kernel pca for novelty detection kernel principal component analysis kernel pca is a non linear extension of pca this study introduces and investigates the use of kernel pca for novelty detection training data are mapped into an infinite dimensional feature space in this space kernel pca extracts the principal components of the data distribution the squared distance to the corresponding principal subspace is the measure for novelty this new method demonstrated a competitive performance on two dimensional synthetic distributions and on two real world data sets handwritten digits and breast cancer cytology

generalized correlation function definition properties and application to blind equalization with an abundance of tools based on kernel methods and information theoretic learning a void still exists in incorporating both the time structure and the statistical distribution of the time series in the same functional measure in this paper a new generalized correlation measure is developed that includes the information of both the distribution and that of the time structure of a stochastic process it is shown how this measure can be interpreted from a kernel method as well as from an information theoretic learning points of view demonstrating some relevant properties to underscore the effectiveness of the new measure a simple blind equalization problem is considered using a coded signal

sparse ensembles using weighted combination methods based on linear programming an ensemble of multiple classifiers is widely considered to be an effective technique for improving accuracy and stability of a single classifier this paper proposes a framework of sparse ensembles and deals with new linear weighted combination methods for sparse ensembles sparse ensemble is to sparsely combine the outputs of multiple classifiers by using a sparse weight vector when the continuous outputs of multiple classifiers are provided in our methods the problem of solving sparse weight vector can be formulated as linear programming problems in which the hinge loss or and the 1 norm regularization are exploited both the hinge loss and the 1 norm regularization are techniques inducing sparsity used in machine learning we only ensemble classifiers with nonzero weight coefficients in these lp based methods the ensemble training error is minimized while the weight vector of ensemble learning is controlled which can be thought as implementing the structure risk minimization rule and naturally explains good performance of these methods the promising experimental results over uci data sets and the radar high resolution range profile data are presented

feature extraction by non parametric mutual information maximization we present a method for learning discriminative feature transforms using as criterion the mutual information between class labels and transformed features instead of a commonly used mutual information measure based on kullback leibler divergence we use a quadratic divergence measure which allows us to make an efficient non parametric implementation and requires no prior assumptions about class densities in addition to linear transforms we also discuss nonlinear transforms that are implemented as radial basis function networks extensions to reduce the computational complexity are also presented and a comparison to greedy feature selection is made

a boundary method for outlier detection based on support vector domain description the support vector domain description svdd is a popular kernel method for outlier detection which tries to fit a class of data with a sphere and uses a few target objects to support its decision boundary the problem is that even with a flexible gaussian kernel function the svdd could sometimes generate such a loose decision boundary that the discrimination ability becomes poor therefore a computationally intensive procedure called kernel whitening is often required to improve the performance in this paper we propose a simple post processing method which tries to modify the svdd boundary in order to achieve a tight data description with no need of kernel whitening with the derivation of the distance between an object and its nearest boundary point in input space the proposed method can efficiently construct a new decision boundary based on the svdd boundary the improvement from the proposed method is demonstrated with synthetic and real world datasets the results show that the proposed decision boundary can fit the shape of synthetic data distribution closely and achieves better or comparable classification performance on real world datasets

maximum correntropy criterion for robust face recognition in this paper we present a sparse correntropy framework for computing robust sparse representations of face images for recognition compared with the state of the art l1norm based sparse representation classifier src which assumes that noise also has a sparse representation our sparse algorithm is developed based on the maximum correntropy criterion which is much more insensitive to outliers in order to develop a more tractable and practical approach we in particular impose nonnegativity constraint on the variables in the maximum correntropy criterion and develop a half quadratic optimization technique to approximately maximize the objective function in an alternating way so that the complex optimization problem is reduced to learning a sparse representation through a weighted linear least squares problem with nonnegativity constraint at each iteration our extensive experiments demonstrate that the proposed method is more robust and efficient in dealing with the occlusion and corruption problems in face recognition as compared to the related state of the art methods in particular it shows that the proposed method can improve both recognition accuracy and receiver operator characteristic roc curves while the computational cost is much lower than the src algorithms

