this information the algorithm searches for an optimal model structure and parameters within a rich non linear model set the model representation is based on the interpolation of a number of simple local models where each local model has a limited range of validity but the local models yield a complete global model when interpolated the method is illustrated using simulated data

mutual information functions versus correlation functions this paper studies one application of mutual information to symbolic sequences the mutual information functionm d this function is compared with the more frequently used correlation function d an exact relation betweenm d and d is derived for binary sequences for sequences with more than two symbols no such general relation exists in particular d 0 may or may not lead tom d 0 this linear but not general independence between symbols separated by a distance is studied for ternary sequences also included is the estimation of the finite size effect on calculating mutual information finally the concept of symbolic noise is discussed

a symmetry based multiobjective clustering technique for automatic evolution of clusters in this paper the problem of automatic clustering a data set is posed as solving a multiobjective optimization moo problem optimizing a set of cluster validity indices simultaneously the proposed multiobjective clustering technique utilizes a recently developed simulated annealing based multiobjective optimization method as the underlying optimization strategy here variable number of cluster centers is encoded in the string the number of clusters present in different strings varies over a range the points are assigned to different clusters based on the newly developed point symmetry based distance rather than the existing euclidean distance two cluster validity indices one based on the euclidean distance xb index and another recently developed point symmetry distance based cluster validity index sym index are optimized simultaneously in order to determine the appropriate number of clusters present in a data set thus the proposed clustering technique is able to detect both the proper number of clusters and the appropriate partitioning from data sets either having hyperspherical clusters or having point symmetric clusters a new semi supervised method is also proposed in the present paper to select a single solution from the final pareto optimal front of the proposed multiobjective clustering technique the efficacy of the proposed algorithm is shown for seven artificial data sets and six real life data sets of varying complexities results are also compared with those obtained by another multiobjective clustering technique mock two single objective genetic algorithm based automatic clustering techniques vgaps clustering and gcuk clustering

face recognition based on the uncorrelated discriminant transformation abstract the extraction of discriminant features is the most fundamental and important problem in face recognition this paper presents a method to extract optimal discriminant features for face images by using the uncorrelated discriminant transformation and kl expansion experiments on the orl database and the nust603 database have been performed experimental results show that the uncorrelated discriminant transformation is superior to the foley sammon discriminant transformation and the new method to extract uncorrelated discriminant features for face images is very effective an error rate of 2 5 is obtained with the experiments on the orl database an average error rate of 1 2 is obtained with the experiments on the nust603 database experiments show that by extracting uncorrelated discriminant features face recognition could be performed with higher accuracy on lower than 16 16 resolution mosaic images it is suggested that for the uncorrelated discriminant transformation the optimal face image resolution can be regarded as the resolution m n which makes the dimensionality n mn of the original image vector space be larger and closer to the number of known face classes

a homotopic deformation along p of a leray schauder degree result and existence for u p 2u ƒ t u 0 u 0 u t 0 p 1 soit f 0 1 r r une fonction continue et soit o p r r definie par o p s s p 2 s pour p fixe 1 on considere le probleme de dirichlet suivant o p u f t u 0 u 0 u t 0 ou t est un nombre reel positif

existence theory for functional p laplacian equations with variable exponents in this paper we consider the solvability of equations of the form d dt t u u t u t f t u u t u t for a e t i a b subject to a general type of functional boundary conditions which cover dirichlet and periodic boundary data as particular cases our approach is that of upper and lower solutions together with growth restrictions of nagumo s type an example is provided where a p laplacian with variable p is shown to have a solution between given upper and lower solutions

a study of some fuzzy cluster validity indices genetic clustering and application to pixel classification in this article the effectiveness of variable string length genetic algorithm along with a recently developed fuzzy cluster validity index pbmf has been demonstrated for clustering a data set into an unknown number of clusters the flexibility of a variable string length genetic algorithm vga is utilized in conjunction with the fuzzy indices to determine the number of clusters present in a data set as well as a good fuzzy partition of the data for that number of clusters a comparative study has been performed for different validity indices namely pbmf xb pe and pc the results of the fuzzy vga algorithm are compared with those obtained by the well known fcm algorithm which is applicable only when the number of clusters is fixed a priori moreover another genetic clustering scheme that also requires fixing the value of the number of clusters is implemented the effectiveness of the pbmf index as the optimization criterion along with a genetic fuzzy partitioning technique is demonstrated on a number of artificial and real data sets including a remote sensing image of the city of kolkata

