convex linear combinations of compositions summary when a sampled target composition is suspected of being a mixture of different compositions from a number of independent sources the question of the nature of the mixing mechanism arises for the resolution of this question several models involving convex linear mixtures of compositions are considered and in particular the distributional problem of describing the pattern of variability of the target compositions given information about the source distributions is resolved in terms of approximations involving logistic normal and logistic skew normal distributions the quality of these approximations is shown to be satisfactory through a series of simulations briefly reported the modelling and subsequent statistical inference are motivated by an illustrative application to investigating the nature of pollution at three fishing locations in a scottish loch

fuzzy granular gravitational clustering algorithm for multivariate data abstract a new method for finding fuzzy information granules from multivariate data through a gravitational inspired clustering algorithm is proposed in this paper the proposed algorithm incorporates the theory of granular computing which adapts the cluster size with respect to the context of the given data via an inspiration in newton s law of universal gravitation both conditions of clustering similar data and adapting to the size of each granule are achieved this paper compares the fuzzy granular gravitational clustering algorithm fggca against other clustering techniques on two grounds classification accuracy and clustering validity indices e g rand fm davies bouldin dunn homogeneity and separation the fggca is tested with multiple benchmark classification datasets such as iris wine seeds and glass identification

distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution summary a fairly general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry and to generate a whole set of non symmetric densities the approach is sufficiently general to encompass some recent proposals in the literature variously related to the skew normal distribution the special case of skew elliptical densities is examined in detail establishing connections with existing similar work the final part of the paper specializes further to a form of multivariate skew t density likelihood inference for this distribution is examined and it is illustrated with numerical examples

evaluation of stability of k means cluster ensembles with respect to random initialization many clustering algorithms including cluster ensembles rely on a random component stability of the results across different runs is considered to be an asset of the algorithm the cluster ensembles considered here are based on k means clusterers each clusterer is assigned a random target number of clusters k and is started from a random initialization here we use 10 artificial and 10 real data sets to study ensemble stability with respect to random k and random initialization the data sets were chosen to have a small number of clusters two to seven and a moderate number of data points up to a few hundred pairwise stability is defined as the adjusted rand index between pairs of clusterers in the ensemble averaged across all pairs nonpairwise stability is defined as the entropy of the consensus matrix of the ensemble an experimental comparison with the stability of the standard k means algorithm was carried out for k from 2 to 20 the results revealed that ensembles are generally more stable markedly so for larger k to establish whether stability can serve as a cluster validity index we first looked at the relationship between stability and accuracy with respect to the number of clusters k we found that such a relationship strongly depends on the data set varying from almost perfect positive correlation 0 97 for the glass data to almost perfect negative correlation 0 93 for the crabs data we propose a new combined stability index to be the sum of the pairwise individual and ensemble stabilities this index was found to correlate better with the ensemble accuracy following the hypothesis that a point of stability of a clustering algorithm corresponds to a structure found in the data we used the stability measures to pick the number of clusters the combined stability index gave best results

pasting of lattice ordered effect algebras in this study we present techniques for constructing a lattice ordered effect algebra using a given family of mv effect algebras first we introduce the greechie diagrams of the pastings of a family of mv effect algebras as application of the greechie diagrams we provide some sufficient conditions for pasting a lattice ordered effect algebra using a family of mv effect algebras especially we illustrate a kind of technique of how to obtain a lattice ordered effect algebra by substituting the atoms of an orthomodular lattice with the lattice ordered effect algebras finally we prove a version of the loop lemma for mv effect algebras pasting

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

cumulative voting consensus method for partitions with variable number of clusters over the past few years there has been a renewed interest in the consensus clustering problem several new methods have been proposed for finding a consensus partition for a set of n data objects that optimally summarizes an ensemble in this paper we propose new consensus clustering algorithms with linear computational complexity in n we consider clusterings generated with a random number of clusters which we describe by categorical random variables we introduce the idea of cumulative voting as a solution for the problem of cluster label alignment where unlike the common one to one voting scheme a probabilistic mapping is computed we seek a first summary of the ensemble that minimizes the average squared distance between the mapped partitions and the optimal representation of the ensemble where the selection criterion of the reference clustering is defined based on maximizing the information content as measured by the entropy we describe cumulative vote weighting schemes and corresponding algorithms to compute an empirical probability distribution summarizing the ensemble given the arbitrary number of clusters of the input partitions we formulate the problem of extracting the optimal consensus as that of finding a compressed summary of the estimated distribution that preserves the maximum relevant information an efficient solution is obtained using an agglomerative algorithm that minimizes the average generalized jensen shannon divergence within the cluster the empirical study demonstrates significant gains in accuracy and superior performance compared to several recent consensus clustering algorithms

