research on the unbiased probability estimation of error correcting output coding supervised classification based on error correcting output codes ecoc is an efficient method to solve the problem of multi class classification and how to get the accurate probability estimation via ecoc is also an attractive research direction this paper proposed three kinds of ecoc to get unbiased probability estimates and investigated the corresponding classification performance in depth at the same time two evaluating criterions for ecoc that has better classification performance were concluded which are bayes consistence and unbiasedness of probability estimation experimental results on artificial data sets and uci data sets validate the correctness of our conclusion

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

modified principal component analysis an integration of multiple similarity subspace models we modify the conventional principal component analysis pca and propose a novel subspace learning framework modified pca mpca using multiple similarity measurements mpca computes three similarity matrices exploiting the similarity measurements 1 mutual information 2 angle information and 3 gaussian kernel similarity we employ the eigenvectors of similarity matrices to produce new subspaces referred to as similarity subspaces a new integrated similarity subspace is then generated using a novel feature selection approach this approach needs to construct a kind of vector set termed weak machine cell wmc which contains an appropriate number of the eigenvectors spanning the similarity subspaces combining the wrapper method and the forward selection scheme mpca selects a wmc at a time that has a powerful discriminative capability to classify samples mpca is very suitable for the application scenarios in which the number of the training samples is less than the data dimensionality mpca outperforms the other state of the art pca based methods in terms of both classification accuracy and clustering result in addition mpca can be applied to face image reconstruction mpca can use other types of similarity measurements extensive experiments on many popular real world data sets such as face databases show that mpca achieves desirable classification results as well as has a powerful capability to represent data

flexible discriminant analysis by optimal scoring abstract fisher s linear discriminant analysis is a valuable tool for multigroup classification with a large number of predictors one can find a reduced number of discriminant coordinate functions that are optimal for separating the groups with two such functions one can produce a classification map that partitions the reduced space into regions that are identified with group membership and the decision boundaries are linear this article is about richer nonlinear classification schemes linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups in this paper we obtain nonparametric versions of discriminant analysis by replacing linear regression by any nonparametric regression method in this way any multiresponse regression technique such as mars or neural networks can be postprocessed to improve its classification performance

diffusive logistic equations with indefinite weights population models in disrupted environments the dynamics of a population inhabiting a strongly heterogeneous environment are modelledby diffusive logistic equations of the form u t d u m x cu u in 0 where u represents the population density c d 0 are constants describing the limiting effects of crowding and the diffusion rate of the population respectively and m x describes the local growth rate of the population if the environment is bounded and is surrounded by uninhabitable regions then u 0 on 0 the growth rate m x is positive on favourablehabitats and negative on unfavourable ones the object of the analysis is to determine how the spatial arrangement of favourable and unfavourable habitats affects the population being modelled the models are shown to possess a unique stable positive steady state implying persistence for the population provided l d where is the principle positive eigenvalue for the problem m x in 0 on analysis of how depends on m indicates that environments with favourable and unfavourable habitats closely intermingled are worse for the population than those containing large regions of uniformly favourable habitat in the limit as the diffusion rate d 0 the solutions tend toward the positive part of m x c and if m is discontinuous develop interior transition layers the analysis uses bifurcation and continuation methods the variational characterisation of eigenvalues upper and lower solution techniques and singular perturbation theory

a likelihood mpec approach to target classification in this paper we develop a method for classifying an unknown data vector as belonging to one of several classes this method is based on the statistical methods of maximum likehood and borrowed strength estimation we develop an mpec procedure for mathematical program with equilibrium constraints for the classification of a multi dimensional observation using a finite set of observed training data as the inputs to a bilevel optimization problem we present a penalty interior point method for solving the resulting mpec and report numerical results for a multispectral minefield classification application related approaches based on conventional maximum likehood estimation and a bivariate normal mixture model as well as alternative surrogate classification objective functions are described

