robust multiple classification of known signals in additive noise an asymptotic weak signal approach the problem of extracting one out of a finite number of possible signals of known form given observations in an additive noise model is considered two approaches are studied either the signal with shortest distance to the observed data or the signal having maximal correlation with some transformation of the observed data is chosen with a weak signal approach the limiting error probability is a monotone function of the pitman efficacy and it is the same for both the distance based and correlation based detectors using the minimax theory of huber it is possible to derive robust choices of distance correlation when the limiting error probability is used as performance criterion this generalizes previous work in the area from two signals to an arbitrary number of signals considered are m type and r type distances and also one dimensional and two dimensional signals some monte carlo simulations are performed to compare the finite sample size error probabilities with the asymptotic error probabilities

improving performance of similarity based clustering by feature weight learning similarity based clustering is a simple but powerful technique which usually results in a clustering graph for a partitioning of threshold values in the unit interval the guiding principle of similarity based clustering is similar objects are grouped in the same cluster to judge whether two objects are similar a similarity measure must be given in advance the similarity measure presented in the paper is determined in terms of the weighted distance between the features of the objects thus the clustering graph and its performance which is described by several evaluation indices defined in the paper will depend on the feature weights the paper shows that by using gradient descent technique to learn the feature weights the clustering performance can be significantly improved it is also shown that our method helps to reduce the uncertainty fuzziness and nonspecificity of the similarity matrix this enhances the quality of the similarity based decision making

on the 2 tuples based genetic tuning performance for fuzzy rule based classification systems in imbalanced data sets when performing a classification task we may find some data sets with a different class distribution among their patterns this problem is known as classification with imbalanced data sets and it appears in many real application areas for this reason it has recently become a relevant topic in the area of machine learning the aim of this work is to improve the behaviour of fuzzy rule based classification systems frbcss in the framework of imbalanced data sets by means of a tuning step specifically we adapt the 2 tuples based genetic tuning approach to classification problems showing the good synergy between this method and some frbcss our empirical results show that the 2 tuples based genetic tuning increases the performance of frbcss in all types of imbalanced data furthermore when the initial rule base built by a fuzzy rule learning methodology obtains a good behaviour in terms of accuracy we achieve a higher improvement in performance for the whole model when applying the genetic 2 tuples post processing step this enhancement is also obtained in the case of cooperation with a preprocessing stage proving the necessity of rebalancing the training set before the learning phase when dealing with imbalanced data

a dual bound algorithm for very fast and exact template matching recently proposed fast template matching techniques employ rejection schemes derived from lower bounds on the match measure this paper generalizes that idea and shows that in addition to lower bounds upper bounds on the match measure can be used to accelerate the search an algorithm is proposed that utilizes both lower and upper bounds to detect the k best matches in an image the performance of this dual bound algorithm is guaranteed it always detects the k best matches theoretical analysis and experimental results show that its runtime compares favorably with previously proposed real time exact template matching schemes

gravitation based classification classification is one of the key issues in the fields of decision sciences and knowledge discovery in this paper we present a new classification method based on gravitational potential energy between particles the basic principle of gravitation based classification gbc algorithm is to find the equilibrium condition of the classifier which is modeled as a classifier line between two groups of fixed particles in the proposed approach the input data is a collection of masses which interact with each other based on newton s universal law of gravitation and the laws of motion we present a convex formulation for this problem that always converges to a global optimum solution the proposed method has been compared with some well known classification approaches and the results confirm the high performance of the proposed method

an optimal global nearest neighbor metric a quadratic metric dao x y x y t ao x y is proposed which minimizes the mean squared error between the nearest neighbor asymptotic risk and the finite sample risk under linearity assumptions a heuristic argument is given which indicates that this metric produces lower mean squared error than the euclidean metric a nonparametric estimate of ao is developed if samples appear to come from a gaussian mixture an alternative parametrically directed distance measure is suggested for nearness decisions within a limited region of space examples of some two class gaussian mixture distributions are included

data gravitation based classification data gravitation based classification dgc is a novel data classification technique based on the concept of data gravitation the basic principle of dgc algorithm is to classify data samples by comparing the data gravitation between the different data classes in the dgc model a kind of force called data gravitation between two data samples is computed data from the same class are combined as a result of gravitation on the other hand data gravitation between different data classes can be compared a larger gravitation from a class means the data sample belongs to a particular class one outstanding advantage of the dgc in comparison with other classification algorithms is its simple classification principle with high performance this makes the dgc algorithm much easier to be implemented feature selection plays an important role in classification problems and a novel feature selection algorithm is investigated based on the idea of dgc and weighted features the proposed method is validated by using 12 well known classification data sets from uci machine learning repository experimental results illustrate that the proposed method is very efficient for data classification and feature selection

correlation coefficient based fast template matching through partial elimination partial computation elimination techniques are often used for fast template matching at a particular search location computations are prematurely terminated as soon as it is found that this location cannot compete with an already known best match location due to the nonmonotonic growth pattern of the correlation based similarity measures partial computation elimination techniques have been traditionally considered inapplicable to speed up these measures in this paper we show that partial elimination techniques may be applied to a correlation coefficient by using a monotonic formulation and we propose basic mode and extended mode partial correlation elimination algorithms for fast template matching the basic mode algorithm is more efficient on small template sizes whereas the extended mode is faster on medium and larger templates we also propose a strategy to decide which algorithm to use for a given data set to achieve a high speedup elimination algorithms require an initial guess of the peak correlation value we propose two initialization schemes including a coarse to fine scheme for larger templates and a two stage technique for small and medium sized templates our proposed algorithms are exact i e having exhaustive equivalent accuracy and are compared with the existing fast techniques using real image data sets on a wide variety of template sizes while the actual speedups are data dependent in most cases our proposed algorithms have been found to be significantly faster than the other algorithms

