kernel based hard clustering methods in the feature space with automatic variable weighting abstract this paper presents variable wise kernel hard clustering algorithms in the feature space in which dissimilarity measures are obtained as sums of squared distances between patterns and centroids computed individually for each variable by means of kernels the methods proposed in this paper are supported by the fact that a kernel function can be written as a sum of kernel functions evaluated on each variable separately the main advantage of this approach is that it allows the use of adaptive distances which are suitable to learn the weights of the variables on each cluster providing a better performance moreover various partition and cluster interpretation tools are introduced experiments with synthetic and benchmark datasets show the usefulness of the proposed algorithms and the merit of the partition and cluster interpretation tools

evaluation of similarity models for expected utility violations a body of work proposes a decision cost argument to explain expected utility eu violations based on pair similarity these similarity models suggest various measures over the risky pairs that define decision costs and benefits this paper assesses the empirical modeling success of these similarity measures in explaining risky choice patterns showing eu independence violations we also compare model fit for these similarity models relative to eu and to a selected generalized eu model although the candidate models exhibit some degree of substitutability our results indicate support for models that use relatively simple measures as instruments for similarity

clustering via kernel decomposition spectral clustering methods were proposed recently which rely on the eigenvalue decomposition of an affinity matrix in this letter the affinity matrix is created from the elements of a nonparametric density estimator and then decomposed to obtain posterior probabilities of class membership hyperparameters are selected using standard cross validation methods

high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

multiple burst correcting array codes two families of binary linear multiple burst correcting array codes are presented the codes consist of all possible n sub 1 n sub 2 arrays over gf 2 where the columns have even parity and the rows belong to any given code of length n sub 2 and minimum distance 2t it is shown that if the bits are read out diagonally instead of horizontally each diagonal followed by the preceding one viewed cyclically then the code can correct up to t bursts of length or tn sub 1 1 if each diagonal is followed by the next one the code can correct up to t bursts of length or 2t n 2 1 for t 1 some of these results are already known decoding algorithms are presented and the case t 1 is discussed in more detail

a quantitative measurement of regret theory this paper introduces a method to measure regret theory a popular theory of decision under uncertainty regret theory allows for violations of transitivity and it may seem paradoxical to quantitatively measure an intransitive theory we adopt the trade off method and show that it is robust to violations of transitivity our method makes no assumptions about the shape of the functions reflecting utility and regret it can be performed at the individual level taking account of preference heterogeneity our data support the main assumption of regret theory that people are disproportionately averse to large regrets even when event splitting effects are controlled for the findings are robust similar results were obtained in two measurements using different stimuli the data support the reliability of the trade off method its measurements could be replicated using different stimuli and were not susceptible to strategic responding

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

an empirical test of gain loss separability in prospect theory we investigate a basic premise of prospect theory that the valuation of gains and losses is separable in prospect theory gain loss separability implies that a mixed gamble is valued by summing the valuations of the gain and loss portions of that gamble two experimental studies demonstrate a systematic violation of the double matching axiom an axiom that is necessary for gain loss separability we document a reversal between preferences for mixed gambles and the associated gain and loss gambles mixed gamble a is preferred to mixed gamble b but the gain and loss portions of b are preferred to the gain and loss portions of a the observed choice patterns are consistent with a process in which individuals are less sensitive to probability differences when choosing among mixed gambles than when choosing among either gain or loss gambles

mercer kernel based clustering in feature space the article presents a method for both the unsupervised partitioning of a sample of data and the estimation of the possible number of inherent clusters which generate the data this work exploits the notion that performing a nonlinear data transformation into some high dimensional feature space increases the probability of the linear separability of the patterns within the transformed space and therefore simplifies the associated data structure it is shown that the eigenvectors of a kernel matrix which defines the implicit mapping provides a means to estimate the number of clusters inherent within the data and a computationally simple iterative procedure is presented for the subsequent feature space partitioning of the data