isomorphism theorems on generalized effect algebras based on atoms a well known fact is that every generalized effect algebra can be uniquely extended to an effect algebra in which it becomes a sub generalized effect algebra and simultaneously a proper order ideal the set theoretic complement of which is its dual poset we show that two non isomorphic generalized effect algebras even finite ones may have isomorphic effect algebraic extensions for archimedean atomic lattice effect algebras we prove isomorphism theorem based on atoms as an application we obtain necessary and sufficient conditions for isomorphism of two prelattice archimedean atomic generalized effect algebras with common or isomorphic effect algebraic extensions

a theoretical study on six classifier fusion strategies we look at a single point in feature space two classes and l classifiers estimating the posterior probability for class spl omega sub 1 assuming that the estimates are independent and identically distributed normal or uniform we give formulas for the classification error for the following fusion methods average minimum maximum median majority vote and oracle

robustness in real life a study of clinical laboratory data previous studies have evaluated the performance of robust estimators of location using computer generated distributions this paper describes how distributions commonly seen in biomedical research differ from the simulated distributions and compares the performance of six families of estimators using samples from four biomedical distributions the biomedical distributions can be asymmetric and have shorter tails and other anomalies such as digit preferences which are not modeled in simulation studies the four biomedical distributions studied differ markedly from the models previously studied and these differences strongly affect the robust estimators in such situations the trimmed mean provides an improvement over the sample mean and its performance is more stable than that of estimators whose psi functions have steeply descending tails the central value and dispersion of each of the estimators are evaluated

the trimmed mean in the linear model pour le modele lineaire general a erreurs independantes on propose et on examine les proprietes de grands echantillons d un estimateur du parametre de regression

hybrid cluster ensemble framework based on the random combination of data transformation operators given a dataset p represented by an nxm matrix where n is the number of data points and m is the number of attributes we study the effect of applying transformations to p and how this affects the performance of different ensemble algorithms specifically a dataset p can be transformed into a new dataset p by a set of transformation operators f in the instance dimension such as sub sampling super sampling noise injection and so on and a corresponding set of transformation operators j in the attribute dimension based on these conventional transformation operators f and j a general form w of the transformation operator is proposed to represent different kinds of transformation operators then two new data transformation operators known respectively as probabilistic based data sampling operator and probabilistic based attribute sampling operator are designed to generate new datasets in the ensemble next three new random transformation operators are proposed which include the random combination of transformation operators in the data dimension in the attribute dimension and in both dimensions respectively finally a new cluster ensemble approach is proposed which integrates the random combination of data transformation operators across different dimensions a hybrid clustering technique a confidence measure and the normalized cut algorithm into the ensemble framework the experiments show that i random combination of transformation operators across different dimensions outperforms most of the conventional data transformation operators for different kinds of datasets ii the proposed cluster ensemble framework performs well on different datasets such as gene expression datasets and datasets in the uci machine learning repository

fractal properties of mv algebra pastings abstract we implement the fractal construction process to the mv algebra pastings pasted mv algebras generate special types of difference posets d posets we compute the dimension of new fractal d posets and show that the fractal structures discussed in this paper have a non integer fractal dimension furthermore we observe an interesting agreement between the fractal dimension of the classical linear fractals cantor sets koch curves and the dimension of fractal d posets cantor fractal d posets and koch fractal d posets

inferential aspects of the skew exponential power distribution when the analysis of real data indicates that normality assumptions are untenable more flexible models that cope with the most prevalent deviations from normality can be adopted in this context the skew exponential power sep distribution warrants special attention because it encompasses distributions having both heavy tails and skewness it allows likelihood inference and it includes the normal model as a special case this article concerns likelihood inference about the parameters of the sep family in particular the information matrix of the maximum likelihood estimators mles is obtained and finite sample properties of the estimators are investigated numerically special attention is given to the properties of the mles and likelihood ratio statistics when the data are drawn from a normal distribution because this case is relevant for using the sep distribution to test for normality application of the sep distribution in robust estimation problems is considered for both independent and depend