stopping criterion for boosting based data reduction techniques from binary to multiclass problem so far boosting has been used to improve the quality of moderately accurate learning algorithms by weighting and combining many of their weak hypotheses into a final classifier with theoretically high accuracy in a recent work sebban nock and lallich 2001 we have attempted to adapt boosting properties to data reduction techniques in this particular context the objective was not only to improve the success rate but also to reduce the time and space complexities due to the storage requirements of some costly learning algorithms such as nearest neighbor classifiers in that framework each weak hypothesis which is usually built and weighted from the learning set is replaced by a single learning instance the weight given by boosting defines in that case the relevance of the instance and a statistical test allows one to decide whether it can be discarded without damaging further classification tasks in sebban nock and lallich 2001 we addressed problems with two classes it is the aim of the present paper to relax the class constraint and extend our contribution to multiclass problems beyond data reduction experimental results are also provided on twenty three datasets showing the benefits that our boosting derived weighting rule brings to weighted nearest neighbor classifiers

humans in groups the importance of contextual information for understanding collective activities in this work we consider the problem of modeling and recognizing collective activities performed by groups of people sharing a common purpose for this aim we take into account the social contextual information of each person in terms of the relative orientation and spatial distribution of people groups we propose a method able to process a video stream and at each time instant associate a collective activity with each individual in the scene by representing the individual or target as a part of a group of nearby people the target group to generalize with respect to the viewpoint we associate each target with a reference frame based on his spatial orientation which we estimate automatically by semi supervised learning then we model the social context of a target by organizing a set of instantaneous descriptors capturing the essence of mutual positions and orientations within the target group in a graph structure classification of collective activities is achieved with a multi class svm endowed with a novel kernel function for graphs we report an extensive experimental analysis on benchmark datasets that validates the proposed solution and shows significant improvements with respect to state of art results

quasistationary distributions for one dimensional diffusions with killing we extend some results on the convergence of one dimensional diffusions killed at the boundary conditioned on extended survival to the case of general killing on the interior we show under fairly general conditions that a diffusion conditioned on long survival either runs off to infinity almost surely or almost surely converges to a quasistationary distribution given by the lowest eigenfunction of the generator in the absence of internal killing only a sufficiently strong inward drift can keep the process close to the origin to allow convergence in distribution an alternative that arises when general killing is allowed is that the conditioned process is held near the origin by a high rate of killing near oo we also extend to the case of general killing the standard result on convergence to a quasistationary distribution of a diffusion on a compact interval

counterexamples to some conjectures on the number of solutions of nonlinear equations on construit trois contre exemples resolvant par la negative certains problemes d analyse non lineaire

a multiclass classification method based on decoding of binary classifiers in this letter we present new methods of multiclass classification that combine multiple binary classifiers misclassification of each binary classifier is formulated as a bit inversion error with probabilistic models by making an analogy to the context of information transmission theory dependence between binary classifiers is incorporated into our model which makes a decoder a type of boltzmann machine we performed experimental studies using a synthetic data set data sets from the uci repository and bioinformatics data sets and the results show that the proposed methods are superior to the existing multiclass classification methods

combining predictions in pairwise classification an optimal adaptive voting strategy and its relation to weighted voting weighted voting is the commonly used strategy for combining predictions in pairwise classification even though it shows good classification performance in practice it is often criticized for lacking a sound theoretical justification in this paper we study the problem of combining predictions within a formal framework of label ranking and under some model assumptions derive a generalized voting strategy in which predictions are properly adapted according to the strengths of the corresponding base classifiers we call this strategy adaptive voting and show that it is optimal in the sense of yielding a map prediction of the class label of a test instance moreover we offer a theoretical justification for weighted voting by showing that it yields a good approximation of the optimal adaptive voting prediction this result is further corroborated by empirical evidence from experiments with real and synthetic data sets showing that even though adaptive voting is sometimes able to achieve consistent improvements weighted voting is in general quite competitive all the more in cases where the aforementioned model assumptions underlying adaptive voting are not met in this sense weighted voting appears to be a more robust aggregation strategy

