a unified framework for model based clustering model based clustering techniques have been widely used and have shown promising results in many applications involving complex data this paper presents a unified framework for probabilistic model based clustering based on a bipartite graph view of data and models that highlights the commonalities and differences among existing model based clustering algorithms in this view clusters are represented as probabilistic models in a model space that is conceptually separate from the data space for partitional clustering the view is conceptually similar to the expectation maximization em algorithm for hierarchical clustering the graph based view helps to visualize critical important distinctions between similarity based approaches and model based approaches the framework also suggests several useful variations of existing clustering algorithms two new variations balanced model based clustering and hybrid model based clustering are discussed and empirically evaluated on a variety of data types

group preference aggregation methods employed in ahp an evaluation and an intrinsic process for deriving members weightages abstract the analytic hierarchy process ahp is one of the popular and powerful techniques for decision making a detailed survey of the literature has revealed that there exists no formal evaluation of the group preference aggregation methods currently employed in ahp this paper provides such an evaluation using well established social choice axioms which govern the process of combining individual opinions to obtain a single group opinion the geometric mean method gmm and the weighted arithmetic mean method wamm are the two methods evaluated it is shown using counter examples that the gmm does not always satisfy the pareto optimality axiom which is one of the prominent and widely accepted social choice axioms this finding is significant as the gmm has been the most commonly used method in ahp for combining individual opinions to form a group opinion the other method viz wamm has satisfied all the axioms except the independence of irrelevant alternatives axiom in order to use the wamm one has to find the weightages importance to be assigned to the members of the group this is often a difficult task especially so if the group is large as in the case of public policy decisions and when judgements are elicited through the use of questionnaires these situations need an objective method to derive members weightages but only a few studies are available in the literature to address such a situation we propose a simple and intuitively appealing eigenvector based method to intrinsically determine the weightages for group members using their own subjective opinions the superiority of the proposed method over the previous methods is brought out in the paper

on the minimum violations ranking of a tournament this paper examines the problem of rank ordering a set of players or objects on the basis of a set of pairwise comparisons arising from a tournament the criterion for deriving this ranking is to have as few cases as possible where player i is ranked above j while i was actually defeated by j in the tournament such a situation is referred to as a violation the objective therefore is to determine the minimum violations ranking mvr while there are situations where this ranking would be allowed to contain ties among subsets of objects we will concern ourselves herein with linear ordering no ties a series of examples are given where this requirement would seem to be appropriate in order to put the mvr problem into proper perspective we introduce the concept of a distance on the set of tournaments a set of natural axioms is presented which any such distance measure should obey and it is proven that in the presence of these axioms a unique such measure exists it is then shown that the mvr problem is equivalent to the minimum distance problem which can be represented in several forms in particular as a problem of determining the minimum feedback edge set in a graph and as a mixed integer generalized network problem this opens up a wide scope of possible solution procedures for the mvr problem an optimal algorithm is presented along with computational results in addition various heuristics are discussed including an improved heuristic referred to as the iterated kendall method

topographic mapping of large dissimilarity data sets topographic maps such as the self organizing map som or neural gas ng constitute powerful data mining techniques that allow simultaneously clustering data and inferring their topological structure such that additional features for example browsing become available both methods have been introduced for vectorial data sets they require a classical feature encoding of information often data are available in the form of pairwise distances only such as arise from a kernel matrix a graph or some general dissimilarity measure in such cases ng and som cannot be applied directly in this article we introduce relational topographic maps as an extension of relational clustering algorithms which offer prototype based representations of dissimilarity data to incorporate neighborhood structure these methods are equivalent to the standard vectorial techniques if a euclidean embedding exists while preventing the need to explicitly compute such an embedding extending these techniques for the general case of non euclidean dissimilarities makes possible an interpretation of relational clustering as clustering in pseudo euclidean space we compare the methods to well known clustering methods for proximity data based on deterministic annealing and discuss how far convergence can be guaranteed in the general case relational clustering is quadratic in the number of data points which makes the algorithms infeasible for huge data sets we propose an approximate patch version of relational clustering that runs in linear time the effectiveness of the methods is demonstrated in a number of examples

relationships between l 1 metrics on linear ranking spaces in this paper we examine various l 1 distance measures on linear ranking spaces beginning with the absolute position measure of blin we construct two offspring measures one based on relative rank positioning the other on relative object positioning the first is shown to be equivalent to the permutation vector method of cook and seiford the other is equivalent to the preference matrix method of kemeny and snell we also prove that the kemeny and snell method can be formulated as a quadratic assignment problem