the c loss function for pattern classification this paper presents a new loss function for neural network classification inspired by the recently proposed similarity measure called correntropy we show that this function essentially behaves like the conventional square loss for samples that are well within the decision boundary and have small errors and l0 or counting norm for samples that are outliers or are difficult to classify depending on the value of the kernel size parameter the proposed loss function moves smoothly from convex to non convex and becomes a close approximation to the misclassification loss ideal 0 1 loss we show that the discriminant function obtained by optimizing the proposed loss function in the neighborhood of the ideal 0 1 loss function to train a neural network is immune to overfitting more robust to outliers and has consistent and better generalization performance as compared to other commonly used loss functions even after prolonged training the results also show that it is a close competitor to the svm since the proposed method is compatible with simple gradient based online learning it is a practical way of improving the performance of neural network classifiers highlightswe propose a new classification method the method is based on the recently proposed similarity measure called correntropy the method is robust against overfitting and less sensitive to system parameters we obtain better performance as compared to several conventional classifiers

compact quantum ergodic systems we develop theory of multiplicity maps for compact quantum groups as an application we obtain a complete classification of right coideal c algebras of c suq 2 for q 1 1 0 they are labeled with dynkin diagrams but classification results for positive and negative cases of q are different many of the coideals are quantum spheres or quotient spaces by quantum subgroups but we do have other ones in our classification list

regularization theory and neural networks architectures we had previously shown that regularization principles lead to approximation schemes that are equivalent to networks with one layer of hidden units called regularization networks in particular s

decision combination in multiple classifier systems a multiple classifier system is a powerful solution to difficult pattern recognition problems involving large class sets and noisy input because it allows simultaneous use of arbitrary feature descriptors and classification procedures decisions by the classifiers can be represented as rankings of classifiers and different instances of a problem the rankings can be combined by methods that either reduce or rerank a given set of classes an intersection method and union method are proposed for class set reduction three methods based on the highest rank the borda count and logistic regression are proposed for class set reranking these methods have been tested in applications of degraded machine printed characters and works from large lexicons resulting in substantial improvement in overall correctness

mining data with random forests a survey and results of new tests random forests rf has become a popular technique for classification prediction studying variable importance variable selection and outlier detection there are numerous application examples of rf in a variety of fields several large scale comparisons including rf have been performed there are numerous articles where variable importance evaluations based on the variable importance measures available from rf are used for data exploration and understanding apart from the literature survey in rf area this paper also presents results of new tests regarding variable rankings based on rf variable importance measures we studied experimentally the consistency and generality of such rankings results of the studies indicate that there is no evidence supporting the belief in generality of such rankings a high variance of variable importance evaluations was observed in the case of small number of trees and small data sets

multi class sar atr using shift invariant correlation filters abstract the application of spatial filtering theory for the recognition of targets in synthetic aperture radar sar imagery is proposed shift invariant correlation operations are used to compute distances under an optimum transform to measure similarity between an ideal reference and the input image the transform is a filter which responds to features specifically useful for discrimination the results demonstrate the distortion tolerance of the approach which requires only a similarity in features rather than a precise match in pixel values quadratic terms are unaffected by shifting of the input image while linear terms are computed using shift invariant correlation the system is thus non linear but shift invariant specifically distance vectors are generated by filter banks which are analyzed by a rudimentary rule base to determine whether the input is a target image or clutter an sar automatic target recognizer atr with results for 3 and 5 class problems is described the data used is actual sar imagery of military targets

correntropy properties and applications in non gaussian signal processing the optimality of second order statistics depends heavily on the assumption of gaussianity in this paper we elucidate further the probabilistic and geometric meaning of the recently defined correntropy function as a localized similarity measure a close relationship between correntropy and m estimation is established connections and differences between correntropy and kernel methods are presented as such correntropy has vastly different properties compared with second order statistics that can be very useful in non gaussian signal processing especially in the impulsive noise environment examples are presented to illustrate the technique