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

fuzzy versus nonfuzzy in combining classifiers designed by boosting boosting is recognized as one of the most successful techniques for generating classifier ensembles typically the classifier outputs are combined by the weighted majority vote the purpose of this study is to demonstrate the advantages of some fuzzy combination methods for ensembles of classifiers designed by boosting we ran two fold cross validation experiments on six benchmark data sets to compare the fuzzy and nonfuzzy combination methods on the fuzzy side we used the fuzzy integral and the decision templates with different similarity measures on the nonfuzzy side we tried the weighted majority vote as well as simple combiners such as the majority vote minimum maximum average product and the naive bayes combination in our experiments the fuzzy combination methods performed consistently better than the nonfuzzy methods the weighted majority vote showed a stable performance though slightly inferior to the performance of the fuzzy combiners

combining multiple clusterings using evidence accumulation we explore the idea of evidence accumulation eac for combining the results of multiple clusterings first a clustering ensemble a set of object partitions is produced given a data set n objects or patterns in d dimensions different ways of producing data partitions are 1 applying different clustering algorithms and 2 applying the same clustering algorithm with different values of parameters or initializations further combinations of different data representations feature spaces and clustering algorithms can also provide a multitude of significantly different data partitionings we propose a simple framework for extracting a consistent clustering given the various partitions in a clustering ensemble according to the eac concept each partition is viewed as an independent evidence of data organization individual data partitions being combined based on a voting mechanism to generate a new n times n similarity matrix between the n patterns the final data partition of the n patterns is obtained by applying a hierarchical agglomerative clustering algorithm on this matrix we have developed a theoretical framework for the analysis of the proposed clustering combination strategy and its evaluation based on the concept of mutual information between data partitions stability of the results is evaluated using bootstrapping techniques a detailed discussion of an evidence accumulation based clustering algorithm using a split and merge strategy based on the k means clustering algorithm is presented experimental results of the proposed method on several synthetic and real data sets are compared with other combination strategies and with individual clustering results produced by well known clustering algorithms

the pasting constructions of lattice ordered effect algebras the aim of this paper is to present some ways of constructing a lattice ordered effect algebra from the given family of mv algebras the loop lemma of lattice ordered effect algebras is proved then the definitions of greechie diagrams of effect algebras are given all these results have generalized those of orthomodular lattices as applications of loop lemma and greechie diagrams some lattice ordered effect algebras without states are presented

quantile hydrologic model selection and model structure deficiency assessment 1 theory a theory for quantile based hydrologic model selection and model structure deficiency assessment is presented the paper demonstrates that the degree to which a model selection problem is constrained by the model structure measured by the lagrange multipliers of the constraints quantifies structural deficiency this leads to a formal definition of model structure deficiency or rigidity model structure deficiency introduces a bias in the prediction of an observed quantile which is often not equal across quantiles structure deficiency is therefore diagnosed when any two quantile predictions for a given model structure cross since unequal bias across quantiles result in quantile predictions crossing the analysis further suggests that the optimal value of quantile specific loss functions order different model structures by its structure deficiencies over a range of quantiles in addition to such novelties quantile hydrologic model selection is a frequentist approach that seeks to complement existing bayesian approaches to hydrological model uncertainty

properties and estimation of asymmetric exponential power distribution the new distribution class asymmetric exponential power distribution aepd proposed in this paper generalizes the class of skewed exponential power distributions sepd in a way that in addition to skewness introduces different decay rates of density in the left and right tails our parametrization provides an interpretable role for each parameter we derive moments and moment based measures skewness kurtosis expected shortfall it is demonstrated that a maximum entropy property holds for the aepd distributions we establish consistency asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix where the results apply to the sepd class they enlarge on the current literature also we give a convenient stochastic representation of the distribution our monte carlo study illustrates the theoretical results we also provide some empirical evidence for the usefulness of employing aepd errors in garch type models for predicting downside market risk of financial assets