global identification of risk preferences with revealed preference data abstract the concept of parameter identification for a given specification is differentiated from global identification which specification is right first order conditions for production under risk are shown to admit many alternative specification pairs representing risk preferences and either perceived price risk production risk or the deterministic production structure imposing an arbitrary specification on any of the latter three determines which risk preference specification fits a given dataset undermining global identification even when parameter identification is suggested by typical statistics this lack of identification is not relaxed by increasing the number of observations critical implications for estimation of mean variance specifications are derived

obtaining binary perfect codes out of tilings a tiling of mathbb f 2 n considered as a graph gives rise to a perfect code according to a given metric if the basic tile is a metric ball we are concerned with metrics on mathbb f 2 n that are determined by a weight which respects the support of vectors ts metrics and in this case a perfect code is called ts perfect we consider all the tilings of mathbb f 2 n by tiles with up to 8 elements which are classified in the literature and determine which of them give rise to a ts perfect code in the sequence for those tilings that give rise to a perfect code for some ts metric we classify the ts metrics up to equivalence that turn it into a perfect code also we give a general construction to obtain ts perfect codes out of given ts perfect codes by proving that concatenation of two ts perfect codes is by itself a ts perfect code

reformulating decision theory using fuzzy set theory and shafer s theory of evidence abstract utilities and probabilities in decision theory are usually assessed by asking individuals to indicate their preferences between various uncertain choices in this paper we argue that 1 the utility of a consequence can be assessed as the membership function of the consequence in the fuzzy set satisfactory 2 the probability of an event instead of being directly assessed should be inferred from the evidence associated with that event the degree of evidence is quantified using shaferian basic probability assignments in addition we use the heisenberg uncertainty principle to argue for a change in one of the technical assumptions underlying decision theory as a result of this change some kinds of evidence will be observable in certain experiments but unobservable in others since probabilities are defined over the potential outcomes of an experiment they will only be defined over some but not all the evidence as a result the probabilities associated with different experiments could be inconsistent this formulation emphasizes the importance of new distinctions and not just new information in updating probabilities we argue that this formulation addresses many of the observed empirical deviations between decision theory and experiment it also addresses the anomalies of quantum physics we close with a brief discussion of directions for further research

a survey of kernel and spectral methods for clustering clustering algorithms are a useful tool to explore data structures and have been employed in many disciplines the focus of this paper is the partitioning clustering problem with a special interest in two recent approaches kernel and spectral methods the aim of this paper is to present a survey of kernel and spectral clustering methods two approaches able to produce nonlinear separating hypersurfaces between clusters the presented kernel clustering methods are the kernel version of many classical clustering algorithms e g k means som and neural gas spectral clustering arise from concepts in spectral graph theory and the clustering problem is configured as a graph cut problem where an appropriate objective function has to be optimized an explicit proof of the fact that these two paradigms have the same objective is reported since it has been proven that these two seemingly different approaches have the same mathematical foundation besides fuzzy kernel clustering methods are presented as extensions of kernel k means clustering algorithm

parameter free elicitation of utility and probability weighting functions this paper proposes a two step method to successively elicit utility functions and decision weights under rank dependent expected utility theory and its more descriptive version cumulative prospect theory the novelty of the method is that it is parameter free and thus elicits the whole individual preference functional without imposing any prior restriction this method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains concave utility functions are obtained for gains and convex utility functions for losses the elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations the data also show that the probability weighting function for losses is more elevated than for gains