combined 5 2 cv f test for comparing supervised classification learning algorithms dietterich 1998 reviews five statistical tests and proposes the 5 2 cv t test for determining whether there is a significant difference between the error rates of two classifiers in our experiments we noticed that the 5 2 cv t test result may vary depending on factors that should not affect the test and we propose a variant the combined 5 2 cv f test that combines multiple statistics to get a more robust test simulation results show that this combined version of the test has lower type i error and higher power than 5 2 cv proper

simple and prime crossed products of c algebras by compact quantum group coactions let g a be a compact quantum group and a coaction of g on a c algebra b we give necessary and sufficient conditions for the simplicity and primeness of the crossed product b g in terms of certain fixed point algebras

locally compact group actions on c algebras and compact subgroups be a compact subgroup in this paper we shall give necessary and sufficient conditions in order that the crossed product g x a be simple or prime our conditions are in terms of the dual 2 of the com pact subgroup k the paper is organized as follows in the second section we summarize some preliminary definitions and results about continuous banach representations of compact groups the same section contains the definitions of the subspaces of spherical functions sn nl l 7 n e e those of the algebras s i and the relations between these subspaces section 3 contains a study of saturated actions of g on a in terms of the ideals s s we mention that for compact groups the notion of saturated action has been defined by rieffel see 19 chap 73 the same section contains conditions in order that the crossed product be simple for compact abelian groups g our result reduces to the following g x

spectra for compact quantum group coactions and crossed products we present definitions of both connes spectrum and strong connes spectrum for actions of compact quantum groups on c algebras and obtain necessary and sufficient conditions for a crossed product to be a prime or a simple c algebra our results extend to the case of compact quantum ac tions the results in 8 which in turn generalize results by connes olesen and pedersen and kishimoto for abelian group actions we prove in addition that the connes spectra are closed under tensor products these results are new for compact nonabelian groups as well

a random forests quantile classifier for class imbalanced data abstract extending previous work on quantile classifiers q classifiers we propose the q classifier for the class imbalance problem the classifier assigns a sample to the minority class if the minority class conditional probability exceeds 0

one class classification with gaussian processes detecting instances of unknown categories is an important task for a multitude of problems such as object recognition event detection and defect localization this article investigates the use of gaussian process gp priors for this area of research focusing on the task of one class classification we analyze different measures derived from gp regression and approximate gp classification we also study important theoretical connections to other approaches and discuss their underlying assumptions experiments are performed using a large number of datasets and different image kernel functions our findings show that our approaches can outperform the well known support vector data description approach indicating the high potential of gaussian processes for one class classification furthermore we show the suitability of our methods in the area of attribute prediction defect localization bacteria recognition and background subtraction these applications and experiments highlight the easy applicability of our method as well as its state of the art performance compared to established methods

optimizing the data dependent kernel under a unified kernel optimization framework the kernel functions play a central role in kernel methods accordingly over the years the optimization of kernel functions has been a promising research area ideally fisher discriminant criteria can be used as an objective function to optimize the kernel function to augment the margin between different classes unfortunately fisher criteria are optimal only in the case that all the classes are generated from underlying multivariate normal distributions of common covariance matrix but different means and each class is expressed by a single cluster due to the assumptions fisher criteria obviously are not a suitable choice as a kernel optimization rule in some applications such as the multimodally distributed data in order to solve this problem recently many improved discriminant criteria dc have been also developed therefore to apply these discriminant criteria to kernel optimization in this paper based on a data dependent kernel function we propose a unified kernel optimization framework which can use any discriminant criteria formulated in a pairwise manner as the objective functions under the kernel optimization framework to employ different discriminant criteria one has to only change the corresponding affinity matrices without having to resort to any complex derivations in feature space experimental results based on some benchmark data demonstrate the efficiency of our method

selective ensemble of svdds with renyi entropy based diversity measure abstract in this paper a novel selective ensemble strategy for support vector data description svdd using the renyi entropy based diversity measure is proposed to deal with the problem of one class classification in order to obtain compact classification boundary the radius of ensemble is defined as the inner product of the vector of combination weights and the vector of the radii of svdds to make the center of ensemble achieve the optimal position the renyi entropy of the kernelized distances between the images of samples and the center of ensemble in the high dimensional feature space is defined as the diversity measure moreover to fulfill the selective ensemble an l 1 norm based regularization term is introduced into the objective function of the proposed ensemble the optimal combination weights can be iteratively obtained by the half quadratic optimization technique experimental results on two synthetic data sets and twenty benchmark data sets demonstrate that the proposed selective ensemble method is superior to the single svdd and the other four related ensemble approaches

