the em algorithm for kernel matrix completion with auxiliary data in biological data it is often the case that observed data are available only for a subset of samples when a kernel matrix is derived from such data we have to leave the entries for unavailable samples as missing in this paper the missing entries are completed by exploiting an auxiliary kernel matrix derived from another information source the parametric model of kernel matrices is created as a set of spectral variants of the auxiliary kernel matrix and the missing entries are estimated by fitting this model to the existing entries for model fitting we adopt the em algorithm distinguished from the em algorithm of dempster et al 1977 based on the information geometry of positive definite matrices we will report promising results on bacteria clustering experiments using two marker sequences 16s and gyrb

interactive group decision making procedure under incomplete information this paper deals with multiple criteria decision making problem with incomplete information when multiple decision makers multiple criteria group decision making mcgdm are involved usually decision makers dms are willing or able to provide only incomplete information because of time pressure lack of knowledge or data and their limited expertise related with problem domain there have been just a few studies considering incomplete information in group settings this incompletely specified information constructs region of linear constraints and therefore pairwise dominance relationship between alternatives reduces to intractable nonlinear programmings hence to handle this difficulty we suggest a method utilizing individual decision results to form group consensus final group consensus ranking toward more agreement of participants can be built through solving a series of linear programmings using individual decision results under group members possibly different weight constraints

learning a mahalanobis metric from equivalence constraints many learning algorithms use a metric defined over the input space as a principal tool and their performance critically depends on the quality of this metric we address the problem of learning metrics using side information in the form of equivalence constraints unlike labels we demonstrate that this type of side information can sometimes be automatically obtained without the need of human intervention we show how such side information can be used to modify the representation of the data leading to improved clustering and classification specifically we present the relevant component analysis rca algorithm which is a simple and efficient algorithm for learning a mahalanobis metric we show that rca is the solution of an interesting optimization problem founded on an information theoretic basis if dimensionality reduction is allowed within rca we show that it is optimally accomplished by a version of fisher s linear discriminant that uses constraints moreover under certain gaussian assumptions rca can be viewed as a maximum likelihood estimation of the within class covariance matrix we conclude with extensive empirical evaluations of rca showing its advantage over alternative methods

tools for interactive multiattribute decisionmaking with incompletely identified information abstract the aim of this paper is to present tools or techniques for an interactive multiattribute decisionmaking with the decision maker s incomplete information that is 1 we formally describe mathematical models under certainty and uncertainty for establishing pairwise dominance where the incomplete information becomes the set of constraints in the model 2 we present a description on styles of incomplete parameter value information 3 the characteristic of a weak dominance is described when the decision maker is not willing or able to provide more information on parameters the weak dominance technique is useful for a final choicemaking 4 we propose a dominance graph and also present an algorithm of generating the dominance graph based on the information of pairwise dominance the dominance graph compactly displays the dominance structure of all alternatives thus it can be used for aiding the selection of preferable alternatives

a consistency improving method in the analytic hierarchy process in this paper we propose a method to modify a given comparison matrix by which the consistency ratio cr value of the modified matrix is less than that of the original one and give an algorithm to derive a positive reciprocal matrix with acceptable consistency i e cr 0 1 then the convergence theorem for the given algorithm is established and its practicality is shown by some examples

algorithms for improving consistency or consensus of reciprocal 0 1 valued preference relations we investigate the consistency and consensus of reciprocal 0 1 valued preference relations also called fuzzy preference relations by many authors based on the multiplicative consistency property which is an important issue in fuzzy set theory an algorithm is first developed to improve the consistency level of a reciprocal 0 1 valued preference relation and the corresponding algorithm for the incomplete reciprocal 0 1 valued preference relation is also developed we further propose the consensus improving algorithms for individual reciprocal 0 1 valued preference relations or incomplete ones the convergence and robustness of the algorithms are proven and some important conclusions are obtained in addition the proposed algorithms can improve the consistency or consensus of reciprocal 0 1 valued preference relations with less interactions with the decision makers which can save a lot of time and obtain the results quickly