relational duals of the c means clustering algorithms abstract the hard and fuzzy c means algorithms are widely used effective tools for the problem of clustering n objects into hard or fuzzy groups of similar individuals when the data is available as object data consisting of a set of n feature vectors in rp however object data algorithms are not directly applicable when the n objects are implicitly described in terms of relational data which consists of a set of n2 measurements of relations between each of the pairs of objects new relational versions of the hard and fuzzy c means algorithms are presented here for the case when the relational data can reasonably be viewed as some measure of distance some convergence properties of the algorithms are given along with a numerical example

a novel group ranking model for revealing sequence and quantity knowledge abstract the aggregation of individuals preferences into a consensus ranking is a group ranking problem which has been widely utilized in various applications such as decision support systems recommendation systems and voting systems gathering the comparison of preferences and aggregate them to gain consensuses is a conventional issue for example b c d a indicates that b is favorable to c and c d is somewhat favorable but not fully favorable to d a where and are comparators and a b c and d are items recently a new type of ranking model was proposed to provide temporal orders of items the order b c a means that b and c can occur simultaneously and are also before a although this model can derive the order ranking of items the knowledge about quantity related items is also of importance to approach more real life circumstances for example when enterprises or individuals handle their portfolios in financial management two considerations the sequences and the amount of money for investment objects should be raised initially in this study we propose a model for discovering consensus sequential patterns with quantitative linguistic terms experiments using synthetic and real datasets showed the model s computational efficiency scalability and effectiveness

a new consensus ranking approach for correlated ordinal information based on mahalanobis distance the cohesiveness among experts opinions is addressed from a global point of view a new procedure to codify ordinal information is provided and characterized a measurement of the degree of dissensus designed for possibly correlated alternatives is defined a procedure to obtain a social consensus solution based on the mahalanobis distance is investigated we investigate from a global point of view the existence of cohesiveness among experts opinions we address this general issue from three basic essentials the management of experts opinions when they are expressed by ordinal information the measurement of the degree of dissensus among such opinions and the achievement of a group solution that conveys the minimum dissensus to the experts group accordingly we propose and characterize a new procedure to codify ordinal information we also define a new measurement of the degree of dissensus among individual preferences based on the mahalanobis distance it is especially designed for the case of possibly correlated alternatives finally we investigate a procedure to obtain a social consensus solution that also includes the possibility of alternatives that are correlated in addition we examine the main traits of the dissensus measurement as well as the social solution proposed the operational character and intuitive interpretation of our approaches are illustrated by an explanatory example

a stochastic self organizing map for proximity data we derive an efficient algorithm for topographic mapping of proximity data tmp which can be seen as an extension of kohonen s self organizing map to arbitrary distance measures the tmp cost function is derived in a baysian framework of folded markov chains for the description of autoencoders it incorporates the data by a dissimilarity matrix and the topographic neighborhood by a matrix of transition probabilities from the principle of maximum entropy a nonfactorizing gibbs distribution is obtained which is approximated in a mean field fashion this allows for maximum likelihood estimation using an expectation maximization algorithm in analogy to the transition from topographic vector quantization to the self organizing map we suggest an approximation to tmp that is computationally more efficient in order to prevent convergence to local minima an annealing scheme in the temperature parameter is introduced for which the critical temperature of the first phase transition is calculated in terms o

information and preference in partial orders a bimatrix representation this paper presents a bimatrix structure for examining ordinal partial rankings a set of axioms is given similar to those of kemeny and snell 1962 and bogart 1973 which uniquely determines the distance between any pair of such rankings thel 1 norm is shown to satisfy this set of axioms and to be equivalent to the kemeny and snell distance on their subspace of weak orderings consensus formation is discussed

on the borda kendall consensus method for priority ranking problems this paper investigates the borda kendall method for the determination of a consensus ranking it is shown that in the case of ties the method does not perform as claimed a minimum variance method for determining the consensus ranking is proposed and its properties examined it is shown to be equivalent to the borda kendall method if ties are not allowed an algorithm to determine the minimum variance consensus ranking in the case of ties is described results obtained from the solution of problems of various sizes are discussed

