using parametric classification trees for model selection with applications to financial risk management abstract we describe two parametric classification tree methods which allow formal selection of a member of a class of generalised distributions in the paper we consider generalised beta distributions for non negative random variables and the generalised skew student distribution for random variables distributed on the real line we introduce a class of symmetric generalised multivariate student distributions members of which may also be selected using the classification trees we present two versions of the parametric classification tree specific to general and general to specific we apply the classification methods to daily returns on stocks from a selection of 15 major mid cap and emerging markets the results show that the majority of return distributions follow student s t but that a non negligible minority follow a symmetric generalised student distribution we confirm a well known stylised fact about skewness it tends not to be persistent by contrast kurtosis is persistent using the symmetric generalised multivariate student distribution we present a risk management study based on efficient portfolios constructed from ukftse250 stocks and specifically concerned with the computation of value at risk the case study demonstrates that the model selection procedures based on the classification trees lead to more accurate computation of var than those based on the normal distribution or on non parametric approaches the study also shows that the normal distribution may be used for var computations for larger portfolios when the holding period is longer

entropy constrained vector quantization an iterative descent algorithm based on a lagrangian formulation for designing vector quantizers having minimum distortion subject to an entropy constraint is discussed these entropy constrained vector quantizers ecvqs can be used in tandem with variable rate noiseless coding systems to provide locally optimal variable rate block source coding with respect to a fidelity criterion experiments on sampled speech and on synthetic sources with memory indicate that for waveform coding at low rates about 1 bit sample under the squared error distortion measure about 1 6 db improvement in the signal to noise ratio can be expected over the best scalar and lattice quantizers when block entropy coded with block length 4 even greater gains are made over other forms of entropy coded vector quantizers for pattern recognition it is shown that the ecvq algorithm is a generalization of the k means and related algorithms for estimating cluster means in that the ecvq algorithm estimates the prior cluster probabilities as well experiments on multivariate gaussian distributions show that for clustering problems involving classes with widely different priors the ecvq outperforms the k means algorithm in both likelihood and probability of error

equipartition and mean square responses in large undamped structures it is shown that the smoothed spectral energy density at one point in a large complex structure may be approximated in a simple manner as proportional to the frequency smoothed admittance at the receiver and at the source and inversely proportional to the global modal density thus the mean square response may be estimated with little computational burden knowing only the local properties at source and receiver and the size of the system the approximate predictions are compared with the results of direct numerical simulations and found to be accurate except in the presence of anderson localization work supported by nsf

optimal partitioning for classification and regression trees an iterative algorithm that finds a locally optimal partition for an arbitrary loss function in time linear in n for each iteration is presented the algorithm is a k means like clustering algorithm that uses as its distance measure a generalization of kullback s information divergence moreover it is proven that the globally optimal partition must satisfy a nearest neighbour condition using divergence as the distance measure these results generalize similar results of l breiman et al 1984 to an arbitrary number of classes or regression variables and to an arbitrary number of bills experimental results on a text to speech example are provided and additional applications of the algorithm including the design of variable combinations surrogate splits composite nodes and decision graphs are suggested

an interpretable classification rule mining algorithm obtaining comprehensible classifiers may be as important as achieving high accuracy in many real life applications such as knowledge discovery tools and decision support systems this paper introduces an efficient evolutionary programming algorithm for solving classification problems by means of very interpretable and comprehensible if then classification rules this algorithm called the interpretable classification rule mining icrm algorithm is designed to maximize the comprehensibility of the classifier by minimizing the number of rules and the number of conditions the evolutionary process is conducted to construct classification rules using only relevant attributes avoiding noisy and redundant data information the algorithm is evaluated and compared to nine other well known classification techniques in 35 varied application domains experimental results are validated using several non parametric statistical tests applied on multiple classification and interpretability metrics the experiments show that the proposal obtains good results improving significantly the interpretability measures over the rest of the algorithms while achieving competitive accuracy this is a significant advantage over other algorithms as it allows to obtain an accurate and very comprehensible classifier quickly

