on ppm sequences with good autocorrelation properties the problem of designing sequences of q ary pulse position modulation ppm symbols that have good periodic autocorrelation properties is investigated two cases are considered in the first it is assumed that only slot synchronization is present and thus cyclic shifts are one slot at a time in the second ppm symbol synchronization is present in which case cyclic shifts are by one symbol q slots at a time in both cases upper bounds are derived on the maximum peak to sidelobe distance which are shown through a computer search to be nearly tight when symbol synchronization is present the bound reduces to the plotkin bound but it is slightly tighter in general

a direct approach to the exit problem this paper considers the problem of exit for a dynamical system driven by small white noise from the domain of attraction of a stable state a direct singular perturbation analysis of the forward equation is presented based on kramers approach in which the solution to the stationary fokker planck equation is constructed for a process with absorption at the boundary and a source at the attractor in this formulation the boundary and matching conditions fully determine the uniform expansion of the solution without resorting to external selection criteria for the expansion coefficients such as variational principles or the lagrange identity as in our previous theory the exit density and the mean first passage time to the boundary are calculated from the solution of the stationary fokker planck equation as the probability current density and as the inverse of the total flux on the boundary respectively as an application a uniform expansion is constructed for the escape rate in kramers problem o

sensitivity analysis of the stochastically and periodically forced brusselator abstract the problem of sensitivity of nonlinear system limit cycle with respect to small stochastic and periodic disturbances is considered sensitivity analysis on the basis of quasipotential function is performed the quasipotential is used widely in statistical physics for instance by graham for analysis of nonequilibrium thermodynamics problem we consider an application of quasipotential technique to sensitivity problem for the plane orbit case an approximation of quasipotential is expressed by some scalar function this function sensitivity function is introduced as a base tool of a quantitative description for a system response on the external disturbances new cycle characteristics sensitivity factor parameter of stiffness are considered the analysis of the forced brusselator based on sensitivity function is shown from this analysis the critical value of brusselator parameter is found the dynamics of forced brusselator for this critical value is investigated for small stochastic disturbances the burst of response amplitude is shown for small periodic disturbances the period doubling regime of the transition to chaos scenario is demonstrated

modulation and coding for throughput efficient optical systems optical direct detection systems are currently being considered for some high speed intersatellite links where data rates of a few hundred megabits per second are envisioned under power and pulsewidth constraints the authors investigate the capacity cutoff rate and error probability performance of uncoded and trellis coded systems for various modulation schemes and under throughput and power constraints modulation schemes considered are on off keying pulse position modulation ppm overlapping ppm and multipulse combinatorial ppm

on using prototype reduction schemes to enhance the computation of volume based inter class overlap measures in most pattern recognition pr applications it is advantageous if the accuracy or error rate of the classifier can be evaluated or bounded prior to testing it in a real life setting it is also well known that if the two class conditional distributions have a large overlapping volume almost all the available work on overlapping of classes deals with the case when there are only two classes the classification accuracy is poor this is because if we intend to use the classification accuracy as a criterion for evaluating a pr system the points within the overlapping volume tend to lead to maximal misclassification unfortunately the computation of the indices which quantify the overlapping volume is expensive in this vein we propose a strategy of using a prototype reduction scheme prs to approximately but quickly compute the latter in this paper we demonstrate first of all that this is an extremely expedient proposition indeed we show that by completely discarding we are not aware of any reported scheme which discards irrelevant sample training points and which simultaneously attains to an almost comparable accuracy the points not included by the prs we can obtain a reduced set of sample points using which in turn the measures for the overlapping volume can be computed the value of the corresponding figures is comparable to those obtained with the original training set i e the one which considers all the data points even though the computations required to obtain the prototypes and the corresponding measures are significantly less the proposed method has been rigorously tested on artificial and real life datasets and the results obtained are in our opinion quite impressive sometimes faster by two orders of magnitude

domains of competence of the semi naive bayesian network classifiers the motivation for this paper comes from observing the recent tendency to assert that rather than a unique and globally superior classifier there exist local winners hence the proposal of new classifiers can be seen as an attempt to cover new areas of the complexity space of datasets or even to compete with those previously assigned to others several complexity measures for supervised classification have been designed to define these areas in this paper we want to discover which type of datasets defined by certain range values of the complexity measures for supervised classification fits for some of the most well known semi naive bayesian network classifiers this study is carried out on continuous and discrete domains for naive bayes and averaged one dependence estimators aode which are two widely used incremental classifiers that provide some of the best trade offs between error performance and efficiency furthermore an automatic procedure to advise on the best semi naive bnc to use for classification based on the values of certain complexity measures is proposed