the golden number and fibonacci sequences in the design of voting structures abstract some distinguished types of voters as vetoes passers or nulls as well as some others play a significant role in voting systems because they are either the most powerful or the least powerful voters in the game independently of the measure used to evaluate power in this paper we are concerned with the design of voting systems with at least one type of these extreme voters and with few types of equivalent voters with this purpose in mind we enumerate these special classes of games and find out that its number always follows a fibonacci sequence with smooth polynomial variations as a consequence we find several families of games with the same asymptotic exponential behavior except for a multiplicative factor which is the golden number or its square from a more general point of view our studies are related with the design of voting structures with a predetermined importance ranking

indefinite proximity learning a review efficient learning of a data analysis task strongly depends on the data representation most methods rely on symmetric similarity or dissimilarity representations by means of metric inner products or distances providing easy access to powerful mathematical formalisms like kernel or branch and bound approaches similarities and dissimilarities are however often naturally obtained by nonmetric proximity measures that cannot easily be handled by classical learning algorithms major efforts have been undertaken to provide approaches that can either directly be used for such data or to make standard methods available for these types of data we provide a comprehensive survey for the field of learning with nonmetric proximities first we introduce the formalism used in nonmetric spaces and motivate specific treatments for nonmetric proximity data second we provide a systematization of the various approaches for each category of approaches we provide a comparative discussion of the individual algorithms and address complexity issues and generalization properties in a summarizing section we provide a larger experimental study for the majority of the algorithms on standard data sets we also address the problem of large scale proximity learning which is often overlooked in this context and of major importance to make the method relevant in practice the algorithms we discuss are in general applicable for proximity based clustering one class classification classification regression and embedding approaches in the experimental part we focus on classification tasks

properties of ladder tournaments abstract ladder tournaments use work trials to screen workers for positions in organizations despite being common in many industries their properties remain poorly understood especially in organizations characterized by complex complementarities and externalities in their production process in this study we formalize the ranking rule generated by a ladder tournament and derive measures of relative performance that can be used to compare workers when their true inputs cannot be observed we show that this rule is reflexive but not generally transitive unless the organization has fewer than three layers of hierarchy or is complete it follows that complete organizations have an embedded merit based hierarchical structure we also study the relationship between a worker s tournament rank and his utility or usefulness as measured by the frequency with which he plays a pivotal role we show that a worker s likelihood of being pivotal is a weakly increasing function of his rank this finding implies that in complete organizations ladder tournaments discriminate more effectively between workers than do mechanisms based on pivotability or marginal productivity

accurate algorithms for identifying the median ranking when dealing with weak and partial rankings under the kemeny axiomatic approach abstract preference rankings virtually appear in all fields of science political sciences behavioral sciences machine learning decision making and so on the well known social choice problem consists in trying to find a reasonable procedure to use the aggregate preferences or rankings expressed by subjects to reach a collective decision this turns out to be equivalent to estimate the consensus central ranking from data and it is known to be a np hard problem a useful solution has been proposed by emond and mason in 2002 through the branch and bound algorithm bb within the kemeny and snell axiomatic framework as a matter of fact bb is a time demanding procedure when the complexity of the problem becomes untractable i e a large number of objects with weak and partial rankings in presence of a low degree of consensus as an alternative we propose an accurate heuristic algorithm called fast that finds at least one of the consensus ranking solutions found by bb saving a lot of computational time in addition we show that the building block of fast is an algorithm called quick that finds already one of the bb solutions so that it can be fruitfully considered to speed up even more the overall searching procedure if the number of objects is low simulation studies and applications on real data allows to show the accuracy and the computational efficiency of our proposal

ranking in tournaments and group decisionmaking this paper fully discusses methods for ranking a set of alternatives in the fairest possible way according to a minimum violations criterion new methods based on finding paths and circuits in graphs are presented for ranking participants in round robin and generalized tournaments and for consensus and group decisionmaking problems the objective of the paper is to review existing methods for tackling these problems and compare them with the new methods according to a fairness criterion and the amount of computing required to reach a solution it is shown that the new methods often exceed the existing methods in both fairness and reduced computing requirements in particular the new methods are generally more versatile than existing methods this allows organizations to obtain the fairest ranking of a number of alternatives according to their managers or employees wishes particular attention is given to incomplete rankings where insufficient exposure of an individual to some alternatives restricts that individual to ranking only the remaining alternatives