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

piecewise linear classifiers using binary tree structure and genetic algorithm abstract a linear decision binary tree structure is proposed in constructing piecewise linear classifiers with the genetic algorithm ga being shaped and employed at each nonterminal node in order to search for a linear decision function optimal in the sense of maximum impurity reduction the methodology works for both the two class and multi class cases in comparison to several other well known methods the proposed binary tree genetic algorithm btga is demonstrated to produce a much lower cross validation misclassification rate finally a modified btga is applied to the important pap smear cell classification this results in a spectrum for the combination of the highest desirable sensitivity along with the lowest possible false alarm rate ranging from 27 34 sensitivity 0 62 false alarm rate to 97 02 sensitivity 50 24 false alarm rate from resubstitution validation the multiple choices offered by the spectrum for the sensitivity false alarm rate combination will provide the flexibility needed for the pap smear slide classification

a bernstein type theorem on a randers space we consider finsler spaces with a randers metric f on the three dimensional real vector space where is the euclidean metric and is a 1 form with norm b 0 b 1 by using the notion of mean curvature for immersions in finsler spaces introduced by z shen we obtain the partial differential equation that characterizes the minimal surfaces which are graphs of functions for each b 0 b 1 open image in new window we prove that it is an elliptic equation of mean curvature type then the bernstein type theorem and other properties such as the nonexistence of isolated singularities of the solutions of this equation follow from the theory developped by l simon for b 1 open image in new window the differential equation is not elliptic moreover for every b 1 open image in new window b 1 we provide solutions which describe minimal cones with an isolated singularity at the origin

insights into the energy equipartition principle in large undamped structures the question of energy sharing among complex engineering vibrating systems is still an open problem on the basis of some recent investigations this paper is addressed to the prediction of the equilibrium energies of interacting conservative resonators and to a better understanding of the principle of energy equipartition for large undamped systems the analysis explores the field of linear and nonlinear vibrations the effects of inhomogeneity the weak or the strong coupling as well as the effect of the initial energy distribution among the subsystems the principle of energy equipartition is shown to react in a different fashion to these factors some general arguments supported by the results of numerical experiments enlightening promoting or inhibiting factors to the reaching of energy equipartition conditions are given

face membership authentication using svm classification tree generated by membership based lle data partition this paper presents a new membership authentication method by face classification using a support vector machine svm classification tree in which the size of membership group and the members in the membership group can be changed dynamically unlike our previous svm ensemble based method which performed only one face classification in the whole feature space the proposed method employed a divide and conquer strategy that first performs a recursive data partition by membership based locally linear embedding lle data clustering then does the svm classification in each partitioned feature subset our experimental results show that the proposed svm tree not only keeps the good properties that the svm ensemble method has such as a good authentication accuracy and the robustness to the change of members but also has a considerable improvement on the stability under the change of membership group size

on the ensemble variance of reverberation room transmission functions the effect of spectral rigidity abstract the modal statistics of the gaussian orthogonal ensemble of large random symmetric matrices are applied to reverberation room acoustics these statistics are found to predict spectral fluctuations which are weaker than those predicted by the assumption of modal independence and are also in better agreement with observations

gp coach genetic programming based learning of compact and accurate fuzzy rule based classification systems for high dimensional problems in this paper we propose gp coach a genetic programming based method for the learning of compact and accurate fuzzy rule based classification systems for high dimensional problems gp coach learns disjunctive normal form rules generated by means of a context free grammar coded as one rule per tree the population constitutes the rule base so it is a genetic cooperative competitive learning approach gp coach uses a token competition mechanism to maintain the diversity of the population and this obliges the rules to compete and cooperate among themselves and allows the obtaining of a compact set of fuzzy rules the results obtained have been validated by the use of non parametric statistical tests showing a good performance in terms of accuracy and interpretability

minimal surfaces in a randers sphere with the rotational killing vector field abstract the minimal surfaces in finsler geometry with respect to the busemann hausdorff measure and the holmes thompson measure are called bh minimal and ht minimal surfaces respectively let p 1 p 2 p 3 p 4 be the coordinates of r 4 and s 3 f be a randers sphere of flag curvature k 1 with the navigation data h w where h is the standard sphere metric and w e 0 0 p 4 p 3 0 e 1 is a killing vector field in this paper we study the rotationally invariant minimal surface in s 3 f generated by rotating the curve x s y s z s 0 in the upper half sphere of s 2 around the p 1 p 2 plane s r we first show that such a rotational bh minimal surface in s 3 f is either a great 2 sphere or the catenoid in s 3 h then we give a classification of the rotational ht minimal surfaces where we use the angle data to analyze the solutions of the system of ode that characterizes the ht minimality and prove that such a rotational ht minimal surface must be a great 2 sphere an ht minimal torus or a rotational surface of unduloid type as a special case we obtain a distinguished embedded compact ht minimal torus depending on e the completeness of these surfaces is also studied