mountain pass solutions to euler lagrange equations with general anisotropic operator abstract using the mountain pass theorem we show that the problem d d t l v t u t u t l x t u t u t for a e t a b u a u b 0 has a solution in anisotropic orlicz sobolev space we consider lagrangian l f t x v v t x f t x with growth conditions determined by anisotropic g function and some geometric conditions of ambrosetti rabinowitz type

robust cluster validity indexes cluster validity indexes can be used to evaluate the fitness of data partitions produced by a clustering algorithm validity indexes are usually independent of clustering algorithms however the values of validity indexes may be heavily influenced by noise and outliers these noise and outliers may not influence the results from clustering algorithms but they may affect the values of validity indexes in the literature there is little discussion about the robustness of cluster validity indexes in this paper we analyze the robustness of a validity index using the f function of m estimate and then propose several robust type validity indexes firstly we discuss the validity measure on a single data point and focus on those validity indexes that can be categorized as the mean type of validity indexes we then propose median type validity indexes that are robust to noise and outliers comparative examples with numerical and real data sets show that the proposed median type validity indexes work better than the mean type validity indexes

preconditioning for feature selection and regression in high dimensional problems we consider regression problems where the number of predictors greatly exceeds the number of observations we propose a method for variable selection that first estimates the regression function yielding a preconditioned response variable the primary method used for this initial regression is supervised principal components then we apply a standard procedure such as forward stepwise selection or the lasso to the preconditioned response variable in a number of simulated and real data examples this two step procedure outperforms forward stepwise selection or the usual lasso applied directly to the raw outcome we also show that under a certain gaussian latent variable model application of the lasso to the preconditioned response variable is consistent as the number of predictors and observations increases moreover when the observational noise is rather large the suggested procedure can give a more accurate estimate than lasso we illustrate our method on some real problems including survival analysis with microarray data

cluster validity measure and merging system for hierarchical clustering considering outliers clustering algorithms have evolved to handle more and more complex structures however the measures that allow to qualify the quality of such clustering partitions are rare and have been developed only for specific algorithms in this work we propose a new cluster validity measure cvm to quantify the clustering performance of hierarchical algorithms that handle overlapping clusters of any shape and in the presence of outliers this work also introduces a cluster merging system cms to group clusters that share outliers when located in regions of cluster overlap these outliers may be issued by a mixture of nearby cores the proposed cvm and cms are applied to hierarchical extensions of the support vector and gaussian process clustering algorithms both in synthetic and real experiments these results show that the proposed metrics help to select the appropriate level of hierarchy and the appropriate hyperparameters highlightscluster validity measure for arbitrary shaped clusters with outliers cluster merging system grouping cluster cores based on the outliers structure truly hierarchical variants of support vector and gaussian process clustering benefits for unsupervised change detection applications are presented

efficient learning and feature selection in high dimensional regression we present a novel algorithm for efficient learning and feature selection in high dimensional regression problems we arrive at this model through a modification of the standard regression model enabling us to derive a probabilistic version of the well known statistical regression technique of backfitting using the expectation maximization algorithm along with variational approximation methods to overcome intractability we extend our algorithm to include automatic relevance detection of the input features this variational bayesian least squares vbls approach retains its simplicity as a linear model but offers a novel statistically robust black box approach to generalized linear regression with high dimensional inputs it can be easily extended to nonlinear regression and classification problems in particular we derive the framework of sparse bayesian learning the relevance vector machine with vbls at its core offering significant computational and robustness advantages for this class of methods the iterative nature of vbls makes it most suitable for real time incremental learning which is crucial especially in the application domain of robotics brain machine interfaces and neural prosthetics where real time learning of models for control is needed we evaluate our algorithm on synthetic and neurophysiological data sets as well as on standard regression and classification benchmark data sets comparing it with other competitive statistical approaches and demonstrating its suitability as a drop in replacement for other generalized linear regression techniques

a validity index approach for network partitions abstract the validity index has been used to evaluate the fitness of partitions produced by clustering algorithms for points in euclidean space in this paper we propose a new validity index for network partitions which can provide a measure of goodness for the community structure of networks it is defined as a product of two factors and involves the compactness and separation for each partition the simulated annealing strategy is used to minimize such a validity index function in coordination with our previous k means algorithm based on the optimal reduction of a random walker markovian dynamics on the network it is demonstrated that the algorithm can efficiently find the community structure during the cooling process the number of communities can be automatically determined without any prior knowledge of the community structure moreover the algorithm is successfully applied to three real world networks