a generalized network formulation of the pairwise comparison consensus ranking model one of the best known and most widely referenced models for representing ordinal preferences is that due to kemeny and snell kemeny j g l j snell 1962 preference ranking an axiomatic approach mathematical models in the social sciences glnn new york 9 23 this model is designed to accommodate pairwise comparison data with an l1 norm used to measure voter disagreement while this model possesses many of the necessary properties for a social choice function solution procedures developed to date have been capable of handling only small problems due to the difficulty of modelling the transitivity requirements of an optimal consensus ranking this paper shows how the consensus formation problem for strict linear orderings can be modelled as a generalized network since efficient computer codes already exist for handling this special structure this approach will permit the solution of much larger problems than has been the case previously

achievable hierarchies in voting games with abstention abstract it is well known that he influence relation orders the voters the same way as the classical banzhaf and shapley shubik indices do when they are extended to the voting games with abstention vga in the class of complete games moreover all hierarchies for the influence relation are achievable in the class of complete vga the aim of this paper is twofold firstly we show that all hierarchies are achievable in a subclass of weighted vga the class of weighted games for which a single weight is assigned to voters secondly we conduct a partial study of achievable hierarchies within the subclass of h complete games that is complete games under stronger versions of influence relation

a new measure for analyzing and fusing sequences of objects this work is related to the combinatorial data analysis problem of seriation used for data visualization and exploratory analysis seriation re sequences the data so that more similar samples or objects appear closer together whereas dissimilar ones are further apart despite the large number of current algorithms to realize such re sequencing there has not been a systematic way for analyzing the resulting sequences comparing them or fusing them to obtain a single unifying one we propose a new positional proximity measure that evaluates the similarity of two arbitrary sequences based on their agreement on pairwise positional information of the sequenced objects furthermore we present various statistical properties of this measure as well as its normalized version modeled as an instance of the generalized correlation coefficient based on this measure we define a new procedure for consensus seriation that fuses multiple arbitrary sequences based on a quadratic assignment problem formulation and an efficient way of approximating its solution we also derive theoretical links with other permutation distance functions and present their associated combinatorial optimization forms for consensus tasks the utility of the proposed contributions is demonstrated through the comparison and fusion of multiple seriation algorithms we have implemented using many real world datasets from different application domains

a cardinal dissensus measure based on the mahalanobis distance abstract in this paper we address the problem of measuring the degree of consensus dissensus in a context where experts or agents express their opinions on alternatives or issues by means of cardinal evaluations to this end we propose a new class of distance based consensus model the family of the mahalanobis dissensus measures for profiles of cardinal values we set forth some meaningful properties of the mahalanobis dissensus measures finally an application over a real empirical example is presented and discussed

dominance based rough set approach for group decisions the objective of this paper is to propose an approach to support group multicriteria classification the approach is composed of three phases the first phase exploits the knowledge provided by each decision maker to individually approximate the decision classes using rough approximation the second phase seeks to combine the outputs of individual approximation phase into a collective decision table by using an appropriate aggregation procedure the third phase uses the collective decision table in order to infer a set of collective decision rules which synthesize the judgements and perspectives of the different decision makers and to permit the classification of all decision objects the proposed approach relies on the dominance based rough set approach drsa which is used at two different levels first the drsa is used during the first phase to approximate the input data relative to each decision maker second the drsa is used during the third phase to approximate the collective decision table and generate the collective decision rules this paper presents the theoretical foundation of the proposed approach three case studies using real world data and a comparative study of recent similar proposals

concordance and consensus this paper deals with the measurement of concordance and the construction of consensus in preference data either in the form of preference rankings or in the form of response distributions with likert items we propose a set of axioms of concordance in preference orderings and a new class of concordance measures the measures outperform classic measures like kendall s t and w and spearman s r in sensitivity and apply to large sets of orderings instead of just to pairs of orderings for sets of n orderings of n items we present very efficient and flexible algorithms that have a time complexity of only o nn 2 remarkably the algorithms also allow for fast calculation of all longest common subsequences of the full set of orderings we experimentally demonstrate the performance of the algorithms a new and simple measure for assessing concordance on likert items is proposed