positive operators and elliptic eigenvalue problems on considere le probleme aux valeurs propres lu mu sur et u 0 sur dans un domaine borne lisse cr n l est une expression differentielle uniformement elliptique a coefficients a valeurs reels continus de holder le coefficient de u dans l est non negatif est nu x est une fonction continue a valeur reelle on utilise la theorie abstraite des operateurs positifs pour retrouver certains resultats

logarithms of the derivative of univalent functions in qp spaces abstract for a univalent function d we study the membership of log to the space q p we look for geometric conditions and also a description involving the schwarzian derivative is given

classification by pairwise coupling we discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes and then coupling the estimates together the coupling model is similar to the bradley terry method for paired comparisons we study the nature of the class probability estimates that arise and examine the performance of the procedure in real and simulated data sets classifiers used include linear discriminants nearest neighbors adaptive nonlinear methods and the support vector machine

locally univalent functions vmoa and the dirichlet space we study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g belongs either to the dirichlet space d vmoa or the little bloch space b 0 concerning vmoa and b 0 our findings generalize the corresponding results for conformal maps shown by pommerenke in the late 1970s in the case of d we give a strictly geometric necessary condition for g to satisfy log g is an element of d and also offer two different semi geometric characterizations of when log g is an element of d

incorporating prior probabilities into high dimensional classifiers in standard parametric classifiers or classifiers based on nonparametric methods but where there is an opportunity for estimating population densities the prior probabilities of the respective populations play a key role however those probabilities are largely ignored in the construction of high dimensional classifiers partly because there are no likelihoods to be constructed or bayes risks to be estimated nevertheless including information about prior probabilities can reduce the overall error rate particularly in cases where doing so is most important i e when the classification problem is particularly challenging and error rates are not close to zero in this paper we suggest a general approach to reducing error rate in this way by using a method derived from breiman s bagging idea the potential improvements in performance are identified in theoretical and numerical work the latter involving both applications to real data and simulations the method is simple and explicit to apply and does not involve choice of any tuning parameters

on the principal eigenvalue of a second order linear elliptic problem on considere le probleme de dirichlet 7b lu mu dans u 0 sur dans un domaine borne r n a frontiere lisse 7b l est un operateur differentiel uniformement elliptique sur de la forme 7b lu i n j 1 a ij 2 u x j x i i n 1 a i u x i a 0 u a coefficients a valeurs reels appartenant a c 0 1

forelli rudin estimates carleson measures and f p q s functions abstract a classical theorem of l carleson states that the injection map from the hardy space h p into l p d is bounded if and only if the positive measure on the unit disc is a bounded carleson measure in this paper forelli rudin estimates for arbitrary positive measures on the unit disc are proved and then these estimates are applied to characterize bounded s carleson measures in terms of bloch and f p q s functions

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

spectral bound and reproduction number for infinite dimensional population structure and time heterogeneity spectral bounds of quasi positive matrices are crucial mathematical threshold parameters in population models that are formulated as systems of ordinary differential equations the sign of the spectral bound of the variational matrix at 0 decides whether at low density the population becomes extinct or grows another important threshold parameter is the reproduction number mathcal r which is the spectral radius of a related positive matrix as is well known the spectral bound and mathcal r 1 have the same sign provided that the matrices have a particular form the relation between spectral bound and reproduction number extends to models with infinite dimensional state space and then holds between the spectral bound of a resolvent positive closed linear operator and the spectral radius of a positive bounded linear operator we also extend an analogous relation between the spectral radii of two positive linear operators which is relevant for discrete time models we illustrate the general theory

a sufficient condition for the existence of a principal eigenvalue for nonlocal diffusion equations with applications abstract considerable work has gone into studying the properties of nonlocal diffusion equations the existence of a principal eigenvalue has been a significant portion of this work while there are good results for the existence of a principal eigenvalue equations on a bounded domain few results exist for unbounded domains on bounded domains the krein rutman theorem on banach spaces is a common tool for showing existence this article shows that generalized krein rutman can be used on unbounded domains and that the theory of positive operators can serve as a powerful tool in the analysis of nonlocal diffusion equations in particular a useful sufficient condition for the existence of a principal eigenvalue is given

a reformative kernel fisher discriminant analysis abstract a reformative kernel fisher discriminant method is proposed which is directly derived from the naive kernel fisher discriminant analysis with superiority in classification efficiency in the novel method only a part of training patterns called significant nodes are necessary to be adopted in classifying one test pattern a recursive algorithm for selecting significant nodes which is the key of the novel method is presented in detail the experiment on benchmarks shows that the novel method is effective and much efficient in classifying