modeling spatial processes with unknown extremal dependence class abstractmany environmental processes exhibit weakening spatial dependence as events become more extreme well known limiting models such as max stable or generalized pareto processes cannot capture this which can lead to a preference for models that exhibit a property known as asymptotic independence however weakening dependence does not automatically imply asymptotic independence and whether the process is truly asymptotically in dependent is usually far from clear the distinction is key as it can have a large impact upon extrapolation that is the estimated probabilities of events more extreme than those observed in this work we present a single spatial model that is able to capture both dependence classes in a parsimonious manner and with a smooth transition between the two cases the model covers a wide range of possibilities from asymptotic independence through to complete dependence and permits weakening dependence of extremes even under asymptotic dependence censored likelihood based

on weakly cut stable maps a mapping f p q between posets p and q is called weakly cut stable if f can be naturally extended to a weakly complete lattice homomorphism i e preserving non empty meets and joins f n p n q between the corresponding dedekind macneille completions these mappings are studied and described by the 1st order language

sinh arcsinh distributions we introduce the sinh arcsinh transformation and hence by applying it to a generating distribution with no parameters other than location and scale usually the normal a new family of sinh arcsinh distributions this four parameter family has symmetric and skewed members and allows for tailweights that are both heavier and lighter than those of the generating distribution the central place of the normal distribution in this family affords likelihood ratio tests of normality that are superior to the state of the art in normality testing because of the range of alternatives against which they are very powerful likelihood ratio tests of symmetry are also available and are very successful three parameter symmetric and asymmetric subfamilies of the full family are also of interest heavy tailed symmetric sinh arcsinh distributions behave like johnson su distributions while their light tailed counterparts behave like sinh normal distributions the sinh arcsinh family allowing a seamless transition between the two via the normal controlled by a single parameter the sinh arcsinh family is very tractable and many properties are explored likelihood inference is pursued including an attractive reparameterization illustrative examples are given a multivariate version is considered options and extensions are discussed

asymptotic form of the kullback leibler divergence for multivariate asymmetric heavy tailed distributions abstract an asymptotic expression for the kullback leibler kl divergence measure of multivariate skew t distributions mst is derived this novel class of flexible family distributions incorporates a shape and degree of freedom parameters in order to manipulate the skewness and heavy tail presence of the data respectively the quadratic form expressions of mst models are used to provide asymptotic measures additional inequalities for mst entropy and simulation studies are reported finally the expected values of the kl divergence of a sample correlation matrix obtained by pearson s correlation coefficient are discussed

a note on the operating characteristics of the modified f test brownie boos and hughes oliver 1990 biometrics 46 259 266 suggested a modification to the fixed effects analysis of variance anova f test for use in situations where treatments are likely to affect mean response while simultaneously increasing between subject variability these authors suggest that the modified test 1 is robust against departures from population normality 2 is more powerful than its classical counterpart when the expected alternative form is encountered and 3 will suffer only minor power losses relative to the usual test when alternatives are in the form of simple shifts in location this study shows that the modified test is not generally robust when sampling is from nonnormal distributions and is likely to produce unacceptably high type i error inflations when sampling is from heavy tailed or skewed distributions some power results are also provided for the multisample situation to supplement those of brownie et al who generated results only for the two sample case

ensemble clustering using factor graph in this paper we propose a new ensemble clustering approach termed ensemble clustering using factor graph ecfg compared to the existing approaches our approach has three main advantages 1 the cluster number is obtained automatically and need not to be specified in advance 2 the reliability of each base clustering can be estimated in an unsupervised manner and exploited in the consensus process 3 our approach is efficient for processing ensembles with large data sizes and large ensemble sizes in this paper we introduce the concept of super object which serves as a compact and adaptive representation for the ensemble data and significantly facilitates the computation through the probabilistic formulation we cast the ensemble clustering problem into a binary linear programming blp problem the blp problem is np hard to solve this optimization problem we propose an efficient solver based on factor graph the constrained objective function is represented as a factor graph and the max product belief propagation is utilized to generate the solution insensitive to initialization and converged to the neighborhood maximum extensive experiments are conducted on multiple real world datasets which demonstrate the effectiveness and efficiency of our approach against the state of the art approaches highlightsintroduce the super object representation to facilitate the consensus process probabilistically formulate the ensemble clustering problem into a blp problem propose an efficient solver for the blp problem based on factor graph the cluster number of the consensus clustering is estimated automatically our method achieves the state of the art performance in effectiveness and efficiency