a general framework for distance based consensus in ordinal ranking models abstract the problem of aggregating a set of ordinal rankings of n alternatives has given rise to a number of consensus models among the most common of these models are those due to borda and kendall which amount to using average ranks and the l1 and l2 distance models a common criticism of these approaches is their use of ordinal rank position numbers directly as the values of being ranked at those levels this paper presents a general framework for associating value or worth with ordinal ranks and develops models for deriving a consensus based on this framework it is shown that the lp distance models using this framework are equivalent to the conventional ordinal models for any p 1 this observation can be seen as a form of validation of the practice of using ordinal data in a manner for which it was presumably not designed in particular it establishes the robustness of the simple borda kendall and median ranking models

a flexible approach to ranking with an application to mba programs we develop a model for flexibly ranking multi dimensional alternatives units into preference classes via mixed integer programming we consider a linear aggregation model but allow the criterion weights to vary within pre specified ranges this allows the individual alternatives units to play to their strengths we illustrate the use of the model by considering the financial times global mba program rankings and discuss the implications we argue that in many applications neither the data nor the weights or the aggregation model itself is precise enough to warrant a complete ranking providing an argument for sorting or what we call flexible ranking

distance based and ad hoc consensus models in ordinal preference ranking abstract this paper examines the problem of aggregating ordinal preferences on a set of alternatives into a consensus this problem has been the subject of study for more than two centuries and many procedures have been developed to create a compromise or consensus we examine a variety of structures for preference specification and in each case review the related models for deriving a consensus two classes of consensus models are discussed namely ad hoc methods evolving primarily from parliamentary settings over the past 200 years and distance or axiomatic based methods we demonstrate the levels of complexity of the various distance based models by presenting the related mathematical programming formulations for them we also present conditions for equivalence that is for yielding the same consensus ranking for some of the methods finally we discuss various extensions of the basic ordinal ranking structures paying specific attention to partial ranking voting member weighted consensus ranking with intensity of preference and rank correlation methods as alternative approaches to deriving a consensus suggestions for future research directions are given

optimal cluster preserving embedding of nonmetric proximity data for several major applications of data analysis objects are often not represented as feature vectors in a vector space but rather by a matrix gathering pairwise proximities such pairwise data often violates metricity and therefore cannot be naturally embedded in a vector space concerning the problem of unsupervised structure detection or clustering in this paper a new embedding method for pairwise data into euclidean vector spaces is introduced we show that all clustering methods which are invariant under additive shifts of the pairwise proximities can be reformulated as grouping problems in euclidian spaces the most prominent property of this constant shift embedding framework is the complete preservation of the cluster structure in the embedding space restating pairwise clustering problems in vector spaces has several important consequences such as the statistical description of the clusters by way of cluster prototypes the generic extension of the grouping procedure to a discriminative prediction rule and the applicability of standard preprocessing methods like denoising or dimensionality reduction

on the information and representation of non euclidean pairwise data two common data representations are mostly used in intelligent data analysis namely the vectorial and the pairwise representation pairwise data which satisfy the restrictive conditions of euclidean spaces can be faithfully translated into a euclidean vectorial representation by embedding non metric pairwise data with violations of symmetry reflexivity or triangle inequality pose a substantial conceptual problem for pattern recognition since the amount of predictive structural information beyond what can be measured by embeddings is unclear we show by systematic modeling of non euclidean pairwise data that there exists metric violations which can carry valuable problem specific information furthermore euclidean and non metric data can be unified on the level of structural information contained in the data stable component analysis selects linear subspaces which are particularly insensitive to data fluctuations experimental results from different domains support our pattern recognition strategy

a new group ranking approach for ordinal preferences based on group maximum consensus sequences group ranking problems involve aggregating individual rankings to generate group ranking which represents consolidated group preference group ranking problems are commonly applied in real world decision making problems however supporting a group decision making process is difficult due to the existence of multiple decision makers each with his her own opinions hence determining how to best aid the group ranking process is an important consideration this study aims to determine a total ranking list which meets group consensus preferences for group ranking problems a new group consensus mining approach based on the concept of tournament matrices and directed graphs is first developed an optimization model involving maximum consensus sequences is then constructed to achieve a total ranking list compared to previous methods the proposed approach can generate a total ranking list involving group consensus preferences it can also determine maximum consensus sequences without the need for tedious candidate generation processes while also providing flexibility in solving ranking problems using different input preferences that vary in format and completeness in addition consensus levels are adjustable