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

characterizing the scale dimension of a high dimensional classification problem classi cation of high dimensional data is inherently di1cult we present an exploratory data analysis methodology for characterizing the scale dimension of a classi cation problem the idea is to characterize the support of one distinguished target class as a collection of balls covering the class with each ball centeredat an observation in that class such that the radius is maximal without containing observations from the other classes the scale dimension is de ned to be the number of distinct radii ball sizes required to cover the class without covering observations from the other class a greedy algorithm is used to t the balls the balls then provide a description of the support of the target class with information about the complexity of the classi cation problem implicit in the number radii adjacency and position of the balls clustering the balls by radius and pruning the cluster tree yields an estimate of the scale dimension for the problem we illustrate the methodology with pedagogical simulations anda chemical sensor data analysis application publishedby elsevier science ltdon behalf of pattern recognition society

a novel method for fisher discriminant analysis abstract a novel model for fisher discriminant analysis is developed in this paper in the new model maximal fisher criterion values of discriminant vectors and minimal statistical correlation between feature components extracted by discriminant vectors are simultaneously required then the model is transformed into an extreme value problem in the form of an evaluation function based on the evaluation function optimal discriminant vectors are worked out experiments show that the method presented in this paper is comparative to the winner between fslda and ulda

dirichlet and vmoa domains via schwarzian derivative abstract short proofs of the following results concerning a bounded conformal map g of the unit disc d are presented 1 log g belongs to the dirichlet space if and only if the schwarzian derivative s g of g satisfies s g z 1 z 2 l 2 d 2 log g vmoa if and only if s g z 2 1 z 2 3 is a vanishing carleson measure on d analogous results for besov and q p 0 spaces are also given

a fast kernel based nonlinear discriminant analysis for multi class problems nonlinear discriminant analysis may be transformed into the form of kernel based discriminant analysis thus the corresponding discriminant direction can be solved by linear equations from the view of feature space the nonlinear discriminant analysis is still a linear method and it is provable that in feature space the method is equivalent to fisher discriminant analysis we consider that one linear combination of parts of training samples called significant nodes can replace the total training samples to express the corresponding discriminant vector in feature space to some extent in this paper an efficient algorithm is proposed to determine significant nodes one by one the principle of determining significant nodes is simple and reasonable and the consequent algorithm can be carried out with acceptable computation cost depending on the kernel functions between test samples and all significant nodes classification can be implemented the proposed method is called fast kernel based nonlinear method fknm it is noticeable that the number of significant nodes may be much smaller than that of the total training samples as a result for two class classification problems the fknm will be much more efficient than the naive kernel based nonlinear method nknm the fknm can be also applied to multi class via two approaches one against the rest and one against one although there is a view that one against one is superior to one against the rest in classification efficiency it seems that for the fknm one against the rest is more efficient than one against one experiments on benchmark and real datasets illustrate that for two class and multi class classifications the fknm is effective feasible and much efficient

theory analysis on fslda and ulda abstract it is first revealed that the fisher criterion ratio of each fslda discriminant vector must not be less than that of corresponding ulda discriminant vector so the phenomenon in yang et al pattern recognition 35 2002 2665 is not strange but certain and must be available in all experiments in addition it is also first illustrated that in fact ulda discriminant vectors are the s t orthogonal eigenvectors of a generalized eigenequation as a result the algorithms to obtain s t orthogonal eigenvectors of the generalized eigenequation are equivalent to the ulda algorithm consequently it is possible to work out ulda discriminant vectors more efficiently

what s wrong with fisher criterion in this paper a seemingly contradictory experimental result concerning fisher criterion is first exhibited then we analyze this result from the statistical correlation point of view and give a reasonable explanation more importantly we emphasize that fisher criterion is not an absolute criterion and it should be associated with the statistical correlation together to assess the discrimination of a set of discriminant vectors