effective search for pittsburgh learning classifier systems via estimation of distribution algorithms pittsburgh style learning classifier systems lcss in which an entire candidate solution is represented as a set of variable number of rules combine supervised learning with genetic algorithms gas to evolve rule based classification models it has been shown that standard crossover operators in gas do not guarantee an effective evolutionary search in many sophisticated problems that contain strong interactions between features in this paper we propose a pittsburgh style learning classifier system based on the bayesian optimization algorithm with the aim of improving the effectiveness and efficiency of the rule structure exploration in the proposed method classifiers are generated and recombined at two levels at the lower level single rules contained in classifiers are produced by sampling bayesian networks which characterize the global statistical information extracted from the current promising rules in the search space at the higher level classifiers are recombined by rule wise uniform crossover operators to keep the semantics of rules in each classifier experimental studies on both artificial and real world binary classification problems show that the proposed method converges faster while achieving solutions with the same or even higher accuracy compared with the original pittsburgh style lcss

optimal pruning with applications to tree structured source coding and modeling an algorithm introduced by l breiman et al 1984 in the context of classification and regression trees is reinterpreted and extended to cover a variety of applications in source coding and modeling in which trees are involved these include variable rate and minimum entropy tree structured vector quantization minimum expected cost decision trees variable order markov modeling optimum bit allocation and computer graphics and image processing using quadtrees a concentration on the first of these and a detailed analysis of variable rate tree structured vector quantization are provided it is found that variable rate tree structured vector quantization outperforms not only the fixed rate variety but also full search vector quantization the successive approximation character of variable rate tree structured vector quantization permits it to degrade gracefully if the rate is reduced at the encoder this has applications to the problem of buffer overflow

energy flow models from finite element analysis computationally efficient methods are described by which the results of a finite element analysis of a system may be post processed to form energy flow models yielding time and perhaps frequency average subsystem energies as well as input and dissipated powers the methods are particularly efficient for excitation which is spatially distributed or broadband e g rain on the roof or if the frequency average response is required first a method based on a global finite element analysis is presented this involves a global modal decomposition and a reordering of the subsequent numerical calculations the properties of the distribution of the excitation and the system s mass and stiffness lead to subsystem force distribution mass distribution and stiffness distribution matrices the response is given by a sum of terms involving the interaction of a pair of global modes the contribution of each pair depending on the appropriate elements of the distribution matrices frequency averaging is performed by separating the resulting frequency dependent terms and integrating in most practical cases this integration can be done analytically next an alternative method involving component mode synthesis is described in this individual finite element analyses are performed for each subsystem using here the fixed interface method these are then assembled to perform a global modal analysis with the order of the model being much reduced the consequent results are then post processed in the same way finally a system comprising three coupled plates is presented as a numerical example

mean and mean square responses of a prototypical master fuzzy structure analytical estimates are made for mean and mean square transient responses of a single degree of freedom master oscillator attached to an undamped n degree of freedom random substructure the ensemble averaged response is found to be asymptotically for a large number of substructural degrees of freedom in accord with the predictions of the pierce sparrow russell theory in particular the mean response of the master oscillator manifests an apparent damping corrections to this behavior are also predicted but are found to lie well below the root mean square level of the fluctuations the corrections are therefore for practical purposes unimportant the ensemble average of the square of the response is also investigated and found to take a value at later times that is in accord with simple equipartition arguments advanced in an earlier paper the power spectral density of the late time behavior is shown to be proportional to the square of the power spectrum of the early time response and thus to be a n

a hybrid coevolutionary algorithm for designing fuzzy classifiers rule learning is one of the most common tasks in knowledge discovery in this paper we investigate the induction of fuzzy classification rules for data mining purposes and propose a hybrid genetic algorithm for learning approximate fuzzy rules a novel niching method is employed to promote coevolution within the population which enables the algorithm to discover multiple rules by means of a coevolutionary scheme in a single run in order to improve the quality of the learned rules a local search method was devised to perform fine tuning on the offspring generated by genetic operators in each generation after the ga terminates a fuzzy classifier is built by extracting a rule set from the final population the proposed algorithm was tested on datasets from the uci repository and the experimental results verify its validity in learning rule sets and comparative advantage over conventional methods

minimum cross entropy pattern classification and cluster analysis this paper considers the problem of classifying an input vector of measurements by a nearest neighbor rule applied to a fixed set of vectors the fixed vectors are sometimes called characteristic feature vectors codewords cluster centers models reproductions etc the nearest neighbor rule considered uses a non euclidean information theoretic distortion measure that is not a metric but that nevertheless leads to a classification method that is optimal in a well defined sense and is also computationally attractive furthermore the distortion measure results in a simple method of computing cluster centroids our approach is based on the minimization of cross entropy also called discrimination information directed divergence k l number and can be viewed as a refinement of a general classification method due to kullback the refinement exploits special properties of cross entropy that hold when the probability densities involved happen to be minimum cross entropy densities the approach is a generalization of a recently developed speech coding technique called speech coding by vector quantization