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

complexity measures of supervised classification problems we studied a number of measures that characterize the difficulty of a classification problem focusing on the geometrical complexity of the class boundary we compared a set of real world problems to random labelings of points and found that real problems contain structures in this measurement space that are significantly different from the random sets distributions of problems in this space show that there exist at least two independent factors affecting a problem s difficulty we suggest using this space to describe a classifier s domain of competence this can guide static and dynamic selection of classifiers for specific problems as well as subproblems formed by confinement projection and transformations of the feature vectors

l1 norm based kpca for novelty detection novelty detection is a one class classification problem and it builds up the model with only normal samples based on which the novelty is detected though conventional kpca is an effective method of building one class classification models it is prone to being affected by the presence of outliers due to its inherent properties of l2 norm in this paper we propose a new optimization problem l1 norm based kpca which is robust to outliers correspondingly we present the algorithm and the measure of novelty the proposed method is applied to novelty detection and performs well on the simulation data sets

adjusted weight voting algorithm for random forests in handling missing values a novel algorithm based on random forests with surrogate splits is proposed to address the classification problem of incomplete data without imputation the algorithm allows each tree to cast a vote even the voting process is interrupted by missing attributes experimental results on various acknowledged datasets show that the proposed method is robust and efficient random forests rf is known as an efficient algorithm in classification however it depends on the integrity of datasets conventional methods in dealing with missing values usually employ estimation and imputation approaches whose efficiency is tied to the assumptions of data features recently algorithm of surrogate decisions in rf was developed and this paper proposes a random forests algorithm with modified surrogate splits adjusted weight voting random forest awvrf which is able to address the incomplete data without imputation differing from the present surrogate method in awvrf algorithm when the primary splitting attribute and the surrogate attributes of an internal node are all missing the undergoing instance is allowed to exit at the current node with a vote then the weight of the vote is adjusted by the strength of the involved attributes and the final decision is made by weighted voting awvrf does not comprise imputation step thus it is independent of data features awvrf is compared with the methods of mean imputation leofill knnimpute bpcafill and conventional rf with surrogate decisions surrrf using 50 times repeated 5 fold cross validation on 10 acknowledged datasets in a total of 22 experiment settings the method of awvrf harvests the highest accuracy in 14 settings and the largest auc in 7 settings exhibiting its superiority over other methods compared with surrrf awvrf is significantly more efficient and remain good discrimination of prediction experimental results show that the present awvrf algorithm can successfully handle the classification task for incomplete data

novelty detection using level set methods this paper presents a level set boundary description lsbd approach for novelty detection that treats the nonlinear boundary directly in the input space the proposed approach consists of level set function lsf construction boundary evolution and termination of the training process it employs kernel density estimation to construct the lsf of the initial boundary for the training data set then a sign of the lsf based algorithm is proposed to evolve the boundary and make it fit more tightly in the data distribution the training process terminates when an expected fraction of rejected normal data is reached the evolution process utilizes the signs of the lsf values at all training data points to decide whether to expand or shrink the boundary extensive experiments are conducted on benchmark data sets to evaluate the proposed lsbd method and compare it against four representative novelty detection methods the experimental results demonstrate that the novelty detector modeled with the proposed lsbd can effectively detect anomalies