new support vector algorithms we propose a new class of support vector algorithms for regression and classification in these algorithms a parameter lets one effectively control the number of support vectors while this can be useful in its own right the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm the accuracy parameter epsilon in the regression case and the regularization constant c in the classification case we describe the algorithms give some theoretical results concerning the meaning and the choice of and report experimental results

efficient leave one out cross validation of kernel fisher discriminant classifiers abstract mika et al in neural network for signal processing vol ix ieee press new york 1999 pp 41 48 apply the kernel trick to obtain a non linear variant of fisher s linear discriminant analysis method demonstrating state of the art performance on a range of benchmark data sets we show that leave one out cross validation of kernel fisher discriminant classifiers can be implemented with a computational complexity of only o l 3 operations rather than the o l 4 of a naive implementation where l is the number of training patterns leave one out cross validation then becomes an attractive means of model selection in large scale applications of kernel fisher discriminant analysis being significantly faster than conventional k fold cross validation procedures commonly used

probability estimation for multi class classification using adaboost abstract it is a general viewpoint that adaboost classifier has excellent performance on classification problems but could not produce good probability estimations in this paper we put forward a theoretical analysis of probability estimation model and present some verification experiments which indicate that adaboost can be used for probability estimation with the theory we suggest some useful measures for using adaboost algorithms properly and then we deduce a probability estimation model for multi class classification by pairwise coupling unlike previous approximate methods we provide an analytical solution instead of a special iterative procedure moreover a new problem that how to get a robust prediction with classifier scores is proposed experiments show that the traditional predict framework which chooses one with the highest score from all classes as the prediction is not always good while our model performs well

solving multi class problems with linguistic fuzzy rule based classification systems based on pairwise learning and preference relations this paper deals with multi class classification for linguistic fuzzy rule based classification systems the idea is to decompose the original data set into binary classification problems using the pairwise learning approach confronting all pair of classes and to obtain an independent fuzzy system for each one of them along the inference process each fuzzy rule based classification system generates an association degree for both of its corresponding classes and these values are encoded into a fuzzy preference relation our analysis is focused on the final step that returns the predicted class label specifically we propose to manage the fuzzy preference relation using a non dominance criterion on the different alternatives contrasting the behaviour of this model with both the classical weighted voting scheme and a decision rule that combines the fuzzy relations of preference conflict and ignorance by means of a voting strategy our experimental study is carried out using two different linguistic fuzzy rule learning methods for which we show that the non dominance criterion is a good alternative in comparison with the previously mentioned aggregation mechanisms this empirical analysis is supported through the corresponding statistical analysis using non parametrical tests

online learning of complex prediction problems using simultaneous projections we describe and analyze an algorithmic framework for online classification where each online trial consists of multiple prediction tasks that are tied together we tackle the problem of updating the online predictor by defining a projection problem in which each prediction task corresponds to a single linear constraint these constraints are tied together through a single slack parameter we then introduce a general method for approximately solving the problem by projecting simultaneously and independently on each constraint which corresponds to a prediction sub problem and then averaging the individual solutions we show that this approach constitutes a feasible albeit not necessarily optimal solution of the original projection problem we derive concrete simultaneous projection schemes and analyze them in the mistake bound model we demonstrate the power of the proposed algorithm in experiments with synthetic data and with multiclass text categorization tasks