a vector quantization approach to universal noiseless coding and quantization a two stage code is a block code in which each block of data is coded in two stages the first stage codes the identity of a block code among a collection of codes and the second stage codes the data using the identified code the collection of codes may be noiseless codes fixed rate quantizers or variable rate quantizers we take a vector quantization approach to two stage coding in which the first stage code can be regarded as a vector quantizer that quantizes the input data of length n to one of a fixed collection of block codes we apply the generalized lloyd algorithm to the first stage quantizer using induced measures of rate and distortion to design locally optimal two stage codes on a source of medical images two stage variable rate vector quantizers designed in this way outperform standard one stage fixed rate vector quantizers by over 9 db the tail of the operational distortion rate function of the first stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two stage codes we show that there exist two stage universal noiseless codes fixed rate quantizers and variable rate quantizers whose per letter rate and distortion redundancies converge to zero as k 2 n sup 1 log n when the universe of sources has finite dimension k this extends the achievability part of rissanen s theorem from universal noiseless codes to universal quantizers further we show that the redundancies converge as o n sup 1 when the universe of sources is countable and as o n sup 1 spl epsiv when the universe of sources is infinite dimensional under appropriate conditions

an approach to the theoretical background of statistical energy analysis applied to structural vibration rayleigh s classical approach to the study of vibration of systems having a finite number of degrees of freedom is applied to the problem of coupling of subsystems in a complicated structure in order to probe the regions of applicability of the approach to vibration analysis usually known as statistical energy analysis sea the classical method has advantages of simplicity and rigor over previous approaches to the background of sea in certain cases and provides extensions and simplifications in several areas of the theory it also suggests modifications to sea modeling strategy depending on the type of coupling involved even when that coupling is weak so that earlier analyses might be thought to apply

statistical energy analysis and structural fuzzy the concepts and derivations of the effects of a minor or secondary structure on the dynamics of a well defined major or primary structure have been recently presented as a fuzzy structure interacting with a deterministic one on the face of it this appears like a halfway sea system in that one of the two systems is well defined while the other is probabilistic in the sea sense it is therefore interesting to see if a full sea treatment of the system would lead to difference in at least some of the quoted results the second and more important purpose of this paper is to relate the dynamics of potential minor structures to the properties of the fuzzy system since these properties have been presented in some of the fuzzy literature in rather general terms

a deterministic annealing approach for parsimonious design of piecewise regression models a new learning algorithm is proposed for piecewise regression modeling it employs the technique of deterministic annealing to design space partition regression functions while the performance of traditional space partition regression functions such as cart and mars is limited by a simple tree structured partition and by a hierarchical approach for design the deterministic annealing algorithm enables the joint optimization of a more powerful piecewise structure based on a voronoi partition the new method is demonstrated to achieve consistent performance improvements over regular cart as well as over its extension to allow arbitrary hyperplane boundaries comparison tests on several benchmark data sets from the regression literature are provided

a model and numerical method in the medium frequency range for vibroacoustic predictions using the theory of structural fuzzy in linear dynamical analysis of complex mechanical systems the structural fuzzy is defined as the set of minor subsystems that are connected to the master structure but are not accessible by classical modeling the notion of master structure is presently extended to others elements such as an external dense compressible fluid strongly coupled with the primary structure for the low frequency lf dynamical analysis the modeling of the structural fuzzy is commonly made with a system of masses if the lf modeling of the structural fuzzy is applied in the medium frequency mf domain there are some large differences between calculations and experiment it is therefore necessary to take into account internal degrees of freedom of the structural fuzzy a global probabilistic modeling of the structural fuzzy is proposed to improve the calculated estimates of the mf vibrations into the master structure and of the far field radiated by itself in or out of context of the acoustic scattering this paper reviews the author s previous work and introduces the type ii probabilistic constitutive law in this paper 1 a probabilistic modeling of the structural fuzzy is presented 2 two probabilistic constitutive laws of the structural fuzzy are constructed 3 the modeling in the mf range for vibroacoustic predictions using theory of structural fuzzy is developed 4 the fuzzy solution in the mf range is studied and 5 numerical simulations on standard structures and on a submerged complex industrial structure are shown

mining diagnostic rules from clinical databases using rough sets and medical diagnostic model since rule induction methods generate rules whose lengths are the shortest for discrimination between given classes they tend to generate rules too short for medical experts thus these rules are difficult for the experts to interpret from the viewpoint of domain knowledge in this paper the characteristics of experts rules are closely examined and a new approach to generate diagnostic rules is introduced the proposed method focuses on the hierarchical structure of differential diagnosis and consists of the following three procedures first the characterization of decision attributes given classes is extracted from databases and the classes are classified into several generalized groups with respect to the characterization then two kinds of sub rules classification rules for each generalized group and rules for each class within each group are induced finally those two parts are integrated into one rule for each decision attribute the proposed method was evaluated on a medical database the experimental results of which show that induced rules correctly represent experts decision processes