multiresolution estimates of classification complexity in this paper we study two measures of classification complexity based on feature space partitioning purity and neighborhood separability the new measures of complexity are compared with probabilistic distance measures and a number of other nonparametric estimates of classification complexity on a total of 10 databases from the university of california irvine uci repository

solution of the boundary value problem for optimal escape in continuous stochastic systems and maps topologies of invariant manifolds and optimal trajectories are investigated in stochastic continuous systems and maps a topological method is introduced that simplifies the solution of boundary value problems the activation energy is calculated as a function of a set of parameters characterizing the initial conditions of the escape path the method is applied explicitly to compute the optimal escape path and the activation energy for a variety of dynamical systems and maps

chaotic phase similarities and recurrences in a damped driven duffing oscillator we report strong evidence of remarkably close periodic repetitions of the structuring of the parameter space of a damped driven duffing oscillator as the amplitude of the drive increases families of period adding cascades and some intricate networks of periodic oscillations embedded in chaotic phases are also found to recur closely as the driving force grows such surprising regularities suggest that some hitherto unknown renormalization mechanism may be operating in higher codimension controlling the alternation of chaos and order in parameter space of certain flows

forced vibration analysis of a multidegree impact vibrator abstract the dynamics of a multidegree impact vibrator subject to harmonic loading is investigated the system is represented by a lumped mass model which hits and rebounds from a rigid wall during vibration the periodic solution to the equations of motion with n forcing cycles and p impacts is formulated the variational equations and the resulting transition matrix for investigating local stability of the periodic solutions are derived a two degree of freedom example is analysed and a variety of motion types are found chaotic windows are present between regions of periodic response and at these boundaries n p motions are prevalent low velocity impacts are evident at exciting frequencies away from the natural frequencies two basins of attraction are computed and the sensitivity to initial conditions is noted the quality of the n p motion is discussed from an engineering application perspective

2p periodic solutions of duffing s equation with negative stiffness this paper investigates the 2 pi periodic solution of the forced damp duffing s equation with negative stiffness the damping is linear and proportional to the velocity and the constant of proportionality is held fixed during the study the forcing is of fixed frequency and has period 2 pi and is taken to be a multiple of cos t the occurrence and nature of the 2 pi periodic solutions are determined as functions of the forcing amplitude

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

a study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning we investigate essential relationships between generalization capabilities and fuzziness of fuzzy classifiers viz the classifiers whose outputs are vectors of membership grades of a pattern to the individual classes the study makes a claim and offers sound evidence behind the observation that higher fuzziness of a fuzzy classifier may imply better generalization aspects of the classifier especially for classification data exhibiting complex boundaries this observation is not intuitive with a commonly accepted position in traditional pattern recognition the relationship that obeys the conditional maximum entropy principle is experimentally confirmed furthermore the relationship can be explained by the fact that samples located close to classification boundaries are more difficult to be correctly classified than the samples positioned far from the boundaries this relationship is expected to provide some guidelines as to the improvement of generalization aspects of fuzzy classifiers

frame synchronization for optical multi pulse pulse position modulation we investigate frame synchronization algorithms for direct detection multi pulse pulse position modulation mppm optical communication systems the optimal rules in a maximum likelihood sense are derived approximations to them that are computationally easier to implement are identified and upper bounds on the synchronization probability are obtained it is seen that the high snr rules have a performance nearly equal to that of the ml rules but provide a significant performance improvement over the simple correlation rules and are virtually as simple to implement for a wide range of signal energies we also address the problem of designing periodic mppm synchronization sequences with good autocorrelation properties based on a maximum worst case peak to sidelobe distance criterion upper bounds on the peak to sidelobe distance for such sequences are derived and a few sequences generated by computer simulations for different synchronization sequence lengths are given