the probability weighting function a probability weighting finction w p is a prominent feature of several non expected utility theories including prospect theoiy and rank dependent models empirical esti mates indicate that w p is regressive first w p p then iv p p s shaped first concave then convex and asymmetrical intersecting the diagonal at about 1 3 the paper states axioms for several w p forms including the compound invariant w p exp ln p 1 0 a 1 which is regressive s shaped and with an invariant fixed point and inflection point at i e 37 the common ratio effect allais 1953 refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects thus a person who prefers a sure gain of 100 000 over a coin toss for 300 000 or nothing might also prefer a one in a million lottery ticket for 300 000 over a two in a million lottery ticket for 100 000 this contradicts expected utility but not common sense there is a world of difference between certainty and a 50 50 shot the difference between one or two chances in a million is negligible the example has all the force and simplicity of classical arguments for nonlinear utility where the utility interval from say 10 and 20 is taken as self evidently greater than the utility interval from 1 000 010 and 1 000 020 both arguments appeal directly to our intuitions about numbers a major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability ratio a minor difference is that in the money domain a constant interval has less impact as the numbers get larger while in the probability domain a constant ratio has less impact as the numbers get smaller putting the two demonstrations side by side like this raises an interesting question namely whether an account of nonlinearity in probabilities can be somehow adapted from classical utility theory modulo a log transformation converting statements about probability ratios into statements about utility intervals indeed in their seminal paper on prospect theory kahneman and tversky 1979 explained the common ratio effect by means of a nonlinear transformation of probabilities into decision weights p w p with log w

random expected utility we develop and analyze a model of random choice and random expected utility a decision problem is a finite set of lotteries that describe the feasible choices a random choice rule associates with each decision problem a probability measure over choices a random utility function is a probability measure over von neumann morgenstern utility functions we show that a random choice rule maximizes some random utility function if and only if it is mixture continuous monotone the probability that a lottery is chosen does not increase when other lotteries are added to the decision problem extreme lotteries that are not extreme points of the decision problem are chosen with probability 0 and linear satisfies the independence axiom

support vector clustering we present a novel clustering method using the approach of support vector machines data points are mapped by means of a gaussian kernel to a high dimensional feature space where we search for the minimal enclosing sphere this sphere when mapped back to data space can separate into several components each enclosing a separate cluster of points we present a simple algorithm for identifying these clusters the width of the gaussian kernel controls the scale at which the data is probed while the soft margin constant helps coping with outliers and overlapping clusters the structure of a dataset is explored by varying the two parameters maintaining a minimal number of support vectors to assure smooth cluster boundaries we demonstrate the performance of our algorithm on several datasets

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

classification of niederreiter rosenbloom tsfasman block codes poset and block metrics were introduced in recent years as alternative metrics to study error correcting codes poset block codes were introduced in 2008 encompassing both poset and block metrics in this paper we study a family of such metrics the niederreiter rosenbloom tsfasman block metrics in this context we classify the classes of equivalent codes describe canonical representatives of each class and develop much of the classical theory of error correcting codes for niederreiter rosenbloom tsfasman block codes including determination of packing radius and classification of mds and perfect codes determination of covering radius and characterization of quasi perfect codes and the description of an algorithm for syndrome decoding

rapid and brief communication evaluation of the performance of clustering algorithms in kernel induced feature space by using a kernel function data that are not easily separable in the original space can be clustered into homogeneous groups in the implicitly transformed high dimensional feature space kernel k means algorithms have recently been shown to perform better than conventional k means algorithms in unsupervised classification however few reports have examined the benefits of using a kernel function and the relative merits of the various kernel clustering algorithms with regard to the data distribution in this study we reformulated four representative clustering algorithms based on a kernel function and evaluated their performances for various data sets the results indicate that each kernel clustering algorithm gives markedly better performance than its conventional counterpart for almost all data sets of the kernel clustering algorithms studied in the present work the kernel average linkage algorithm gives the most accurate clustering results

two dimensional error pattern correcting codes two dimensional 2d cyclic codes are presented which correct any single occurrence of known 2d error patterns within a 2d array of bits applications for this type of codes include storage and display devices the code construction begins with a generation of distinct syndrome sets for all targeted 2d error patterns a method to refine the syndrome sets is then presented for making each syndrome set to contain distinct members thereby guaranteeing full correction capability for the given list of known error patterns using an example construction the effectiveness of the proposed coding approach is demonstrated versus the maximum distance separable mds random error correcting code and known 2d burst correcting codes for a 2d intersymbol interference isi channel that yields a few dominant but relatively large error patterns