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

effect algebraic extensions of generalized effect algebras and two valued states d posets and effect algebras are very natural structures to be carriers of probabilities for events with fuzziness uncertainty or unsharpness in spite of that there are effect algebras admitting no states and probabilities we give necessary and sufficient conditions for existence of two valued states on archimedean atomic effect algebras consequently a construction of states probabilities from bounded orthogonally additive measures existing on some ideal sub generalized effect algebras is shown

a clustering ensemble the aim of clustering ensemble is to combine multiple base partitions into a robust stable and accurate partition one of the key problems of clustering ensemble is how to exploit the cluster structure information in each base partition evidence accumulation is an effective framework which can convert the base partitions into a co association matrix this matrix describes the frequency of a pair of points partitioned into the same cluster but ignores some hidden information in the base partitions in this paper we reveal some of those information by refining the co association matrix from data point and base cluster level from the data point level as pairs of points in the same base cluster may have varied similarities their contributions to the co association matrix can be different from the cluster level since the base clusters may have diversified qualities the contribution of a base cluster as a whole can also be different from those of others after being refined the co association matrix is transformed into a path based similarity matrix so that more global information of the cluster structure is incorporated into the matrix finally spectral clustering is applied to the matrix to generate the final clustering result experimental results on 8 synthetic and 8 real data sets demonstrate that the clustering ensemble based on the refined co association matrix outperforms some state of the art clustering ensemble schemes highlightsa two level refined co association matrix for cluster ensemble is proposed the refined co association matrix is transformed by path based measure a theoretical background of the refinement is given the proposed method outperforms some state of the art ensemble methods

neural gas network for vector quantization and its application to time series prediction a neural network algorithm based on a soft max adaptation rule is presented this algorithm exhibits good performance in reaching the optimum minimization of a cost function for vector quantization data compression the soft max rule employed is an extension of the standard k means clustering procedure and takes into account a neighborhood ranking of the reference weight vectors it is shown that the dynamics of the reference weight vectors during the input driven adaptation procedure are determined by the gradient of an energy function whose shape can be modulated through a neighborhood determining parameter and resemble the dynamics of brownian particles moving in a potential determined by the data point density the network is used to represent the attractor of the mackey glass equation and to predict the mackey glass time series with additional local linear mappings for generating output values the results obtained for the time series prediction compare favorably with the results achieved by backpropagation and radial basis function networks

clustering ensembles models of consensus and weak partitions clustering ensembles have emerged as a powerful method for improving both the robustness as well as the stability of unsupervised classification solutions however finding a consensus clustering from multiple partitions is a difficult problem that can be approached from graph based combinatorial or statistical perspectives this study extends previous research on clustering ensembles in several respects first we introduce a unified representation for multiple clusterings and formulate the corresponding categorical clustering problem second we propose a probabilistic model of consensus using a finite mixture of multinomial distributions in a space of clusterings a combined partition is found as a solution to the corresponding maximum likelihood problem using the em algorithm third we define a new consensus function that is related to the classical intraclass variance criterion using the generalized mutual information definition finally we demonstrate the efficacy of combining partitions generated by weak clustering algorithms that use data projections and random data splits a simple explanatory model is offered for the behavior of combinations of such weak clustering components combination accuracy is analyzed as a function of several parameters that control the power and resolution of component partitions as well as the number of partitions we also analyze clustering ensembles with incomplete information and the effect of missing cluster labels on the quality of overall consensus experimental results demonstrate the effectiveness of the proposed methods on several real world data sets

the nontruncated marginal of a truncated bivariate normal distribution inference is considered for the marginal distribution ofx when x y has a truncated bivariate normal distribution they variable is truncated but only thex values are observed the relationship of this distribution to azzalini s skew normal distribution is obtained method of moments and maximum likelihood estimation are compared for the three parameter azzalini distribution samples that are uniformative about the skewness of this distribution may occur even for largen profile likelihood methods are employed to describe the uncertainty involved in parameter estimation a sample of 87 otis test scores is shown to be well described by this model