minimality of totally geodesic submanifolds in finsler geometry using the symplectic definition of the holmes thompson volume we prove that totally geodesic submanifolds of a finsler manifold are minimal for this volume thanks to well suited technics the minimality of totally geodesic hypersurfaces see alvarez paiva and berck in adv math 204 2 647 663 2006 and 2 dimensional totally geodesic surfaces see alvarez paiva and berck in adv math 204 2 647 663 2006 ivanov in algebra i analiz 13 1 26 38 2001 had already been proved however the corresponding statement for the hausdorff measure is known to be wrong even in the simplest case of totally geodesic 2 dimensional surfaces in a 3 dimensional finsler manifold see alvarez paiva and berck in adv math 204 2 647 663 2006

energy equipartition and frequency distribution in complex attachments as reported in several recent publications an undamped simple oscillator with a complex attachment that consists of a set of undamped parallel resonators can exhibit unusual energy sharing properties the conservative set of oscillators of the attachment can absorb nearly all the impulsive energy applied to the primary oscillator to which it is connected the key factor in the ability of the attachment to absorb energy with near irreversibility correlates with the natural frequency distribution of the resonators within it the reported results also show that a family of optimal frequency distributions can be determined on the basis of a variational approach minimizing a certain functional related to the system response the present paper establishes a link between these optimal frequency distributions and the energy equipartition principle optimal frequency distributions are those that spread the injected energy as uniformly as possible over the degrees of freedom or over the modes of the system theoretical as well as numerical results presented support this point of view

minimal surfaces in some 4 dimensional general α β spaces abstract in this paper we study minimal submanifolds in some general spaces we firstly establish the equations for minimal submanifolds in a general space then we construct some kinds of minimal surfaces in some 4 dimensional general space

dynamic programming approach to optimization of approximate decision rules this paper is devoted to the study of an extension of dynamic programming approach which allows sequential optimization of approximate decision rules relative to the length and coverage we introduce an uncertainty measure r t which is the number of unordered pairs of rows with different decisions in the decision table t for a nonnegative real number b we consider b decision rules that localize rows in subtables of t with uncertainty at most b our algorithm constructs a directed acyclic graph d b t which nodes are subtables of the decision table t given by systems of equations of the kind attribute value this algorithm finishes the partitioning of a subtable when its uncertainty is at most b the graph d b t allows us to describe the whole set of so called irredundant b decision rules we can describe all irredundant b decision rules with minimum length and after that among these rules describe all rules with maximum coverage we can also change the order of optimization the consideration of irredundant rules only does not change the results of optimization this paper contains also results of experiments with decision tables from uci machine learning repository

combining gp operators with sa search to evolve fuzzy rule based classifiers abstract the genotype phenotype encoding of fuzzy rule bases in ga along with their corresponding crossover and mutation operators can be used by other search schemes improving the behavior of these last ones as a practical consequence of this a simulated annealing based method for inducting both parameters and structure of a fuzzy classifier has been developed the adjacency operator in sa has been replaced with a macromutation taken from tree shaped genotype gas we will show that results of sa search are similar to those of gp in both the efficiency of the learned classifiers and in its linguistic interpretability while the memory consumption of the learning process is lower

the relative variance of the transmission function of a reverberation room the transmission function of a reverberation room is defined to be the square of the modulus of the ratio of the reverberant field sound pressure to the volume velocity of the sound source the input impedance of a reverberation room is defined to be the ratio of the near field sound pressure to the volume velocity of the sound source lyon s formula for the relative variance of the transmission function is extended to cover the case when the transmission function is averaged over multiple source and receiver positions this extended formula reduces easily to lyon s formula for the relative variance of the real part of the input impedance and thus demonstrates the relationship which exists between the two formulae the above formulae are derived under the assumption that the modal frequencies are randomly distributed lyon also derived a formula for the relative variance of the real part of the input impedance when the modal frequencies tend to repel each other it is shown that this formula of lyon is in error and the correct formula is derived the formula for the relative variance of the transmission function is modified so that it will reduce to the formula for the relative variance of the real part of the input impedance derived under this assumption of modal frequency repulsion these formulae for the relative variance of the transmission function are compared with experimental values of relative variance there is reasonable agreement between these formulae and the experimental results the above formulae are extended to cover the case when the transmission function or the real part of the input impedance is averaged over a frequency band the formulae derived in this paper are important for predicting the precision of sound power measurements in a reverberation room