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

validity index for crisp and fuzzy clusters abstract in this article a cluster validity index and its fuzzification is described which can provide a measure of goodness of clustering on different partitions of a data set the maximum value of this index called the pbm index across the hierarchy provides the best partitioning the index is defined as a product of three factors maximization of which ensures the formation of a small number of compact clusters with large separation between at least two clusters we have used both the k means and the expectation maximization algorithms as underlying crisp clustering techniques for fuzzy clustering we have utilized the well known fuzzy c means algorithm results demonstrating the superiority of the pbm index in appropriately determining the number of clusters as compared to three other well known measures the davies bouldin index dunn s index and the xie beni index are provided for several artificial and real life data sets

on the sobolev embedding theorem for variable exponent spaces in the critical range abstract in this paper we study the sobolev embedding theorem for variable exponent spaces with critical exponents we find conditions on the best constant in order to guaranty the existence of extremals the proof is based on a suitable refinement of the estimates in the concentration compactness theorem for variable exponents and an adaptation of a convexity argument due to p l lions f pacella and m tricarico

existence of periodic solutions to a p laplacian lienard differential equation with a deviating argument abstract by means of mawhin s continuation theorem a kind of p laplacian lienard differential equation with a deviating argument as follows p y t f y t y t h y t g y t t e t is studied a new result on the existence of periodic solutions is obtained the interest is that the relation between the existence of periodic solutions and the deviating argument t is investigated meanwhile the approaches used to estimate a priori bounds of periodic solutions are different from the corresponding ones in the known literature

use of a fuzzy granulation degranulation criterion for assessing cluster validity the identification of a suitable clustering algorithm to partition data and assessment of the validity of the resultant partitioning are ongoing quests in unsupervised learning in this study a fuzzy granulation degranulation criterion is proposed to evaluate the goodness of a fuzzy partitioning of the data this in turn is used to determine the appropriate clustering algorithm suitable for a particular data set in general the quality of a partitioning is measured by computing the variance within it which is a measure of compactness of the obtained partitioning here a new error function which reflects how well the computed cluster centers represent the whole data set is used as the goodness measure of the obtained partitioning thus a clustering algorithm providing a good set of cluster centers which approximate well the whole data set is considered to be the most suited thereafter this new fuzzy granulation degranulation criterion is used to develop six new cluster validity indices these indices mimic the definitions of the existing and well known cluster validity indices such as pbm index xb index ps index fs index k index and sv index but use the new fuzzy granulation degranulation based error function instead of cluster compactness in order to evaluate the effectiveness of the proposed error function in correctly identifying the appropriate clustering algorithm for a particular data set eight well known clustering algorithms k means fuzzy c means gak means genetic algorithm based k means algorithm a newly developed genetic point symmetry based clustering technique gaps clustering average linkage clustering algorithm expectation maximization em clustering algorithm self organizing map som and spectral clustering technique are evaluated on a set of six artificially generated and six real life data sets results show that gak means is the most appropriate for most of the data sets used for the experiments thereafter the effectiveness of the proposed cluster validity indices in identifying the appropriate number of clusters automatically from different data sets are shown for above mentioned 12 data sets for the purpose of comparison results obtained with the original versions of the proposed cluster validity indices and results obtained by a density based clustering technique are also presented

inference of disjoint linear and nonlinear sub domains of a nonlinear mapping this paper investigates new ways of inferring nonlinear dependence from measured data the existence of unique linear and nonlinear sub spaces which are structural invariants of general nonlinear mappings is established and necessary and sufficient conditions determining these sub spaces are derived the importance of these invariants in an identification context is that they provide a tractable framework for minimising the dimensionality of the nonlinear modelling task specifically once the linear nonlinear sub spaces are known by definition the explanatory variables may be transformed to form two disjoint sub sets spanning respectively the linear and nonlinear sub spaces the nonlinear modelling task is confined to the latter sub set which will typically have a smaller number of elements than the original set of explanatory variables constructive algorithms are proposed for inferring the linear and nonlinear sub spaces from noisy data