on the generalized hamming weights of product codes the rth generalized hamming weight of a linear code is the minimum support size of any r dimensional subcode it has been found useful in the studies of cryptography and trellis coding the authors derive several results on expressing the generalized hamming weights of a product code in terms of those of its component codes they also formulate a general conjecture

using bounded rationality to improve decentralized design the design of large scale complex engineering systems requires interaction and communication between multiple disciplines and decentralized subsystems game theory has been used previously to model interactions between distributed multidisciplinary design subsystems and predict convergence and equilibrium solutions these game theoretic models assume that designers make perfectly rational decisions by selecting solutions from their rational reaction set for convergent decentralized design problems the intersection of the designers rational reaction set results in a nash equilibrium solution where designers may converge if they were making rational choices however this equilibrium solution is rarely optimal from a multi objective optimization perspective further empirical studies reject the claim that decision makers always make rational choices and the concept of bounded rationality is used to explain such behavior in this paper a framework is proposed that uses the idea of bounded rationality in conjunction with set based design metamodeling and multi objective optimization techniques to improve solutions for convergent decentralized design problems through the use of this framework convergent decentralized design problems converge to solutions that are superior to the nash equilibrium

probability weighting and l moments abstract several popular generalizations of expected utility theory cumulative prospect theory rank dependent utility and yaari s dual model allow for non linear transformation of de cumulative probabilities this paper shows an unexpected connection between probability weighting and the statistical theory of l moments specifically cubic probability weighting results in a linear tradeoff between the expected value the first l moment gini 1912 mean difference statistic the second l moment also known as l scale and the third l moment measuring skewness inverse s shaped probability weighting function crossing the 45 line at a probability 0 5 reflects an aversion to the dispersion of outcomes and an attraction to positively skewed distributions

kernel based fuzzy clustering and fuzzy clustering a comparative experimental study in this study we present a comprehensive comparative analysis of kernel based fuzzy clustering and fuzzy clustering kernel based clustering has emerged as an interesting and quite visible alternative in fuzzy clustering however the effectiveness of this extension vis a vis some generic methods of fuzzy clustering has neither been discussed in a complete manner nor the performance of clustering quantified through a convincing comparative analysis our focal objective is to understand the performance gains and the importance of parameter selection for kernelized fuzzy clustering generic fuzzy c means fcm and gustafson kessel gk fcm are compared with two typical generalizations of kernel based fuzzy clustering one with prototypes located in the feature space kfcm f and the other where the prototypes are distributed in the kernel space kfcm k both generalizations are studied when dealing with the gaussian kernel while kfcm k is also studied with the polynomial kernel two criteria are used in evaluating the performance of the clustering method and the resulting clusters namely classification rate and reconstruction error through carefully selected experiments involving synthetic and machine learning repository http archive ics uci edu beta data sets we demonstrate that the kernel based fcm algorithms produce a marginal improvement over standard fcm and gk for most of the analyzed data sets it has been observed that the kernel based fcm algorithms are in a number of cases highly sensitive to the selection of specific values of the kernel parameters

stochastically more risk averse a contextual theory of stochastic discrete choice under risk abstract microeconometric treatments of discrete choice under risk are typically homoscedastic latent variable models specifically choice probabilities are given by preference functional differences given by expected utility rank dependent utility etc embedded in cumulative distribution functions this approach has a problem estimated utility function parameters meant to represent agents degree of risk aversion in the sense of pratt 1964 do not imply a suggested stochastically more risk averse relation within such models a new heteroscedastic model called contextual utility remedies this and estimates in one data set suggest it explains and especially predicts as well as or better than other stochastic models