chaos hyperchaos transition the chaos hyperchaos transition occurs when the second lyapunov exponent becomes positive we argue that this transition is mediated by changes in the stability of an infinite number of unstable periodic orbits embedded in the chaotic attractor bifurcations of unstable periodic orbits occur in the neighborhood of the chaos hyperchaos transition point where we observe unstable variable dimensionality we give evidence that the chaos hyperchaos transition is initiated by i the saddle repeller bifurcation of a particular unstable periodic orbit usually of low period ii the appearance of a repelling node in the saddle node bifurcation after which the chaotic attractor becomes riddled or iii the absorption of the repeller unstable node or focus originally located out of the attractor by the growing attractor

pairwise comparison based interval analysis for group decision aiding with multiple criteria interval ahp analytic hierarchy process was proposed to obtain interval weights from a given pairwise comparison matrix showing relative importance between criteria in this paper interval ahp is applied to group decision problems interval ahp is first revised suitably for comparing alternatives from the viewpoint that the interval weight vector shows the set of agreeable weight vectors for the decision maker under individual interval weight vectors obtained from individual pairwise comparison matrices three approaches to obtaining a consensus interval weight vector are proposed one is the perfect incorporation approach that obtains consensus interval weight vectors including all individual interval weight vectors by this approach we can count out indubitably inferior alternatives the second is the common ground approach that obtains consensus interval weight vectors included in all individual interval weight vectors by this approach we can find agreeable group preference between alternatives when all individual opinions are similar the third is the partial incorporation approach that obtains consensus interval weight vectors intersecting all individual interval weight vectors by this approach we can find agreeable group preference between alternatives when individual opinions are not similar the usefulness of the proposed three approaches is demonstrated by simple numerical examples

riddling and chaotic synchronization of coupled piecewise linear lorenz maps abstract we investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise linear lorenz maps riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to another basin in an arbitrarily fine scale which has serious consequences on the predictability of the final state for such a coupled system we found that there are wide parameter intervals for which two piecewise linear lorenz maps exhibit riddled basins globally or locally which indicates that there are riddled basins in coupled lorenz equations as previously suggested by numerical experiments the use of piecewise linear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

robust estimation of priorities in the ahp abstract a pairwise comparison matrix of the analytic hierarchy process ahp is considered as a contingency table that helps to identify unusual or false data elicited from a judge special techniques are suggested for robust estimation of priority vectors they include transformation of a saaty matrix to matrix of shares of preferences and solving an eigenproblem designed for the transformed matrices we also introduce an optimizing objective that produces robust priority estimation numerical results are compared using the ahp with these differing approaches the comparison demonstrates that robust estimations yield priority vectors not prone to influence of possible errors among the elements of a pairwise comparison matrix

parametric local multiview hamming distance metric learning abstract learning an appropriate distance metric is a crucial problem in pattern recognition to confront with the scalability issue of massive data hamming distance on binary codes is advocated since it permits exact sub linear knn search and meanwhile shares the advantage of efficient storage in this paper we study hamming metric learning in the context of multimodal data for cross view similarity search we present a new method called parametric local multiview hamming metric plmh which learns multiview metric based on a set of local hash functions to locally adapt to the data structure of each modality to balance locality and computational efficiency the hash projection matrix of each instance is parameterized with guaranteed approximation error bound as a linear combination of basis hash projections associated with a small set of anchor points the weak supervisory information side information provided by pairwise and triplet constraints are incorporated in a coherent way to achieve semantically effective hash codes a local optimal conjugate gradient algorithm with orthogonal rotations is designed to learn the hash functions for each bit and the overall hash codes are learned in a sequential manner to progressively minimize the bias experimental evaluations on cross media retrieval tasks demonstrate that plmh performs competitively against the state of the art methods

synchronization and partial synchronization of linear maps abstract we study synchronization of low dimensional d 2 3 4 chaotic piecewise linear maps that are coupled bidirectionally for bernoulli maps we find lyapunov exponents and locate the synchronization transition which numerically is found to be discontinuous despite continuously vanishing lyapunov exponent s for tent maps a limit of stability of the synchronized state is used to locate the synchronization transition that numerically is found to be continuous for nonidentical tent maps at the partial synchronization transition the probability distribution of the synchronization error is shown to develop highly singular behavior we suggest that for nonidentical bernoulli maps and perhaps some other discontinuous maps partial synchronization is merely a smooth crossover rather than a well defined transition more subtle analysis in the d 4 case locates the point where the synchronized state becomes stable in some cases however a riddled basin attractor appears and synchronized and chaotic behaviors coexist