shadowed sets in the characterization of rough fuzzy clustering in this study we develop a technique of an automatic selection of a threshold parameter which determines approximation regions in rough set based clustering the proposed approach exploits a concept of shadowed sets all patterns data to be clustered are placed into three categories assuming a certain perspective established by an optimization process as a result a lack of knowledge about global relationships among objects caused by the individual absolute distance in rough c means clustering or individual membership degree in rough fuzzy c means clustering can be circumvented subsequently relative approximation regions of each cluster are detected and described by integrating several technologies of granular computing including fuzzy sets rough sets and shadowed sets we show that the resulting characterization leads to an efficient description of information granules obtained through the process of clustering including their overlap regions outliers and boundary regions comparative experimental results reported for synthetic and real world data illustrate the essence of the proposed idea

a stability based validity method for fuzzy clustering an important goal in cluster analysis is the internal validation of results using an objective criterion of particular relevance in this respect is the estimation of the optimum number of clusters capturing the intrinsic structure of your data this paper proposes a method to determine this optimum number based on the evaluation of fuzzy partition stability under bootstrap resampling the method is first characterized on synthetic data with respect to hyper parameters like the fuzzifier and spatial clustering parameters such as feature space dimensionality clusters degree of overlap and number of clusters the method is then validated on experimental datasets furthermore the performance of the proposed method is compared to that obtained using a number of traditional fuzzy validity rules based on the cluster compactness to separation criteria the proposed method provides accurate and reliable results and offers better generalization capabilities than the classical approaches

a clustering procedure for exploratory mining of vector time series a two step procedure is developed for the exploratory mining of real valued vector multivariate time series using partition based clustering methods the proposed procedure was tested with model generated data multiple sensor based process data as well as simulation data the test results indicate that the proposed procedure is quite effective in producing better clustering results than a hidden markov model hmm based clustering method if there is a priori knowledge about the number of clusters in the data two existing validity indices were tested and found ineffective in determining the actual number of clusters determining the appropriate number of clusters in the case that there is no a priori knowledge is a known unresolved research issue not only for our proposed procedure but also for the hmm based clustering method and further development is necessary

a new fuzzy clustering validity index with a median factor for centroid based clustering determining the number of clusters which is usually approved by domain experts or evaluated by clustering validity indexes is an important issue in clustering analysis this study discusses the effectiveness of clustering validity indexes for centroid based partitional clustering algorithms most general purpose clustering validity indexes take the minimum maximum distance between a pair of data objects a pair of cluster centroids or an object and a centroid as an important evaluation factor however they may present unstable results especially when two centroids are allocated closely to alleviate this problem a new clustering validity index which is termed the wu and li index wli is proposed in this paper our proposed wli partially allows to some extent the existence of closely allocated centroids in the clustering results by considering not only the minimum but the median distances between a pair of centroids as well therefore possessing better stability the performances of wli and some existing clustering validity indexes are evaluated and compared by running the fuzzy c means algorithm for clustering various types of datasets including artificial datasets uci datasets and images experimental results have shown that wli has the more accurate and satisfactory performance than other indexes

principles for constructing three way approximations of fuzzy sets a comparative evaluation based on unsupervised learning abstract three way approximations of fuzzy sets are an important scheme of granular computing by abstracting a fuzzy set to its discrete three option alternatives which adhere to human cognitive behaviors and reduce the computational burden the key point of such three way approximations of fuzzy sets is how to choose a suitable design leading to their realization undesired three way approximations might be produced if the selected mechanism is unsuitable to data distribution in this study the principles for constructing three way approximations of fuzzy sets are summarized the following taxonomy of these principles is provided namely i uncertainty balance based principle ii prototype based principle and iii model based invoking the tradeoff between classification error and the number of data that have to be classified a number of detailed optimization models are discussed in detail to evaluate the performance of different construction principles a general unsupervised learning framework based on three way approximations of fuzzy sets is exhibited some synthetic data sets along with sixteen data sets from uci repository are involved for experiments friedman testing followed by holm bonferroni testing are exploited to test the performance significance of the proposed criteria which can provide insights and deliver guidance when choosing a principle for constructing three way approximations of fuzzy sets in the real world scenarios the research methods in this paper can also be extended to supervised and semi supervised learning areas