predictor output sensitivity and feature similarity based feature selection this paper is concerned with a feature selection technique capable of generating an efficient feature set in a few selection steps the feature saliency measure proposed is based on two factors namely the fuzzy derivative of the predictor output with respect to the feature and the similarity between the feature being considered and the feature set the use of the fuzzy derivative enables modelling the vagueness that occurs in estimating the predictor output sensitivity the feature similarity measure employed allows avoiding utilization of very redundant features the experimental investigations performed on five real world problems have shown the effectiveness of the feature selection technique proposed the technique developed removed a large number of features from the original data sets without reducing the classification accuracy of a classifier in contrast the accuracy of the classifiers utilizing the reduced feature sets was higher than those exploiting all the original features

an analysis of ensemble pruning techniques based on ordered aggregation several pruning strategies that can be used to reduce the size and increase the accuracy of bagging ensembles are analyzed these heuristics select subsets of complementary classifiers that when combined can perform better than the whole ensemble the pruning methods investigated are based on modifying the order of aggregation of classifiers in the ensemble in the original bagging algorithm the order of aggregation is left unspecified when this order is random the generalization error typically decreases as the number of classifiers in the ensemble increases if an appropriate ordering for the aggregation process is devised the generalization error reaches a minimum at intermediate numbers of classifiers this minimum lies below the asymptotic error of bagging pruned ensembles are obtained by retaining a fraction of the classifiers in the ordered ensemble the performance of these pruned ensembles is evaluated in several benchmark classification tasks under different training conditions the results of this empirical investigation show that ordered aggregation can be used for the efficient generation of pruned ensembles that are competitive in terms of performance and robustness of classification with computationally more costly methods that directly select optimal or near optimal subensembles

clustering to minimize the maximum intercluster distance the problem of clustering a set of points so as to minimize the maximum intercluster distance is studied an o kn approximation algorithm where n is the number of points and k is the number of clusters that guarantees solutions with an objective function value within two times the optimal solution value is presented this approximation algorithm succeeds as long as the set of points satisfies the triangular inequality we also show that our approximation algorithm is best possible with respect to the approximation bound if pz np

two class support vector data description support vector data description svdd is a data description method that can give the target data set a spherically shaped description and be used to outlier detection or classification in real life the target data set often contains more than one class of objects and each class of objects need to be described and distinguished simultaneously in this case traditional svdd can only give a description for the target data set regardless of the differences between different target classes in the target data set or give a description for each class of objects in the target data set in this paper an improved support vector data description method named two class support vector data description tc svdd is presented the proposed method can give each class of objects in the target data set a hypersphere shaped description simultaneously if the target data set contains two classes of objects the characteristics of the improved support vector data descriptions are discussed the results of the proposed approach on artificial and actual data show that the proposed method works quite well on the 3 class classification problem with one object class being undersampled severely

the evidence framework applied to classification networks three bayesian ideas are presented for supervised adaptive classifiers first it is argued that the output of a classifier should be obtained by marginalizing over the posterior distribution of the parameters a simple approximation to this integral is proposed and demonstrated this involves a moderation of the most probable classifier s outputs and yields improved performance second it is demonstrated that the bayesian framework for model comparison described for regression models in mackay 1992a b can also be applied to classification problems this framework successfully chooses the magnitude of weight decay terms and ranks solutions found using different numbers of hidden units third an information based data selection criterion is derived and demonstrated within this framework

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

dimensionality reduction via sparse support vector machines we describe a methodology for performing variable ranking and selection using support vector machines svms the method constructs a series of sparse linear svms to generate linear models that can generalize well and uses a subset of nonzero weighted variables found by the linear models to produce a final nonlinear model the method exploits the fact that a linear svm no kernels with l1 norm regularization inherently performs variable selection as a side effect of minimizing capacity of the svm model the distribution of the linear model weights provides a mechanism for ranking and interpreting the effects of variables starplots are used to visualize the magnitude and variance of the weights for each variable we illustrate the effectiveness of the methodology on synthetic data benchmark problems and challenging regression problems in drug design this method can dramatically reduce the number of variables and outperforms svms trained using all attributes and using the attributes selected according to correlation coefficients the visualization of the resulting models is useful for understanding the role of underlying variables