error correction of multidimensional bursts we present several methods and constructions to generate binary codes for correction of a multidimensional cluster error whose shape can be a box error a lee sphere error or an error with an arbitrary shape our codes have very low redundancy close to optimal and a large range of parameters of arrays and clusters our main results are summarized as follows 1 a construction of two dimensional codes capable to correct a rectangular error with considerably more flexible parameters from previously known constructions this construction is easily generalized for d dimensions 2 a novel method based on d colorings of the d dimensional space for constructing d dimensional codes correcting a d dimensional cluster error of various shapes 3 a transformation of the d dimensional space into another d dimensional space in a way that a d dimensional lee sphere is transformed into a shape located in a d dimensional box of a relatively small size 4 applying the coloring method to correct more efficiently a two dimensional error whose shape is a lee sphere 5 a construction of d dimensional codes capable to correct a d dimensional cluster error of size b in which the number of erroneous positions is relatively small compared to b 6 we present a code which corrects a d dimensional arbitrary cluster error with relatively small redundancy

model selection when there is minimal prior information a number of authors argue that a bayesian posterior odds criterion is appropriate for model selection 2 this paper considers how to derive this criterion when there is minimal prior information we propose minimizing measures of prior information relative to the models in question rather than relative to the parameters of the particular models in so doing we obtain an expression for the odds that is invariant to the parameterization of the particular models and overcomes certain well known finite sample limiting problems we illustrate this procedure using two popular measures of information derived from the well known shannon 26 measure by minimizing these measures with the sample size held fixed we obtain the same model selection criterion that schwarz 25 derived asymptotically for large sample sizes this expression has a number of desirable properties and is computationally no more

singleton type bounds for blot correcting codes consider the transmission of codewords over a channel which introduces dependent errors thinking of two dimensional codewords such errors can be viewed as blots of a particular shape on the codeword for such blots of errors the combinatorial metric was introduced by gabidulin 1971 and it was shown that a code with distance d in combinatorial metric can correct d 2 blots we propose an universal singleton type upper bound on the rate r of a blot correcting code with the distance d in arbitrary combinatorial metric the rate is bounded by r spl les 1 d 1 d where d is the maximum possible distance between two words in this metric

general approach to poset and additive metrics let p n leq p be a poset on n 1 2 ldots n mathbb f q n be the linear space of n tuples over a finite field mathbb f q and w be a weight on mathbb f q in this paper we consider metrics on mathbb f q n which are induced by posets over n and weights over mathbb f q such family of metrics extend both the additive metric induced by the weight w when the poset is an anti chain and the poset metrics when the weight is the hamming weight furthermore the pomset metrics is also a particular case of our construction consequently we provide a simpler approach to these metrics without using the multiset structure originally proposed for the general case we provide a complete description of the groups of linear isometries of these metric spaces in terms of a semi direct product which turns out to be similar to the case of poset metric spaces in particular we re obtain the groups of linear isometries of the poset pomset and additive metric spaces when considering a chain order we develop for codes on these spaces several of the invariants and properties found in the classical coding theory our construction of metrics based on partial orders and any weight over the base field highlights the dependence of the poset metric over mathbb f q n with the hamming metric on mathbb f q and the additive property of its extension on mathbb f q n

minkowski metric feature weighting and anomalous cluster initializing in k means clustering this paper represents another step in overcoming a drawback of k means its lack of defense against noisy features using feature weights in the criterion the weighted k means method by huang et al 2008 2004 2005 5 7 is extended to the corresponding minkowski metric for measuring distances under minkowski metric the feature weights become intuitively appealing feature rescaling factors in a conventional k means criterion to see how this can be used in addressing another issue of k means the initial setting a method to initialize k means with anomalous clusters is adapted the minkowski metric based method is experimentally validated on datasets from the uci machine learning repository and generated sets of gaussian clusters both as they are and with additional uniform random noise features and appears to be competitive in comparison with other k means based feature weighting algorithms

the midweight method to measure attitudes toward risk and ambiguity this paper introduces a parameter free method for measuring the weighting functions of prospect theory and rank dependent utility these weighting functions capture risk attitudes subjective beliefs and ambiguity attitudes our method called the midweight method is based on a convenient way to obtain midpoints in the weighting function scale it can be used both for risk known probabilities and for uncertainty unknown probabilities the resulting integrated treatment of risk and uncertainty is particularly useful for measuring ambiguity i e the difference between uncertainty and risk compared to existing methods to measure weighting functions and attitudes toward uncertainty and ambiguity our method is more efficient and can accommodate violations of expected utility under risk an experiment demonstrates the tractability of our method yielding plausible results such as ambiguity aversion for moderate and high likelihoods but ambiguity seeking for low likelihoods as predicted by ellsberg this paper was accepted by george wu decision analysis