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

local linear discriminant analysis framework using sample neighbors the linear discriminant analysis lda is a very popular linear feature extraction approach the algorithms of lda usually perform well under the following two assumptions the first assumption is that the global data structure is consistent with the local data structure the second assumption is that the input data classes are gaussian distributions however in real world applications these assumptions are not always satisfied in this paper we propose an improved lda framework the local lda llda which can perform well without needing to satisfy the above two assumptions our llda framework can effectively capture the local structure of samples according to different types of local data structure our llda framework incorporates several different forms of linear feature extraction approaches such as the classical lda and principal component analysis the proposed framework includes two llda algorithms a vector based llda algorithm and a matrix based llda mllda algorithm mllda is directly applicable to image recognition such as face recognition our algorithms need to train only a small portion of the whole training set before testing a sample they are suitable for learning large scale databases especially when the input data dimensions are very high and can achieve high classification accuracy extensive experiments show that the proposed algorithms can obtain good classification results

an efficient renovation on kernel fisher discriminant analysis and face recognition experiments a reformative kernel algorithm which can deal with two class problems as well as those with more than two classes on fisher discriminant analysis is proposed in the novel algorithm the supposition that in feature space discriminant vector can be approximated by some linear combination of a part of training samples called significant nodes is made if the significant nodes are found out the novel algorithm on kernel fisher discriminant analysis will be superior to the naive one in classification efficiency in this paper a recursive algorithm for selecting significant nodes is developed in detail experiments show that the novel algorithm is effective and much efficient in classifying

schwarzian derivative and general besov type domains abstract we study univalent functions f for which log f belongs to a class of general besov type spaces we give a characterization of the general besov type domains in terms of carleson measure conditions on the schwarzian derivative s f and mention some further connection to teichmuller theory

monotone semiflows generated by functional differential equations abstract this obtains sufficient condition for an autonomous functional differential equation to generate a strongly monotone semiflow on a suitable state space this allows the application to functional differential equations of very powerful recent results on strongly monotone semiflows due to hirsch and matano in addition a very striking relationship is established between such functional differential equations and corresponding ordinary differential equations an example involving a biochemical feedback loop is considered keywords stability steady states

sparse multinomial kernel discriminant analysis smkda dimensionality reduction via canonical variate analysis cva is important for pattern recognition and has been extended variously to permit more flexibility e g by kernelizing the formulation this can lead to over fitting usually ameliorated by regularization here a method for sparse multinomial kernel discriminant analysis smkda is proposed using a sparse basis to control complexity it is based on the connection between cva and least squares and uses forward selection via orthogonal least squares to approximate a basis generalizing a similar approach for binomial problems classification can be performed directly via minimum mahalanobis distance in the canonical variates smkda achieves state of the art performance in terms of accuracy and sparseness on 11 benchmark datasets

a new approach for imbalanced data classification based on data gravitation imbalanced classification is an important machine learning research topic that troubles most general classification models because of the imbalanced class distribution a newly developed physical inspired classification method i e the data gravitation based classification dgc model performs well in many general classification problems however like other general classifiers the performance of dgc suffers in imbalanced tasks in this study we develop a specific dgc model namely imbalanced dgc idgc model for imbalanced problems the amplified gravitation coefficient agc is introduced for gravitation computing agc is a type of coefficient that contains class imbalance information which can strengthen and weaken the gravitational field of the minority and majority classes we also design a fitness evaluation function in the weight optimization procedure of the data distribution to ensure that the model parameters adapt to the imbalanced class distributions a total of 44 binary class data sets and 15 multiclass imbalanced data sets are used to test the performance of the proposed method experimental results show that the adapted dgc model is effective for imbalanced problems

a novel technique for subpixel image classification based on support vector machine this paper presents a novel support vector machine classifier designed for subpixel image classification pixel spectral unmixing the proposed classifier generalizes the properties of svms to the identification and modeling of the abundances of classes in mixed pixels by using fuzzy logic this results in the definition of a fuzzy input fuzzy output support vector machine f2svm classifier that can 1 process fuzzy information given as input to the classification algorithm for modeling the subpixel information in the learning phase of the classifier and 2 provide a fuzzy modeling of the classification results allowing a relation many to one between classes and pixels the presented binary f2svm can address multicategory problems according to two strategies the fuzzy one against all foaa and the fuzzy one against one foao strategies these strategies generalize to the fuzzy case techniques based upon ensembles of binary classifiers used for addressing multicategory problems in crisp classification problems the effectiveness of the proposed f2svm classifier is tested on three problems related to image classification in presence of mixed pixels having different characteristics experimental results confirm the validity of the proposed subpixel classification method