normality based validation for crisp clustering we introduce a new validity index for crisp clustering that is based on the average normality of the clusters unlike methods based on inter cluster and intra cluster distances this index emphasizes the cluster shape by using a high order characterization of its probability distribution the normality of a cluster is characterized by its negentropy a standard measure of the distance to normality which evaluates the difference between the cluster s entropy and the entropy of a normal distribution with the same covariance matrix the definition of the negentropy involves the distribution s differential entropy however we show that it is possible to avoid its explicit computation by considering only negentropy increments with respect to the initial data distribution where all the points are assumed to belong to the same cluster the resulting negentropy increment validity index only requires the computation of covariance matrices we have applied the new index to an extensive set of artificial and real problems where it provides in general better results than other indices both with respect to the prediction of the correct number of clusters and to the similarity among the real clusters and those inferred

evolutionary combination of kernels for nonlinear feature transformation abstract the performance of kernel based feature transformation methods depends on the choice of kernel function and its parameters in addition most of these methods do not consider the classification information and error for the mapping features in this paper we propose to determine a kernel function for kernel principal components analysis kpca and kernel linear discriminant analysis klda considering the classification information to this end we combine the conventional kernel functions using genetic algorithm and genetic programming in linear and non linear forms respectively we use the classification error and the mutual information between features and classes in the kernel feature space as evolutionary fitness functions the proposed methods are evaluated on the basis of the university of california irvine uci datasets and aurora2 speech database we evaluate the methods using clustering validity indices and classification accuracy the experimental results demonstrate that kpca using a nonlinear combination of kernels based on genetic programming and the classification error fitness function outperforms conventional kpca using gaussian kernel and also kpca using linear combination of kernels

orthogonal parameter estimation algorithm for non linear stochastic systems an orthogonal parameter estimation algorithm is derived which allows each parameter in a linear in the parameters non linear difference equation model to be estimated sequentially and quite independently of the other parameters in the model the algorithm can be applied for any persistently exciting input and provides both unbiased estimates in the presence of correlated noise and an indication of which terms to include in the model several simulated examples are included to demonstrate the effectiveness of the algorithm

approximate spectral clustering with utilized similarity information using geodesic based hybrid distance measures spectral clustering has been popular thanks to its ability to extract clusters of varying characteristics without using a parametric model in expense of high computational cost required for eigendecomposition of pairwise similarities in order to utilize its advantages in large datasets where it is infeasible due to its computational burden approximate spectral clustering asc methods apply spectral clustering on a reduced set of points data representatives selected by sampling or quantization this two step approach i e finding the representatives and then clustering them brings new opportunities for precise similarity definition such as manifold based topological relations data distribution within the voronoi polyhedra of the representatives and their geodesic distance information which are often ignored in similarity definition for asc in this study we propose geodesic based hybrid similarity criteria which enable the use of different types of information for accurate similarity representation in asc despite the fact that geodesic concept has been widely used in clustering our contribution is the unique way of representing data topology to form geodesic relations and jointly harnessing various information types including topology distance and density the proposed criteria are tested using both sampling selective sampling and quantization neural gas and k means approaches experiments on artificial datasets well known small medium size real datasets and four large datasets four remote sensing images with different types of clusters show that the proposed geodesic based hybrid similarity criteria outperform traditional similarity criteria in terms of clustering accuracies and several cluster validity indices highlightsgeodesic based hybrid similarity measures are proposed for approximate spectral clustering neighborhood graph required for geodesic approach is effectively constructed by weighted delaunay triangulation conn the proposed geodesic based hybrid similarities outperform in terms of both accuracies and cluster validity indices the proposed geodesic based hybrid similarities can be powerful for clustering of large remote sensing images the proposed similarities are significant especially for quantization based approximate spectral clustering