a novel consistent random forest framework bernoulli random forests random forests rfs are recognized as one type of ensemble learning method and are effective for the most classification and regression tasks despite their impressive empirical performance the theory of rfs has yet been fully proved several theoretically guaranteed rf variants have been presented but their poor practical performance has been criticized in this paper a novel rf framework is proposed named bernoulli rfs brfs with the aim of solving the rf dilemma between theoretical consistency and empirical performance brf uses two independent bernoulli distributions to simplify the tree construction in contrast to the rfs proposed by breiman the two bernoulli distributions are separately used to control the splitting feature and splitting point selection processes of tree construction consequently theoretical consistency is ensured in brf i e the convergence of learning performance to optimum will be guaranteed when infinite data are given importantly our proposed brf is consistent for both classification and regression the best empirical performance is achieved by brf when it is compared with state of the art theoretical consistent rfs this advance in rf research toward closing the gap between theory and practice is verified by the theoretical and experimental studies in this paper

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

ergodic actions of universal quantum groups on operator algebras we construct ergodic actions of compact quantum groups on c algebras and von neumann algebras and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups

consistency of random forests and other averaging classifiers in the last years of his life leo breiman promoted random forests for use in classification he suggested using averaging as a means of obtaining good discrimination rules the base classifiers used for averaging are simple and randomized often based on random samples from the data he left a few questions unanswered regarding the consistency of such rules in this paper we give a number of theorems that establish the universal consistency of averaging rules we also show that some popular classifiers including one suggested by breiman are not universally consistent

the correntropy mace filter the minimum average correlation energy mace filter is well known for object recognition this paper proposes a nonlinear extension to the mace filter using the recently introduced correntropy function correntropy is a positive definite function that generalizes the concept of correlation by utilizing second and higher order moments of the signal statistics because of its positive definite nature correntropy induces a new reproducing kernel hilbert space rkhs taking advantage of the linear structure of the rkhs it is possible to formulate the mace filter equations in the rkhs induced by correntropy and obtained an approximate solution due to the nonlinear relation between the feature space and the input space the correntropy mace cmace can potentially improve upon the mace performance while preserving the shift invariant property additional computation for all shifts will be required in the cmace to alleviate the computation complexity of the solution this paper also presents the fast cmace using the fast gauss transform fgt we apply the cmace filter to the mstar public release synthetic aperture radar sar data set as well as pie database of human faces and show that the proposed method exhibits better distortion tolerance and outperforms the linear mace in both generalization and rejection abilities

linear programming support vector machines abstract based on the analysis of the conclusions in the statistical learning theory especially the vc dimension of linear functions linear programming support vector machines or svms are presented including linear programming linear and nonlinear svms in linear programming svms in order to improve the speed of the training time the bound of the vc dimension is loosened properly simulation results for both artificial and real data show that the generalization performance of our method is a good approximation of svms and the computation complex is largely reduced by our method

the random subspace method for constructing decision forests much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes the dilemma between overfitting and achieving maximum accuracy is seldom resolved a method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity the classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector that is trees constructed in randomly chosen subspaces the subspace method is compared to single tree classifiers and other forest construction methods by experiments on publicly available datasets where the method s superiority is demonstrated we also discuss independence between trees in a forest and relate that to the combined classification accuracy

approximate polytope ensemble for one class classification in this work a new one class classification ensemble strategy called approximate polytope ensemble is presented the main contribution of the paper is threefold first the geometrical concept of convex hull is used to define the boundary of the target class defining the problem expansions and contractions of this geometrical structure are introduced in order to avoid over fitting second the decision whether a point belongs to the convex hull model in high dimensional spaces is approximated by means of random projections and an ensemble decision process finally a tiling strategy is proposed in order to model non convex structures experimental results show that the proposed strategy is significantly better than state of the art one class classification methods on over 200 datasets highlightsthe methodology uses a convex hull for modeling one class classification problems random projections are used to approximate the convex hull in high dimensional spaces expansions of the approximate hulls are considered to set the optimal operating point exhaustive validation is performed on three different typologies of problems