risk and rationality uncovering heterogeneity in probability distortion it has long been recognized that there is considerable heterogeneity in individual risk taking behavior but little is known about the distribution of risk taking types we present a parsimonious characterization of risk taking behavior by estimating a finite mixture model for three different experimental data sets two swiss and one chinese over a large number of real gains and losses we find two major types of individuals in all three data sets the choices of roughly 80 of the subjects exhibit significant deviations from linear probability weighting of varying strength consistent with prospect theory twenty percent of the subjects weight probabilities near linearly and behave essentially as expected value maximizers moreover individuals are cleanly assigned to one type with probabilities close to unity the reliability and robustness of our classification suggest using a mix of preference theories in applied economic modeling

making descriptive use of prospect theory to improve the prescriptive use of expected utility this paper proposes a quantitative modification of standard utility elicitation procedures such as the probability and certainty equivalence methods to correct for commonly observed violations of expected utility traditionally decision analysis assumes expected utility not only for the prescriptive purpose of calculating optimal decisions but also for the descriptive purpose of eliciting utilities however descriptive violations of expected utility bias utility elicitations that such biases are effective became clear when systematic discrepancies were found between different utility elicitation methods that under expected utility should have yielded identical utilities as it is not clear how to correct for these biases without further knowledge of their size or nature most utility elicitations still calculate utilities by means of the expected utility formula this paper speculates on the biases and their sizes by using the quantitative assessments of probability transformation and loss aversion suggested by prospect theory it presents quantitative corrections for the probability and certainty equivalence methods if interactive sessions to correct for biases are not possible then the authors propose to use the corrected utilities rather than the uncorrected ones in prescriptions of optimal decisions in an experiment the discrepancies between the probability and certainty equivalence methods are removed by the authors proposal

investigating generalisations of expected utility theory using experimental data a number of generalizations of the expected utility preference functional are estimated using experimentally generated data involving 100 pairwise choice questions repeated on two separate occasions likelihood ratio tests are conducted to investigate the statistical superiority of the various generalizations and the akaike information criterion is used to distinguish between them the economic superiority of the various generalizations is also explored and the paper concludes that for many subjects the superiority of several of the generalizations is not established copyright 1994 by the econometric society

partitional fuzzy clustering methods based on adaptive quadratic distances this paper presents partitional fuzzy clustering methods based on adaptive quadratic distances the methods presented furnish a fuzzy partition and a prototype for each cluster by optimizing an adequacy criterion based on adaptive quadratic distances these distances change at each algorithm iteration and can either be the same for all clusters or different from one cluster to another moreover various fuzzy partition and cluster interpretation tools are introduced experiments with real and synthetic data sets show the usefulness of these adaptive fuzzy clustering methods and the merit of the fuzzy partition and cluster interpretation tools

a model of probabilistic choice satisfying first order stochastic dominance this paper presents a new model of probabilistic binary choice under risk in this model a decision maker always satisfies first order stochastic dominance if neither lottery stochastically dominates the other alternative a decision maker chooses in a probabilistic manner the proposed model is derived from four standard axioms completeness weak stochastic transitivity continuity and common consequence independence and two relatively new axioms the proposed model provides a better fit to experimental data than do existing models the baseline model can be extended to other domains such as modeling variable consumer demand this paper was accepted by peter wakker decision analysis

generalized hamming weights for linear codes motivated by cryptographical applications the algebraic structure of linear codes from a new perspective is studied by viewing the minimum hamming weight as a certain minimum property of one dimensional subcodes a generalized notion of higher dimensional hamming weights is obtained these weights characterize the code performance on the wire tap channel of type ii basic properties of generalized weights are derived the values of these weights for well known classes of codes are determined and lower bounds on code parameters are obtained several open problems are also listed