a scalable kernel based semisupervised metric learning algorithm with out of sample generalization ability in recent years metric learning in the semisupervised setting has aroused a lot of research interest one type of semisupervised metric learning utilizes supervisory information in the form of pairwise similarity or dissimilarity constraints however most methods proposed so far are either limited to linear metric learning or unable to scale well with the data set size in this letter we propose a nonlinear metric learning method based on the kernel approach by applying low rank approximation to the kernel matrix our method can handle significantly larger data sets moreover our low rank approximation scheme can naturally lead to out of sample generalization experiments performed on both artificial and real world data show very promising results

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

consistency analysis of triangular fuzzy reciprocal preference relations abstract in order to simulate the uncertainty associated with impression or vagueness a decision maker may give her his judgments by means of triangular fuzzy reciprocal preference relations in the process of decision making the study of their consistency becomes a very important aspect to avoid a misleading solution based on the reciprocity property this paper proposes a new definition of consistent triangular fuzzy reciprocal preference relations the new definition is different from that reduced by consistent fuzzy reciprocal preference relations proposed by buckley 1985 the properties of consistent triangular fuzzy reciprocal preference relations in the light of the new definition are studied in detail in addition the shortcomings of the proof procedure of the proposition given by wang and chen 2008 are pointed out and the proposition is reproved by using the new definition of consistent triangular fuzzy reciprocal preference relations finally using the n 1 restricted comparison ratios a method for obtaining consistent triangular fuzzy reciprocal preference relations is proposed and an algorithm is shown to make a consistent decision ranking numerical results are further calculated to illustrate the new definition and the obtained algorithm

fuzzy rationality measures fuzzy preference relations formalize intensity of individual preferences over fixed sets of alternatives it is therefore natural to extend to fuzzy preferences the notion of rationality or consistency with this goal in mind we address in this paper the problem of giving an axiomatic basis for defining the concept of fuzzy rationality specifically we establish a collection of conditions that any fuzzy rationality measure must satisfy some examples of fuzzy rationality measures are then given and analyzed

role of invariant and minimal absorbing areas in chaos synchronization in this paper the method of critical curves a tool for the study of the global dynamical properties of two dimensional noninvertible maps is applied to the study of chaos synchronization and related phenomena of riddling blowout and on off intermittency a general procedure is suggested in order to obtain the boundary of a particular two dimensional compact trapping region called absorbing area containing the onedimensional chaotic set on which synchronized dynamics occur the main purpose of the paper is to show that only invariant and minimal absorbing areas are useful to characterize the global dynamical behavior of the dynamical system when a milnor attractor with locally riddled basin or a chaotic saddle exists and may strongly influence the effects of riddling and blowout bifurcations some examples are given for a system of two coupled logistic maps and some practical methods and numerical tricks are suggested in order to ascertain the properties of invariance and minimality of an absorbing area some general considerations are given concerning the transition from locally riddled to globally riddled basins and the role of the absorbing area in the occurrence of such transition is discussed s1063 651x 98 11611 2

a method based on multiobjective optimization for deriving a ranking from a fuzzy preference relation abstract methods for deriving final ranking from a fuzzy preference relation do not perform well in presence of irrelevant alternatives or in case of complex graphs with numerous circuits a new method for improving the quality of their prescriptions is proposed here it rests on the idea of reducing differences between a global model of preferences and a final ranking via multiobjective optimization this proposal is also more robust than others in relation to irrelevant alternatives it can be seen as an intent of reconciling two schools of thought related to decision aid one approach accepts the fuzziness of preferences the other is based on a system of axioms that model a normative rationality

a goal programming approach to group decision making based on multiplicative preference relations and fuzzy preference relations abstract this paper proposes a goal programming approach to solve group decision making gdm problems where the preference information on alternatives provided by decision makers is represented in two different formats i e multiplicative preference relations and fuzzy preference relations in order to narrow the gap between the collective opinion and each decision maker s opinion a linear goal programming model is constructed to integrate the two different formats of preference relations and to compute the collective ranking values of the alternatives thus the ranking of alternatives or selection of the most desirable alternative s is obtained directly from the computed collective ranking values a numerical example is also used to illustrate the applicability of the proposed approach