a new separation measure for improving the effectiveness of validity indices many validity indices have been proposed for quantitatively assessing the performance of clustering algorithms one limitation of existing indices is their lack of generalizability due to their dependence on the specific algorithms and structures of the data space to handle large scale datasets with arbitrary structures this research study proposes a new cluster separation measure for improving the effectiveness of existing validity indices this is achieved by partitioning the original data space into a grid based structure which allows the introduction of a new measurement for assessing the true data distribution between any two clusters instead of the distance between the two cluster prototypes to validate the effectiveness of the proposed separation measure we adopt two commonly used validity indices the davies bouldin s function db and tibshirani s gap statistic gs these indices are denoted as r db 1 and r gs 1 for clusters with sphere shaped structures and r db 2 and r gs 2 for irregular shaped structures this integration enables the indices to evaluate both partitional algorithms and hierarchical algorithms partitional algorithms including c means cm fuzzy c means fcm and hierarchical algorithms including dbscan and clique are used to test the performance of the new indices two synthetic datasets with spherical structures and four synthetic datasets with irregular shapes are first compared five real datasets from the uci machine learning repository are then used to further test the measure s performance the experimental results provide evidence that the new indices outperform the original indices

an efficient technique for superfamily classification of amino acid sequences feature extraction fuzzy clustering and prototype selection in this article we propose an efficient technique for classifying amino acid sequences into different superfamilies the proposed method first extracts 20 features from a set of training sequences the extracted features are such that they take into consideration the probabilities of occurrences of the amino acids in the different positions of the sequences thereafter a genetic fuzzy clustering approach is used to automatically evolve a set of prototypes representing each class the characteristic of this clustering method is that it does not require the a priori information about the number of clusters and is also able to come out of locally optimal configurations finally the nearest neighbor rule is used to classify an unknown sequence into a particular superfamily class based on its proximity to the prototypes evolved using the genetic fuzzy clustering technique this results in a significant improvement in the time required for classifying unknown sequences results for three superfamilies namely globin trypsin and ras demonstrate the effectiveness of the proposed technique with respect to the case where all the training sequences are considered for classification using the same set of features comparison with the well known technique blast also shows that the proposed method provides a significant improvement in terms of the time required for classification while providing comparable classification performance

on fuzzy cluster validity indices cluster analysis aims at identifying groups of similar objects and helps to discover distribution of patterns and interesting correlations in large data sets especially fuzzy clustering has been widely studied and applied in a variety of key areas and fuzzy cluster validation plays a very important role in fuzzy clustering this paper introduces the fundamental concepts of cluster validity and presents a review of fuzzy cluster validity indices available in the literature we conducted extensive comparisons of the mentioned indices in conjunction with the fuzzy c means clustering algorithm on a number of widely used data sets and make a simple analysis of the experimental results

a cluster validity index for fuzzy clustering a new cluster validity index is proposed for the validation of partitions of object data produced by the fuzzy c means algorithm the proposed validity index uses a variation measure and a separation measure between two fuzzy clusters a good fuzzy partition is expected to have a low degree of variation and a large separation distance testing of the proposed index and nine previously formulated indices on well known data sets shows the superior effectiveness and reliability of the proposed index in comparison to other indices and the robustness of the proposed index in noisy environments

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

gain scheduled controller design an analytic framework directly incorporating non equilibrium plant dynamics a velocity based linearization framework is employed to develop a novel rigorous approach to gain scheduling design the proposed approach enables knowledge concerning the plant dynamics at non equilibrium operating points to be incorporated directly into the controller design since the velocity based linearization framework supports the analysis of the transient response performance considerations can be accommodated the approach retains continuity with linear methods which is central to the existing conventional gain scheduling methodology and since a single type of linearization is employed throughout the design procedure is both straightforward and conceptually appealing

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

embedded local feature selection within mixture of experts a useful strategy to deal with complex classification scenarios is the divide and conquer approach the mixture of experts moe technique makes use of this strategy by jointly training a set of classifiers or experts that are specialized in different regions of the input space a global model or gate function complements the experts by learning a function that weighs their relevance in different parts of the input space local feature selection appears as an attractive alternative to improve the specialization of experts and gate function particularly in the case of high dimensional data in general subsets of dimensions or subspaces are usually more appropriate to classify instances located in different regions of the input space accordingly this work contributes with a regularized variant of moe that incorporates an embedded process for local feature selection using l 1 regularization experiments using artificial and real world datasets provide evidence that the proposed method improves the classical moe technique in terms of accuracy and sparseness of the solution furthermore our results indicate that the advantages of the proposed technique increase with the dimensionality of the data