application of information theory to the construction of efficient decision trees the problem of conversion of decision tables to decision trees is treated in most cases the construction of optimal decision trees is an np complete problem and therefore a heuristic approach to this problem is necessary in this heuristic approach an application of information theoretic concepts to construct efficient decision trees for decision tables which may include don t care entries is made in contrast to most of the existing heuristic algorithms this algorithm is systematic and is intuitively appealing from an information theoretic standpoint the algorithm has low design complexity and yet provides near optimal decision trees

transient energy exchange between a primary structure and a set of oscillators return time and apparent damping in this paper we examine the conditions that influence the return time the time it takes before energy returns from a set of satellite oscillators attached to a primary structure two methods are presented to estimate the return time one estimate is based on an analysis of the reaction force on a rigid base by a finite number of oscillators as compared with an infinite number of continuously distributed oscillators the result gives a lower bound estimate for the return time a more accurate estimation results from considering the dynamic behavior of a set of oscillators as waves in a waveguide such an analogy explains energy flow between a primary structure and the oscillators in terms of pseudowaves and shows that a nonlinear frequency distribution of the oscillators leads to pseudodispersive waves the resulting approximate expressions show the influence of the natural frequency distribution within the set of oscillators and of their number on the return time as compared with the asymptotic case of a continuous set with infinite oscillators in the paper we also introduce a new method based on a hilbert envelope to estimate the apparent damping loss factor of the primary structure during the return time considering transient energy flow from the primary structure before any energy reflects back from the attached oscillators the expressions developed for return time and damping factor show close agreement with direct numerical simulations the paper concludes with a discussion of the return time and its relation to apparent damping and optimum frequency distribution within a set of oscillators that maximize these quantities

evolving decision trees with beam search based initialization and lexicographic multi objective evaluation decision tree induction algorithms represent one of the most popular techniques for dealing with classification problems however traditional decision tree induction algorithms implement a greedy approach for node splitting that is inherently susceptible to local optima convergence evolutionary algorithms can avoid the problems associated with a greedy search and have been successfully employed to the induction of decision trees previously we proposed a lexicographic multi objective genetic algorithm for decision tree induction named legal tree in this work we propose extending this approach substantially particularly w r t two important evolutionary aspects the initialization of the population and the fitness function we carry out a comprehensive set of experiments to validate our extended algorithm the experimental results suggest that it is able to outperform both traditional algorithms for decision tree induction and another evolutionary algorithm in a variety of application domains

a bayes optimal approach for partitioning the values of categorical attributes in supervised machine learning the partitioning of the values also called grouping of a categorical attribute aims at constructing a new synthetic attribute which keeps the information of the initial attribute and reduces the number of its values in this paper we propose a new grouping method modl founded on a bayesian approach the method relies on a model space of grouping models and on a prior distribution defined on this model space this results in an evaluation criterion of grouping which is minimal for the most probable grouping given the data i e the bayes optimal grouping we propose new super linear optimization heuristics that yields near optimal groupings extensive comparative experiments demonstrate that the modl grouping method builds high quality groupings in terms of predictive quality robustness and small number of groups

minimal surfaces of rotation in finsler space with a randers metric we consider finsler spaces with a randers metric f on the three dimensional real vector space where is the euclidean metric and bdx3 is a 1 form with norm b 0 b 1 by using the notion of mean curvature for immersions in finsler spaces introduced by z shen we get the ordinary differential equation that characterizes the minimal surfaces of rotation around the x3 axis we prove that for every b 0 b 1 there exists up to homothety a unique forward complete minimal surface of rotation the surface is embedded symmetric with respect to a plane perpendicular to the rotation axis and it is generated by a concave plane curve moreover for every there are non complete minimal surfaces of rotation which include explicit minimal cones

rate distortion speech coding with a minimum discrimination information distortion measure an information theory approach to the theory and practice of linear predictive coded lpc speech compression systems is developed it is shown that a traditional lpc system can be viewed as a minimum distortion or nearest neighbor system where the distortion measure is a minimum discrimination information between a speech process model and an observed frame of actual speech this distortion measure is used in an algorithm for computer aided design of block source codes subject to a fidelity criterion to obtain a 750 bits s speech compression system that resembles an lpc system but has a much lower rate a larger memory requirement and requires no on line lpc analysis quantitative and informal subjective comparisons are made among our system and lpc systems

near irreversibility in a conservative linear structure with singularity points in its modal density through two complementary approaches using modal response and wave propagation the analyses presented here show the conditions under which a decaying impulse response or a nearly irreversible energy trapping takes place in a linear conservative continuous system the results show that the basic foundation of near irreversibility or apparent damping rests upon the presence of singularity points in the modal density of dynamic systems or analogously in the wave stopping properties associated with these singularities to illustrate the concept of apparent damping in detail a simple undamped beam is modified to introduce a singularity point in its modal density distribution simulations show that a suitable application of a compressive axial force to an undamped beam placed on an elastic foundation attenuates its impulse response with time and develops the characteristics of a nearly irreversible energy trap