distance metric learning for large margin nearest neighbor classification the accuracy of k nearest neighbor knn classification depends significantly on the metric used to compute distances between different examples in this paper we show how to learn a mahalanobis distance metric for knn classification from labeled examples the mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes knn classification using euclidean distances in our approach the metric is trained with the goal that the k nearest neighbors always belong to the same class while examples from different classes are separated by a large margin as in support vector machines svms the margin criterion leads to a convex optimization based on the hinge loss unlike learning in svms however our approach requires no modification or extension for problems in multiway as opposed to binary classification in our framework the mahalanobis distance metric is obtained as the solution to a semidefinite program on several data sets of varying size and difficulty we find that metrics trained in this way lead to significant improvements in knn classification sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster we show how to learn and combine these local metrics in a globally integrated manner

transcritical riddling in a system of coupled maps the transition from fully synchronized behavior to two cluster dynamics is investigated for a system of n globally coupled chaotic oscillators by means of a model of two coupled logistic maps an uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system while the transverse period doubling bifurcation remains essentially unaffected by this asymmetry the transverse pitchfork bifurcation is turned into a saddle node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability we show that the transcritical riddling transition is always hard for this we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle node bifurcation undergo and show how the manifolds of these cycles control the magnitude of asynchronous bursts in the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters the transcritical riddling will be replaced by two subsequent saddle node bifurcations or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold in this way the transcritical riddling bifurcation is substituted by a symmetry breaking bifurcation which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state

some induced ordered weighted averaging operators and their use for solving group decision making problems based on fuzzy preference relations abstract in r r yager d p filev operations for granular computing mixing words and numbers in proceedings of the fuzz ieee world congress on computational intelligence anchorage 1998 pp 123 128 yager and filev introduced the induced ordered weighted averaging iowa operator in this paper we provide some iowa operators to aggregate fuzzy preference relations in group decision making gdm problems these iowa operators when guided by fuzzy linguistic quantifiers allow the introduction of some semantics or meaning in the aggregation and therefore allow for a better control over the aggregation stage developed in the resolution process of the gdm problems in particular we present the importance iowa i iowa operator which applies the ordering of the argument values based upon the importance of the information sources the consistency iowa c iowa operator which applies the ordering of the argument values based upon the consistency of the information sources and the preference iowa p iowa operator which applies the ordering of the argument values based upon the relative preference values associated to each one of them we provide a procedure to deal with ties in respect to the ordering induced by the application of one of these iowa operators it consists of a sequential application of the above iowa operators we also present a selection process for gdm problems based on the concept of fuzzy majority and the above three iowa operators finally we analyse the reciprocity and consistency properties of the collective fuzzy preference relations obtained using iowa operators

group decision making based on multiplicative consistent reciprocal preference relations the main aim of this paper is to investigate the consistency and consensus of multiplicative consistent reciprocal preference relations based on the multiplicative consistency property a straightforward method to obtain the priority vector for multiplicative consistent reciprocal preference relation is introduced together with some of its desired properties in addition some interesting properties on consistency and consensus for reciprocal preference relations are further investigated a consensus optimization model for group decision making with reciprocal preference relations is proposed which enables the decision makers to reach consensus with the highest overall consensus level numerical examples are provided to make a discussion and comparison with some existing similar methods

riddling bifurcations in coupled piecewise linear maps abstract a mechanism for riddling bifurcations in the system of coupled piecewise linear maps is described we give sufficient conditions for the occurrence of locally and globally riddled basins based on the properties of absorbing areas of the chaotic attractors on the invariant manifold it is also shown that riddled basins are preserved upon bifurcation of the chaotic attractors as long as the attractor after bifurcation is located in the absorbing area of the attractor before bifurcation

fuzzy relational inequalities and equations fuzzy quasi orders closures and openings of fuzzy sets the paper deals with systems of fuzzy relation equations known in the literature as eigen fuzzy set equations as well as with systems of related fuzzy relation inequalities our main results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities and algorithms for computing the greatest solutions to the considered systems of fuzzy relation equations the systems are studied in the framework of complete residuated lattices as the structure of membership values by means of fuzzy quasi orders and closures and openings on a collection of fuzzy sets