singularities of fluctuational paths for an overdamped two well system driven by white noise abstract noise induced escape from a metastable state in an overdamped double well system is investigated with the wkb approximation employed the pattern of fluctuational paths is given by using the action plot which gives rise to mpeps the pattern is divided into various regions where fluctuational paths inside show qualitatively distinguished characteristics the global quasi potential is calculated and its value at the saddle on the boundary agrees with the one obtained by action plot we show a contour and 3d plot of the quasi potential to illustrate the relative stabilities of metastable states the bifurcations of singularities as the system parameter varies are analyzed by the second order term of the wkb expansion in the vicinity of x axis its asymptotic behavior determines the positions of cusps and furthermore its evolution turns out to delineate the twisting structure of the lagrangian manifold

crossing the quasi threshold manifold of a noise driven excitable system we consider the noise induced escapes in an excitable system possessing a quasi threshold manifold along which there exists a certain point of minimal quasi potential in the weak noise limit the optimal escaping path turns out to approach this particular point asymptotically making it analogous to an ordinary saddle numerical simulations are performed and an elaboration on the effect of small but finite noise is given which shows that the ridges where the prehistory probability distribution peaks are located mainly within the region where the quasi potential increases gently the cases allowing anisotropic noise are discussed and we found that varying the noise term in the slow variable would dramatically raise the whole level of quasi potentials leading to significant changes in both patterns of optimal paths and exit locations

constructive analysis of noise induced transitions for coexisting periodic attractors of the lorenz model we study the stochastically forced lorenz model in the parameter zone admitting two coexisting limit cycles under the transition to chaos via period doubling bifurcations noise induced transitions between both different parts of the single attractor and two coexisting separate attractors are demonstrated the effects of structural stabilization and noise symmetrization are discussed we suggest a stochastic sensitivity function technique for the analysis of noise induced transitions between two coexisting limit cycles this approach allows us to construct the dispersion ellipses of random trajectories for any poincare sections possibilities of our descriptive geometric method for a detailed analysis of noise induced transitions between two periodic attractors of lorenz model are demonstrated

complexity measures of supervised classification problems we studied a number of measures that characterize the difficulty of a classification problem focusing on the geometrical complexity of the class boundary we compared a set of real world problems to random labelings of points and found that real problems contain structures in this measurement space that are significantly different from the random sets distributions of problems in this space show that there exist at least two independent factors affecting a problem s difficulty we suggest using this space to describe a classifier s domain of competence this can guide static and dynamic selection of classifiers for specific problems as well as subproblems formed by confinement projection and transformations of the feature vectors

topological features of large fluctuations to the interior of a limit cycle received 29 october 1996 we investigate the pattern of optimal paths along which a dynamical system driven by weak noise moves with overwhelming probability when it fluctuates far away from a stable state our emphasis is on systems that perform self sustained periodic vibrations and have an unstable focus inside a stable limit cycle we show that in the vicinity of the unstable focus the flow field of optimal paths generically displays a pattern of singularities in particular it contains a switching line that separates areas to which the system arrives along optimal paths of topologically different types the switching line spirals into the focus and has a self similar structure depending on the behavior of the system near the focus it may be smooth or have finite length branches our results are based on an analysis of the topology of the lagrangian manifold for an auxiliary purely dynamical problem that determines the optimal paths we illustrate our theory by studying both theoretically and numerically a van der pol oscillator driven by weak white noise s1063 651x 97 02703 7 many nonlinear dissipative systems display stable periodic oscillations i e their state spaces contain stable limit cycles 1 examples include lasers 2 radiofrequency generators 1 a chemical 3 a and biological 3 b systems in many cases the vibrations are nonsinusoidal as in a multimode laser with strong mode coupling 4 passive optically bistable elements 5 and various sorts of engineering structure 6 fluctuations in periodically oscillating systems play an extremely important role they eventually destroy periodicity of the self sustained oscillations so that the oscillation phase becomes random and a stationary probability distribution in the state space of the system is formed 7 8 this distribution reaches a maximum at the cycle does not vary much along the cycle and falls off rapidly in directions transverse to the cycle the shape of the maximum depends on the character of small transverse fluctuations away from the cycle if the fluctuations are due to the system being perturbed by weak noise of intensity d the transverse falloff will usually be approximately gaussian 7 9 with standard deviation proportional to d 1 2 as d 0