inferring decision trees using the minimum description length principle abstract we explore the use of rissanen s minimum description length principle for the construction of decision trees empirical results comparing this approach to other methods are given

dynamics of structures coupled with elastic media a review of numerical models and methods abstract this paper reviews issues and developments in the field of structure environment interaction problems in which the environment is an elastic body possibly unbounded it covers in particular the fields of soil structure interaction ground borne noise and vibration emitted by transportation systems and wave diffraction by obstacles in an elastic medium the general setting for a linear bounded structure coupled to an unbounded linear environment through a bounded interface is first recalled and the domain decomposition technique classically used for its description is put up extensions for the cases of nonlinear structure and uncertain environment are then discussed finally the ongoing research in the fields of unbounded interface moving interface and multiple interfaces are reviewed and summarized

data mining with genetic algorithms on binary trees abstract this paper focuses on the automatic interaction detection aid technique which belongs to the class of decision tree data mining techniques the aid technique explains the variance of a dependent variable through an exhaustive and repeated search of all possible relations between the binary predictor variables and the dependent variable this search results in a tree in which non terminal nodes represent the binary predictor variables edges represent the possible values of these predictor variables and terminal nodes or leafs correspond to classes of subjects despite of being self evident the aid technique has its weaknesses to overcome these drawbacks a technique is developed that uses a genetic algorithm to find a set of diverse classification trees all having a large explanatory power from this set of trees the data analyst is able to choose the tree that fulfils his requirements and does not suffer from the weaknesses of the aid technique the technique developed in this paper uses some specialised genetic operators that are devised to preserve the structure of the trees and to preserve high fitness from being destroyed an implementation of the algorithm exists and is freely available some experiments were performed which show that the algorithm uses an intensification stage to find high fitness trees after that a diversification stage recombines high fitness building blocks to find a set of diverse solutions

anytime learning of decision trees the majority of existing algorithms for learning decision trees are greedy a tree is induced top down making locally optimal decisions at each node in most cases however the constructed tree is not globally optimal even the few non greedy learners cannot learn good trees when the concept is difficult furthermore they require a fixed amount of time and are not able to generate a better tree if additional time is available we introduce a framework for anytime induction of decision trees that overcomes these problems by trading computation speed for better tree quality our proposed family of algorithms employs a novel strategy for evaluating candidate splits a biased sampling of the space of consistent trees rooted at an attribute is used to estimate the size of the minimal tree under that attribute and an attribute with the smallest expected tree is selected we present two types of anytime induction algorithms a contract algorithm that determines the sample size on the basis of a pre given allocation of time and an interruptible algorithm that starts with a greedy tree and continuously improves subtrees by additional sampling experimental results indicate that for several hard concepts our proposed approach exhibits good anytime behavior and yields significantly better decision trees when more time is available

a multiobjective evolutionary programming framework for graph based data mining subgraph mining is the process of identifying concepts describing interesting and repetitive subgraphs within graph based data the exponential number of possible subgraphs makes the problem very challenging existing methods apply a single objective subgraph search with the view that interesting subgraphs are those capable of not merely compressing the data but also enhancing the interpretation of the data considerably usually the methods operate by posing simple constraints or user defined thresholds such as returning all subgraphs whose frequency is above a specified threshold such search approach may often return either a large number of solutions in the case of a weakly defined objective or very few in the case of a very strictly defined objective in this paper we propose a framework based on multiobjective evolutionary programming to mine subgraphs by jointly maximizing two objectives support and size of the extracted subgraphs the proposed methodology is able to discover a nondominated set of interesting subgraphs subject to tradeoff between the two objectives which otherwise would not be achieved by the single objective search besides it can use different specific multiobjective evolutionary programming methods experimental results obtained by three of the latter methods on synthetically generated as well as real life graph based datasets validate the utility of the proposed methodology when benchmarked against classical single objective methods and their previous nonevolutionary multiobjective extensions

the ensemble variance of random noise in a reverberation room the literature contains conflicting results for the ensemble relative variance of the intensity of a frequency band of random noise which has been passed through a reverberation room some theoretical and experimental results suggest that passing a band of noise through a reverberation room has no effect on its ensemble relative variance other theoretical and experimental results show that the ensemble relative variance is doubled this paper shows that the magnitude of the effect depends on the ratio of the integrating time of the detector to the integrating time of the reverberation room if this ratio is small the reverberation room has no effect if the ratio is large the ensemble relative variance is doubled this explains why conflicting results have appeared in the literature