mixture symmetry and quadratic utility the independence axiom of expected utility theory has recently been weakened to the betweenness axiom in this paper an even weaker axiom called mixture symmetry is presented the corresponding functional structure is such that utility is a betweenness functional on part of its domain and quadratic in probabilities elsewhere the experimental evidence against betweenness provides one motivation for the more general theory presented here another advantage of the mixture symmetric class of utility functions is that it is sufficiently flexible to permit the disentangling of attitudes towards risk and towards randomization

a novel kernel method for clustering kernel methods are algorithms that by replacing the inner product with an appropriate positive definite function implicitly perform a nonlinear mapping of the input data into a high dimensional feature space in this paper we present a kernel method for clustering inspired by the classical k means algorithm in which each cluster is iteratively refined using a one class support vector machine our method which can be easily implemented compares favorably with respect to popular clustering algorithms like k means neural gas and self organizing maps on a synthetic data set and three uci real data benchmarks iris data wisconsin breast cancer database spam database

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

a new kernel based fuzzy clustering approach support vector clustering with cell growing in this paper the support vector clustering is extended to an adaptive cell growing model which maps data points to a high dimensional feature space through a desired kernel function this generalized model is called multiple spheres support vector clustering which essentially identifies dense regions in the original space by finding their corresponding spheres with minimal radius in the feature space a multisphere clustering algorithm based on adaptive cluster cell growing method is developed whereby it is possible to obtain the grade of memberships as well as cluster prototypes in partition the effectiveness of the proposed algorithm is demonstrated for the problem of arbitrary cluster shapes and for prototype identification in an actual application to a handwritten digit data set

experience weighted attraction learning in normal form games in experience weighted attraction ewa learning strategies have attractions that reflect initial predispositions are updated based on payoff experience and determine choice probabilities according to some rule e g logit a key feature is a parameter that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded relative to reinforcement of chosen strategies according to received payoffs the other key features are two discount rates and which separately discount previous attractions and an experience weight ewa includes reinforcement learning and weighted fictitious play belief learning as special cases and hybridizes their key elements when 0 and 0 cumulative choice reinforcement results when 1 and levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs using three sets of experimental data parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample estimates of are generally around 50 around 8 1 and varies from 0 to reinforcement and belief learning special cases are generally rejected in favor of ewa though belief models do better in some constant sum games ewa is able to combine the best features of previous approaches allowing attractions to begin and grow flexibly as choice reinforcement does but reinforcing unchosen strategies substantially as belief based models implicitly do

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

the predictive utility of generalized expected utility theories many alternative theories have been proposed to explain violations of expected utility eu theory observed in experiments several recent studies test some of these alternative theories against each other formal tests used to judge the theories usually count the number of responses consistent with the theory ignoring systematic variation in responses that are inconsistent we develop a maximum likelihood estimation method which uses all the information in the data creates test statistics that can be aggregated across studies and enables one to judge the predictive utility the fit and parsimony of utility theories analyses of 23 data sets using several thousand choices suggest a menu of theories which sacrifice the least parsimony for the biggest improvement in fit the menu is mixed fanning prospect theory eu and expected value which theories are best is highly sensitive to whether gambles in a pair have the same support eu fits better or not eu fits poorly our method may have application to other domains in which various theories predict different subsets of choices e g refinements of nash equilibrium in noncooperative games