dynamic stability of weakly damped oscillators with elastic impacts and wear the dynamics of non linear oscillators comprising of a single degree of freedom system and beams with elastic two sided amplitude constraints subject to harmonic loads is analyzed the beams are clamped at one end and constrained against unilateral contact sites near the other end the structures are modelled by a bernoulli type beam supported by springs using the finite element method rayleigh damping is assumed symmetric and elastic double impact motions both harmonic and sub harmonic are studied by way of a poincare mapping that relates the states at subsequent impacts stability and bifurcation analyses are performed for these motions and domains of instability are delineated impact work rate which is the rate of energy dissipation to the impacting surfaces is evaluated and discussed in addition an experiment conducted by moon and shaw on the vibration of a cantilevered beam with one sided amplitude constraining stop is modelled bifurcation observed in the experiment could be captured

shared domains of competence of approximate learning models using measures of separability of classes in this work we jointly analyze the performance of three classic artificial neural network models and one support vector machine with respect to a series of data complexity measures known as measures of separability of classes in particular we consider a radial basis function network a multi layer perceptron a learning vector quantization while the sequential minimal optimization method is used to model the support vector machine we consider five measures of separability of classes over a wide range of data sets built from real data which have proved to be very discriminative when analyzing the performance of classifiers we find that two of them allow us to extract common behavior patterns for the four learning methods due to their related nature we obtain rules using these two metrics that describe both good or bad performance of the artificial neural networks and the support vector machine with the obtained rules we characterize the performance of the methods from the data set complexity metrics and therefore their common domains of competence are established using these domains of competence the shared good and bad capabilities of these four models can be used to know if the approximative models will perform well or poorly or if a more complex configuration of the model is needed for a given problem in advance

numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations the computation of periodic orbits of autonomous ordinary differential equations is considered a new method especially suited for computing limit cycles that bifurcate from stationary solutions is established this novel approach is very easy to implement the method requiring the programming of the right hand side only another topic of this paper is the demonstration of how a direct method should be applied in the computation of hopf bifurcation points these methods solve boundary value problems by means of standard software only the methods are tested on four examples arising in different application areas including chemistry and biology

acquisition sequences in ppm communications corresp in pulse position modulation ppm communications an acquisition sequence is needed to establish frame synchronization for subsequent data transmission this sequence must have ppm structure one pulse per frame and desirable autocorrelation properties for its detection the problem of finding aperiodic ppm acquisition sequences having the minimum possible autocorrelation for all off shifted positions is investigated sequences with the maximum possible number of frames have been found up to frame size 15 examples are given for every frame length up to 88 and powers of two up to 1024 an interesting relation between the ppm sequence problem costas and sonar arrays and golomb s ruler is explored

use of hamiltonian mechanics in systems driven by colored noise the evaluation of the path integral representation for stochastic processes in the weak noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics we show that even when the noise is colored these may be put into a hamiltonian form which leads to better insights and improved numerical treatments we concentrate on solving hamilton s equations over an infinite time interval in order to determine the leading order contribution to the mean escape time for a bistable potential the paths may be oscillatory and inherently unstable in which case one must use a multiple shooting numerical technique over a truncated time period in order to calculate the infinite time optimal paths to a given accuracy we look at two systems in some detail the underdamped langevin equation driven by external exponentially correlated noise and the overdamped langevin equation driven by external quasi monochromatic noise we deduce that caustics focusing and bifurcation of the optimal path are general features of all but the simplest stochastic processes

frame synchronization for optical overlapping pulse position modulation systems the maximum likelihood rules for locating data frames in direct detection optical communication systems utilizing overlapping pulse position modulation oppm are derived under two distinct assumptions of symbol and chip synchronization respectively various approximations to the optimal rules are identified as well as upper and lower bounds on the probability of correct synchronization further the problem of sequence design based on a maximum peak to sidelobe distance criterion is studied and upper bounds on peak to sidelobe distance for sequences of oppm symbols are derived some good sequences are obtained through a computer search

stationary probability distribution near stable limit cycles far from hopf bifurcation points we obtain analytic results for the stationary probability distribution in the vicinity of a stable limit cycle for markov systems described by a fokker planck equation or a birth death master equation the results apply best for ranges of parameters removed from hopf bifurcation points as a by product we demonstrate that there holds a liouville like theorem for the stationary probability distribution the product of the velocity along the limit cycle times the area of the cross section of the probability distribution transverse to the cycle is a constant a numerical simulation of a chemical model system with a limit cycle shows good agreement with the analytic results