nerf c means non euclidean relational fuzzy clustering abstract the relational fuzzy c means rfcm algorithm can be used to cluster a set of n objects described by pair wise dissimilarity values if and only if there exist n points in r n 1 whose squared euclidean distances precisely match the given dissimilarity data this strong restriction on the dissimilarity data renders rfcm inapplicable to most relational clustering problems this paper substantially improves rfcm by generalizing it to the case of arbitrary symmetric dissimilarity data the generalization is obtained using a computationally efficient modification of the existing algorithm that is equivalent to applying a spreading transformation to the dissimilarity data while the method given applies specifically to dissimilarity data a simple transformation can be used to convert similarity relations into dissimilarity data so the method is applicable to any numerical relational data that are positive reflexive or anti reflexive and symmetric numerical examples illustrate and compare the present approach to problems that can be studied with alternatives such as the linkage algorithms

a unified approach to pattern recognition abstract the paper is an outline of a new approach to pattern recognition developed by the author a fuller introduction to the approach will appear soon 1 within the proposed framework the two principal approaches to pattern recognition vector and syntactic are unified

distance based consensus models for fuzzy and multiplicative preference relations this paper proposes a distance based consensus model for fuzzy preference relations where the weights of fuzzy preference relations are automatically determined two indices an individual to group consensus index ici and a group consensus index gci are introduced an iterative consensus reaching algorithm is presented and the process terminates until both the ici and gci are controlled within predefined thresholds the model and algorithm are then extended to handle multiplicative preference relations finally two examples are illustrated and comparative analyses demonstrate the effectiveness of the proposed methods

priority ranking and consensus formation the case of ties this paper investigates the problem of obtaining a compromise consensus from a set of ordinal rankings of n objects supplied by m committee members earlier work by cook and seiford cook wade d lawrence m seiford 1978 priority ranking and consensus formation management sci 24 16 1721 1732 dealt with the problem of consensus when attention was restricted to complete rankings only that is no ties were permitted this paper examines the general problem which allows for tied preferences a convex polyhedral representation is given of the feasible solution space and a branch and bound procedure is developed for determining an optimal ranking computational results for various problem sizes are presented generalizations and directions for further research are discussed

flat covers of complexes abstract in this article we define and study flat complexes over any ring also we prove that any complex over a commutative noetherian ring with finite krull dimension has a flat cover and a dg flat cover

auslander type conditions and cotorsion pairs we study the properties of rings satisfying auslander type conditions if an artin algebra satisfies the auslander condition that is is an gorenstein artin algebra then we construct two kinds of subcategories which form functorially finite cotorsion pairs

gorenstein flat covers of modules over gorenstein rings abstract a left and right noetherian ring r is called gorenstein if both r r and r r have finite injective dimensions these rings were studied by bass for the commutative case and iwanaga for the noncommutative case in this paper we define gorenstein flat modules over a gorenstein ring these modules are a generalization of flat modules after discussing the properties of modules over a gorenstein ring we prove that every module over a gorenstein ring has a gorenstein flat cover or a minimal right approximation by a gorenstein flat module in auslander and reiten s terminology

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

a theory of proximity based clustering structure detection by optimization abstract in this paper a systematic optimization approach for clustering proximity or similarity data is developed starting from fundamental invariance and robustness properties a set of axioms is proposed and discussed to distinguish different cluster compactness and separation criteria the approach covers the case of sparse proximity matrices and is extended to nested partitionings for hierarchical data clustering to solve the associated optimization problems a rigorous mathematical framework for deterministic annealing and mean field approximation is presented efficient optimization heuristics are derived in a canonical way which also clarifies the relation to stochastic optimization by gibbs sampling similarity based clustering techniques have a broad range of possible applications in computer vision pattern recognition and data analysis as a major practical application we present a novel approach to the problem of unsupervised texture segmentation which relies on statistical tests as a measure of homogeneity the quality of the algorithms is empirically evaluated on a large collection of brodatz like micro texture mondrians and on a set of real word images to demonstrate the broad usefulness of the theory of proximity based clustering the performances of different criteria and algorithms are compared on an information retrieval task for a document database the superiority of optimization algorithms for clustering is supported by extensive experiments