robust fit of bayesian mixed effects regression models with application to colony forming unit count in tuberculosis research early bactericidal activity of tuberculosis drugs is conventionally assessed using statistical regression modeling of colony forming unit cfu counts over time typically most cfu counts deviate little from the regression curve but gross outliers due to erroneous sputum sampling are occasionally present and can markedly influence estimates of the rate of change in cfu count which is the parameter of interest a recently introduced bayesian nonlinear mixed effects regression model was adapted to offer a robust approach that accommodates both outliers and potential skewness in the data at its most general the proposed regression model fits the skew student t distribution to residuals and random coefficients deviance information criterion statistics and compound laplace metropolis marginal likelihoods were used to discriminate between alternative bayesian nonlinear mixed effects regression models we present a relatively easy method to calculate the marginal likelihoods required to determine compound laplace metropolis marginal likelihoods by adapting methods available in currently available statistical software the robust methodology proposed in this paper was applied to data from 6 clinical trials the results provide strong evidence that the distribution of cfu count is often heavy tailed and negatively skewed suggesting the presence of outliers therefore we recommend that robust regression models such as those proposed here should be fitted to cfu count

diversity control for improving the analysis of consensus clustering consensus clustering has emerged as a powerful technique for obtaining better clustering results where a set of data partitions ensemble are generated which are then combined to obtain a consolidated solution consensus partition that outperforms all of the members of the input set the diversity of ensemble partitions has been found to be a key aspect for obtaining good results but the conclusions of previous studies are contradictory therefore ensemble diversity analysis is currently an important issue because there are no methods for smoothly changing the diversity of an ensemble which makes it very difficult to study the impact of ensemble diversity on consensus results indeed ensembles with similar diversity can have very different properties thereby producing a consensus function with unpredictable behavior in this study we propose a novel method for increasing and decreasing the diversity of data partitions in a smooth manner by adjusting a single parameter thereby achieving fine grained control of ensemble diversity the results obtained using well known data sets indicate that the proposed method is effective for controlling the dissimilarity among ensemble members to obtain a consensus function with smooth behavior this method is important for facilitating the analysis of the impact of ensemble diversity in consensus clustering

lattice effect algebras with o continuous faithful valuations we prove that if there exists an order continuous faithful valuation on a lattice effect algebra e then e is modular separable and order continuous it is also shown that such an effect algebra e can be supremum and infimum densely embedded into a complete effect algebra e which is also modular separable and order continuous since the valuation can be extended to a unique order continuous faithful valuation on e

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

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

likelihood inferences on semiparametric odds ratio model a flexible semiparametric odds ratio model has been proposed to unify and to extend both the log linear model and the joint normal model for data with a mix of discrete and continuous variables the semiparametric odds ratio model is particularly useful for analyzing biased sampling designs however statistical inference of the model has not been systematically studied when more than one nonparametric component is involved in the model in this article we study the maximum semiparametric likelihood approach to estimation and inference of the semiparametric odds ratio model we show that the maximum semiparametric likelihood estimator of the odds ratio parameter is consistent and asymptotically normally distributed we also establish statistical inference under a misspecified semiparametric odds ratio model which is important when handling weak identifiability in conditionally specified models under biased sampling designs we use simulation studies to demonstrate that the proposed approaches have satis

correlation curves measures of association as functions of covariate values for experiments where the strength of association between a response variable y and a covariate x is different over different regions of values for the covariate x we propose local nonparametric dependence functions which measure the strength of association between y and x as a function of x x our dependence functions are extensions of galton s idea of strength of co relation from the bivariate normal case to the nonparametric case in particular a dependence function is obtained by expressing the usual galton pearson correlation coefficient in terms of the regression line slope 3 and the residual variance o 2 and then replacing 3 and 72 by a nonparametric regression slope 13 x and a nonparametric residual variance o 2 x var yix respectively our local dependence functions are standardized nonparametric regression curves which provide universal scale free measures of the strength of the relationship between variables in nonlinear models they share most of the properties of the correlation coefficient and they reduce to the usual correlation coefficient in the bivariate normal case for this reason we call them correlation curves we show that in a certain sense they quantify lehmann s notion of regression dependence finally the correlation curve concept is illustrated using data from a study of the relationship between cholesterol levels x and triglyceride concentrations y of heart patients