risk sensitive loss functions for sparse multi category classification problems in this paper we propose two risk sensitive loss functions to solve the multi category classification problems where the number of training samples is small and or there is a high imbalance in the number of samples per class such problems are common in the bio informatics medical diagnosis areas the most commonly used loss functions in the literature do not perform well in these problems as they minimize only the approximation error and neglect the estimation error due to imbalance in the training set the proposed risk sensitive loss functions minimize both the approximation and estimation error we present an error analysis for the risk sensitive loss functions along with other well known loss functions using a neural architecture classifiers incorporating these risk sensitive loss functions have been developed and their performance evaluated for two real world multi class classification problems viz a satellite image classification problem and a micro array gene expression based cancer classification problem to study the effectiveness of the proposed loss functions we have deliberately imbalanced the training samples in the satellite image problem and compared the performance of our neural classifiers with those developed using other well known loss functions the results indicate the superior performance of the neural classifier using the proposed loss functions both in terms of the overall and per class classification accuracy performance comparisons have also been carried out on a number of benchmark problems where the data is normal i e not sparse or imbalanced results indicate similar or better performance of the proposed loss functions compared to the well known loss functions

dynamics of a two degree of freedom periodically forced system with a rigid stop diversity and evolution of periodic impact motions abstract a two degree of freedom periodically forced system with a clearance is considered the correlation between dynamic performance and system parameters is studied to find their feasible matching law the fundamental group of impact motions is defined which have the excitation period and differ by the number p of impacts the generation mechanism of complete and incomplete chattering impact vibration of the system is studied a series of singular points between any two adjacent fundamental impact motions are found at which real grazing and bare grazing bifurcation boundaries of one of them saddle node and period doubling bifurcation boundaries of the other alternately intersect and create two types of transition regions hysteresis and tongue shaped regions subharmonic impact motions are found to regularly appear in the tongue shaped regions based on the sampling ranges of parameters dynamics of the system is studied with emphasis on the influence of system parameters on impact velocities existence regions and correlative distribution of single impact periodic motions by multi parameter and multi performance co simulation analysis

stochastic analysis of a hopf bifurcation master equation approach the effect of inhomogeneous fluctuations in a reaction diffusion system exhibiting a hopf bifurcation is analyzed using the master equation approach a taylor expansion of the logarithm of the stationary probability known as the stochastic potential is calculated this procedure displays marked analogies with the theory of normal forms the critical potential reduced to its local expansion around an arbitrary point of the limit cycle brings out the essential role played by the phase of the oscillating variables a comparison with the langevin analysis of walgraefet al j chem phys 78 6 3043 1983 is performed

recursive support vector machines for dimensionality reduction the usual dimensionality reduction technique in supervised learning is mainly based on linear discriminant analysis lda but it suffers from singularity or undersampled problems on the other hand a regular support vector machine svm separates the data only in terms of one single direction of maximum margin and the classification accuracy may be not good enough in this letter a recursive svm rsvm is presented in which several orthogonal directions that best separate the data with the maximum margin are obtained theoretical analysis shows that a completely orthogonal basis can be derived in feature subspace spanned by the training samples and the margin is decreasing along the recursive components in linearly separable cases as a result a new dimensionality reduction technique based on multilevel maximum margin components and then a classifier with high accuracy are achieved experiments in synthetic and several real data sets show that rsvm using multilevel maximum margin features can do efficient dimensionality reduction and outperform regular svm in binary classification problems

escape problem for irreversible systems the problem of noise induced escape from a metastable state arises in physics chemistry biology systems engineering and other areas the problem is well understood when the underlying dynamics of the system obey detailed balance when this assumption fails many of the results of classical transition rate theory no longer apply and no general method exists for computing the weak noise asymptotic behavior of fundamental quantities such as the mean escape time in this paper we present a general technique for analyzing the weak noise limit of a wide range of stochastically perturbed continuous time nonlinear dynamical systems we simplify the original problem which involves solving a partial differential equation into one in which only ordinary differential equations need be solved this allows us to resolve some old issues for the case when detailed balance holds when it does not hold we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path we also present results on short time behavior and discuss the possibility of ital focusing along the escape path