complexity of strings in the class of markov sources shannon s self information of a string is generalized to its complexity relative to the class of finite state machine fsm defined sources unlike an earlier generalization the new one is valid for both short and long strings the definition is justified in part by a theorem stating that asymptotically the mean complexity provides a tight lower bound for the mean length of all so called regular codes this also generalizes shannon s noiseless coding theorem for a large subclass of fsm sources a simple algorithm is described for computing the complexity

theoretical foundations of apparent damping phenomena and nearly irreversible energy exchange in linear conservative systems this paper discusses a class of unexpected irreversible phenomena that can develop in linear conservative systems and provides a theoretical foundation that explains the underlying principles recent studies have shown that energy can be introduced to a linear system with near irreversibility or energy within a system can migrate to a subsystem nearly irreversibly even in the absence of dissipation provided that the system has a particular natural frequency distribution the present work introduces a general theory that provides a mathematical foundation and a physical explanation for the near irreversibility phenomena observed and reported in previous publications inspired by the properties of probability distribution functions the general formulation developed here is based on particular properties of harmonic series which form the common basis of linear dynamic system models the results demonstrate the existence of a special class of linear nondissipative dynamic systems that exhibit nearly irreversible energy exchange and possess a decaying impulse response in addition to uncovering a new class of dynamic system properties the results have far reaching implications in engineering applications where classical vibration damping or absorption techniques may not be effective furthermore the results also support the notion of nearly irreversible energy transfer in conservative linear systems which until now has been a concept associated exclusively with nonlinear systems

nontrivial minimal surfaces in a class of finsler spheres of vanishing s curvature abstract the minimal surface theory in finsler geometry deserves to be well developed as that in riemannian geometry in this paper we derive the mean curvature of submanifolds in a general manifold by considering the busemann hausdorff measure and holmes thompson measure respectively we then study the rotationally invariant minimal surfaces in the finsler 3 sphere endowed with an metric f k k k k k 1 where is a smooth function s 3 k is the berger sphere e 4 k 1 and k is a killing one form of constant length along the hopf fibers of s 3 we define the energy of the minimal surfaces and by using the volume ratio function introduced by the author and y b shen we give the explicit local expressions of the rotationally invariant bh minimal and ht minimal surfaces in such sphere respectively as a special case we give a detailed study of the rotationally invariant ht minimal surfaces in the 3 sphere with square metric

weighted universal image compression we describe a general coding strategy leading to a family of universal image compression systems designed to give good performance in applications where the statistics of the source to be compressed are not available at design time or vary over time or space the basic approach considered uses a two stage structure in which the single source code of traditional image compression systems is replaced with a family of codes designed to cover a large class of possible sources to illustrate this approach we consider the optimal design and use of two stage codes containing collections of vector quantizers weighted universal vector quantization bit allocations for jpeg style coding weighted universal bit allocation and transform codes weighted universal transform coding further we demonstrate the benefits to be gained from the inclusion of perceptual distortion measures and optimal parsing the strategy yields two stage codes that significantly outperform their single stage predecessors on a sequence of medical images weighted universal vector quantization outperforms entropy coded vector quantization by over 9 db on the same data sequence weighted universal bit allocation outperforms a jpeg style code by over 2 5 db on a collection of mixed test and image data weighted universal transform coding outperforms a single data optimized transform code which gives performance almost identical to that of jpeg by over 6 db

look ahead based fuzzy decision tree induction decision tree induction is typically based on a top down greedy algorithm that makes locally optimal decisions at each node due to the greedy and local nature of the decisions made at each node there is considerable possibility of instances at the node being split along branches such that instances along some or all of the branches require a large number of additional nodes for classification in this paper we present a computationally efficient way of incorporating look ahead into fuzzy decision tree induction our algorithm is based on establishing the decision at each internal node by jointly optimizing the node splitting criterion information gain or gain ratio and the classifiability of instances along each branch of the node simulations results confirm that the use of the proposed look ahead method leads to smaller decision trees and as a consequence better test performance

a hybrid method for the vibration analysis of complex structural acoustic systems a new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a global set and a local set the global equations of motion are formulated and solved in a standard deterministic manner although due account is taken of the presence of the local degrees of freedom via an approach which is analogous to fuzzy structure theory the local equations of motion are formulated and solved by using statistical energy analysis sea with due account being taken of power input from the global degrees of freedom the method can be considered to encompass a number of existing analysis techniques and to form a flexible framework within which a number of detailed modeling strategies can be devised a simple rod system provides an initial application and it is shown that the method yields very good results from low to high frequency excitation