kernel based hard clustering methods with kernelization of the metric and automatic weighting of the variables this paper presents kernel based hard clustering methods with kernelization of the metric and automatic weighting of the variables the proposed methodology is supported by the fact that a kernel function can be written as a sum of kernels evaluated separately on each variable thus in the proposed algorithms dissimilarity measures are obtained as sums of euclidean distances between patterns and centroids computed individually for each variable by means of kernels the main advantage of this approach over the conventional approach is that it allows the use of kernelized adaptive distances which are suitable to learn the weights of the variables dynamically improving the performance of the algorithms moreover various partition and cluster interpretation tools are introduced experiments with a number of benchmark datasets corroborate the usefulness of the proposed algorithms and the merit of the partition and cluster interpretation tools highlightspresents kernel based clustering methods with automatic weighting of the variables kernelized local and global adaptive distances are introduced the proposed algorithms are suitable to learn the weights of the variables partition and cluster interpretation tools are given experiments with several benchmark data sets corroborate the proposed methods

an optimization algorithm for clustering using weighted dissimilarity measures one of the main problems in cluster analysis is the weighting of attributes so as to discover structures that may be present by using weighted dissimilarity measures for objects a new approach is developed which allows the use of the k means type paradigm to efficiently cluster large data sets the optimization algorithm is presented and the effectiveness of the algorithm is demonstrated with both synthetic and real data sets

choice based elicitation and decomposition of decision weights for gains and losses under uncertainty this paper reports the results of an experimental parameter free elicitation and decomposition of decision weights under uncertainty assuming cumulative prospect theory utility functions were elicited for gains and losses at an individual level using the tradeoff method subsequently decision weights were elicited through certainty equivalents of uncertain two outcome prospects furthermore decision weights were decomposed using observable choice instead of invoking other empirical primitives as in previous experimental studies the choice based elicitation of decision weights allows for a quantitative study of their characteristics and also allows among other things for the examination of the sign dependence hypothesis for observed choice under uncertainty our results confirm concavity of the utility function in the gain domain and bounded subadditivity of decision weights and choice based subjective probabilities we also find evidence for sign dependence of decision weights

modeling viewpoint shifts in probabilistic choice a number of mathematical models for overcoming intransitive choice have been proposed and tested in the literature of decision theory this article presents the development of a new stochastic choice model based on multidimensional scaling this allows decision makers to have multiple viewpoints whereas current multidimensional scaling models are based on the assumption that a subject or group of subjects has only one viewpoint the implication of our model is that subjects make an intransitive choice because they are able to shift their viewpoint this paper also presents the maximum likelihood estimation of the proposed model and reanalyzes tversky s gamble experiment data

gain loss separability and coalescing in risky decision making this experiment tested two behavioral properties of risky decision making gain loss separability gls and coalescing cumulative prospect theory cpt implies both properties but the transfer of attention exchange tax model violates both original prospect theory satisfies gls but may or may not satisfy coalescing depending on whether editing rules are assumed a configural form of cpt proposed by wu and markle wu g a b markle 2004 an empirical test of gain loss separability in prospect theory working paper 06 25 04 graduate school of business university of chicago violates gls but satisfies coalescing new tests were designed and conducted to test these theories against specific predictions of a tax model this model used parameters estimated from previous data together with simple new assumptions to extend tax to gambles with negative and mixed consequences contrary to all three forms of prospect theory systematic violations of both coalescing and gls were observed violations of gls were confirmed by analyses of individual data patterns by means of an error model in which each choice can have a different rate of error without estimating any parameters from the new data the tax model predicted the majority choices in the new data fairly well correctly predicting when modal choices would violate gls when they would satisfy it and when indifference would be observed

characterization of metrics induced by hierarchical posets in this paper we consider metrics determined by hierarchical posets and give explicit formulas for the main parameters of a linear code the minimum distance and the packing covering and chebyshev radii of a code we also present ten characterizations of hierarchical poset metrics including new characterizations and simple new proofs to the known ones

mixture models of choice under risk this paper is concerned with estimating preference functionals for choice under risk from the choice behaviour of individuals we note that there is heterogeneity in behaviour between individuals and within individuals by heterogeneity between individuals we mean that people are different in terms of both their preference functionals and their parameters for these functionals by heterogeneity within individuals we mean that the behaviour may be different even by the same individual for the same choice problem we propose methods of taking into account all forms of heterogeneity concentrating particularly on using a mixture model to capture the heterogeneity of preference functionals