a semi analytical locally transversal linearization method for non linear dynamical systems an numeric analytical implicit and local linearization methodology called the locally transversal linearization ltl is developed in the present paper for analyses and simulations of non linear oscillators the ltl principle is based on deriving the locally linearized equations in such a way that the tangent space of the linearized equations transversally intersects that of the given non linear dynamical system at that particular point in the state space where the solution vector is sought for purposes of numerical implementation two different numerical schemes namely ltl 1 and ltl 2 schemes based on the ltl methodology are presented both ltl 1 and ltl 2 procedures finally reduce the given set of non linear ordinary differential equations odes to a set of transcendental algebraic equations valid over a short interval of time or over a short segment of the evolving trajectories as projected on the phase space while in the ltl 1 scheme the desired solution vector at a forward time point enters the linearized differential equations as an unknown parameter in the ltl 2 scheme a set of unknown residues enters the linearized system as parameters a limited set of examples involving a few well known single degree of freedom sdof non linear oscillators indicate that the ltl methodology is capable of accurately predicting many complicated non linear response patterns including limit cycles quasi periodic orbits and even strange attractors copyright 2001 john wiley sons ltd

a scaling theory of bifurcations in the symmetric weak noise escape problem we consider two dimensional overdamped double well systems perturbed by white noise in the weak noise limit the most probable fluctuational path leading from either point attractor to the separatrix the most probable escape path or mpep must terminate on the saddle between the two wells however as the parameters of a symmetric double well system are varied a unique mpep may bifurcate into two equally likely mpeps at the bifurcation point in parameter space the activation kinetics of the system become non arrhenius we quantify the non arrhenius behavior of a system at the bifurcation point by using the maslov wkb method to construct an approximation to the quasistationary probability distribution of the system that is valid in a boundary layer near the separatrix the approximation is a formal asymptotic solution of the smoluchowski equation our construction relies on a new scaling theory which yields critical exponents describing weak noise behavior at the bifurcation point near the saddle

non chaotic response of non linear oscillators under combined deterministic and weak stochastic excitations non linear oscillators under harmonic and or weak stochastic excitations are considered in this paper under harmonic excitations alone an analytical technique based on a set of exponential transformations followed by harmonic balancing is proposed to solve for a variety of one periodic orbits the stability boundaries for such orbits in the associated parameter space are constructed using the floquet theory under a combination of harmonic and weak stochastic excitations a stochastic perturbation approach around the deterministic orbit is adopted to obtain response statistics in terms of the evolving moment functions in the present study the stochastic perturbation is assumed to be an additive white noise process and equations for the evolving moments are derived using ito differential rule a fifth order cumulant neglect closure is used to close the infinite hierarchy of moment equations limited numerical results are presented to illustrate the implementation of the proposed scheme the method is found to be quite versatile and admits ready extensions to md o f systems under combined harmonic and white or non white multiplicative or additive random excitations

on the approximate solution of a piecewise nonlinear oscillator under super harmonic resonance abstract an approximate solution for the super harmonic resonance response of a periodically excited nonlinear oscillator with a piecewise nonlinear linear characteristic is constructed using both a matching method and a modified averaging method the validity of the developed analysis is confirmed by comparing the approximate solutions with the results of direct numerical integration of the original equation

domains of competence of fuzzy rule based classification systems with data complexity measures a case of study using a fuzzy hybrid genetic based machine learning method the analysis of data complexity is a proper framework to characterize the tackled classification problem and to identify domains of competence of classifiers as a practical outcome of this framework the proposed data complexity measures may facilitate the choice of a classifier for a given problem the aim of this paper is to study the behaviour of a fuzzy rule based classification system and its relationship to data complexity we use as a case of study the fuzzy hybrid genetic based machine learning method presented in h ishibuchi t yamamoto t nakashima hybridization of fuzzy gbml approaches for pattern classification problems ieee transactions on systems man and cybernetics part b cybernetics 35 2 2005 359 365 we examine several metrics of data complexity over a wide range of data sets built from real data and try to extract behaviour patterns from the results we obtain rules which describe both good or bad behaviours of the fuzzy rule based classification system these rules use values of data complexity metrics in their antecedents so we try to predict the behaviour of the method from the data set complexity metrics prior to its application therefore we can establish the domains of competence of this fuzzy rule based classification system