triangulated equivalence between a homotopy category and a triangulated quotient category abstract given two complete hereditary cotorsion pairs q r and q r in a bicomplete abelian category g such that q q and q r q r becker showed that there exists a hereditary abelian model structure m q w r on g where w is a thick subcategory of g we prove that the homotopy category ho m of m is triangulated equivalent to the triangulated quotient category d b g q r k b q r where d b g q r is the subcategory of d b g consisting of all homology bounded complexes with both finite q dimension and r dimension and k b q r is the bounded homotopy category of q r core objects applications are given in the category of modules it is shown that the homotopy category of the gorenstein flat resp ding projective and gorenstein ac projective model structure on the category of modules established by gillespie and his coauthors can be realized as a certain triangulated quotient category

a new correlation coefficient for comparing and aggregating non strict and incomplete rankings abstract we introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non strict i e with ties and incomplete i e unknown preferences the correlation coefficient is designed to enforce a neutral treatment of incompleteness whereby no assumptions are made about individual preferences involving unranked objects the new measure which can be regarded as a generalization of the seminal kendall tau correlation coefficient is proven to satisfy a set of metric like axioms and to be equivalent to a recently developed ranking distance function associated with kemeny aggregation in an effort to further unify and enhance both robust ranking methodologies this work proves the equivalence of an additional distance and correlation coefficient pairing in the space of non strict incomplete rankings these connections induce new exact optimization methodologies a specialized branch and bound algorithm and an exact integer programming formulation moreover the bridging of these complementary theories reinforces the singular suitability of the featured correlation coefficient to solve the general consensus ranking problem the latter premise is bolstered by an accompanying set of experiments on random instances which are generated via a herein developed sampling technique connected with the classic mallows distribution of ranking data associated experiments with the branch and bound algorithm demonstrate that as data becomes noisier the featured correlation coefficient yields relatively fewer alternative optimal solutions and that the aggregate rankings tend to be closer to an underlying ground truth shared by a majority

preference relations on actions and criteria in multicriteria decision making abstract let a be a finite set of feasible actions which are judged following several criteria an outranking relation is defined on a by considering preference of the decision maker as a weak order on each criterion and the relation among criteria as a semi order on the given set of criteria several ways of constructing outranking relations have been proposed one of the most popular introduced by b roy for instance electre s is based on the use of weights related to criteria in our approach the knowledge of weights is replaced by the existence of a semi order a case study is developed it deals with a computer selection problem

a new proposal for fusing individual preference orderings by rank ordered agents a generalization of the yager s algorithm abstract the problem of the aggregation of multi agents preference orderings has received considerable attention in the scientific literature because of its importance for different fields of research yager 2001 proposed an algorithm for addressing this problem when the agents importance is expressed through a rank ordering instead of a set of weights the algorithm by yager is simple and automatable but is subject to some constraints which may limit its range of application i preference orderings should not include incomparable and or omitted alternatives and ii the fused ordering may sometimes not reflect the majority of the multi agent preference orderings the aim of this article is to present a generalized version of the algorithm by yager which overcomes the above limitations and in general is adaptable to less stringent input data a detailed description of the new algorithm is supported by practical examples

on the ordinal equivalence of the johnston banzhaf and shapley power indices abstract in this paper we characterize the games in which johnston shapley shubik and penrose banzhaf coleman indices are ordinally equivalent meaning that they rank players in the same way we prove that these three indices are ordinally equivalent in semicomplete simple games which is a newly defined class that contains complete games and includes most of the real world examples of binary voting systems this result constitutes a twofold extension of diffo lambo and moulen s result diffo lambo and moulen 2002 in the sense that ordinal equivalence emerges for three power indices not just for the shapley shubik and penrose banzhaf coleman indices and it holds for a class of games strictly larger than the class of complete games

covers and envelopes over gr gorenstein rings abstract in this paper we study the existence of gorenstein injective envelopes and gorenstein projective and flat covers in the category of graded modules and we relate them with the corresponding envelopes and covers in the category of modules

edit distance based kernel functions for structural pattern classification a common approach in structural pattern classification is to define a dissimilarity measure on patterns and apply a distance based nearest neighbor classifier in this paper we introduce an alternative method for classification using kernel functions based on edit distance the proposed approach is applicable to both string and graph representations of patterns by means of the kernel functions introduced in this paper string and graph classification can be performed in an implicit vector space using powerful statistical algorithms the validity of the kernel method cannot be established for edit distance in general however by evaluating theoretical criteria we show that the kernel functions are nevertheless suitable for classification and experiments on various string and graph datasets clearly demonstrate that nearest neighbor classifiers can be outperformed by support vector machines using the proposed kernel functions