response of stochastic dynamical systems driven by additive gaussian and poisson white noise solution of a forward generalized kolmogorov equation by a spectral finite difference method abstract a numerical method is given for the solution of the probability density function of the response process of memoryless one and two state dynamical systems having polynomial restoring forces and which are subjected to a combination of gaussian and poisson white noises the method employs the fourier transformed forward generalized kolmogorov equation to arrive at an initial boundary value problem for the characteristic function which is solved using a high order finite difference procedure the probability density function is recovered by numerical inverse fourier transformation several examples are given the results of which are compared with analytical solutions where available and with simulation otherwise

a wreath product group approach to signal and image processing ii convolution correlation and applications for pt i see ibid vol 48 no 1 p 102 32 2000 this paper continues the investigation of the use of spectral analysis on certain noncommutative finite groups wreath product groups in digital signal processing we describe the generalization of discrete cyclic convolution in convolution over these groups and show how it reduces to multiplication in the spectral domain finite group based convolution is defined in both the spatial and spectral domains and its properties established we pay particular attention to wreath product cyclic groups and further describe convolution properties from a geometric view point in terms of operations with specific signals and filters group based correlation is defined in a natural way and its properties follow from those of convolution the detection of similarity of perceptually similar signals and an application of correlation the detection of similarity of group transformed signals several examples using images are included to demonstrate the ideas pictorially

classification by pairwise coupling we discuss a strategy for polychotomous classification that involves estimating class probabilities for each pair of classes and then coupling the estimates together the coupling model is similar to the bradley terry method for paired comparisons we study the nature of the class probability estimates that arise and examine the performance of the procedure in real and simulated data sets classifiers used include linear discriminants nearest neighbors adaptive nonlinear methods and the support vector machine

effective lazy learning algorithm based on a data gravitation model for multi label learning in the last decade an increasing number of real world problems surrounding multi label data have appeared and multi label learning has become an important area of research the data gravitation model is an approach that applies the principles of the universal law of gravitation to resolve machine learning problems one advantage of the data gravitation model compared with other techniques is that it is based on simple principles with high performance levels this paper presents a multi label lazy algorithm based on a data gravitation model named mldgc mldgc directly handles multi label data and considers each instance as an atomic data particle the proposed multi label lazy algorithm was evaluated and compared to several state of the art multi label lazy methods on 34 datasets the results showed that our proposal outperformed state of the art lazy methods the experimental results were validated using non parametric statistical tests confirming the effectiveness of this data gravitation model for multi label lazy learning

an averaging principle for stochastic dynamical systems with levy noise abstract the purpose of this paper is to establish an averaging principle for stochastic differential equations with non gaussian levy noise the solutions to stochastic systems with levy noise can be approximated by solutions to averaged stochastic differential equations in the sense of both convergence in mean square and convergence in probability the convergence order is also estimated in terms of noise intensity two examples are presented to demonstrate the applications of the averaging principle and a numerical simulation is carried out to establish the good agreement

a fast feature weighting algorithm of data gravitation classification the data gravitation classification dgc model is a new classification method that has gained great research interest in recent years feature weights are the key parameters in dgc models because the classification performances of these models are very sensitive to such feature weights the available dgc models use wrapper like algorithms to obtain their optimised feature weights although such algorithms produce high classification accuracies but they contribute to the high computational complexities of the dgc models in this study we propose a fast feature weight algorithm for dgc models called ffw dgc we use the concepts of feature discrimination and redundancy to measure the importance of a feature after which two fuzzy subsets are constructed to respectively represent these concepts next we combine the two fuzzy subsets to compute the feature weights used in gravitational computing we conduct our experiments on 25 standard data sets and 22 imbalance data sets and compare ffw dgc with 11 kinds of classifiers including the swarm intelligence based dgc pso dgc model competitive results of ffw dgc demonstrate that it can obtain high classification accuracies but also hundreds of times of speedup ratios compared with pso dgc

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

probabilistic solution of nonlinear oscillators excited by combined gaussian and poisson white noises abstract the stationary probability density function pdf solution of the stochastic response of nonlinear oscillators is investigated in this paper the external excitation is assumed to be a combination of gaussian and poisson white noises the pdf solution is governed by the generalized kolmogorov equation which is solved by the exponential polynomial closure epc method in order to evaluate the effectiveness of the epc method different nonlinear oscillators are considered in numerical analysis nonlinearity exists either in displacement or in velocity for these nonlinear oscillators the impulse arrival rate mono modal pdf and bi modal pdf are also considered in this study compared to the pdf given by monte carlo simulation the epc method presents good agreement with the simulated result which can also be observed in the tail region of the pdf solution

quadtree structured linear prediction models for image sequence processing a summary is presented of a study on two dimensional linear prediction models for image sequence processing and its application to change detection and scene coding the study focused on two dimensional joint process modeling of interframe relationships the derivation of computationally efficient matching algorithms and the implementation of a block adaptive interframe predictor for use in interframe predictive coding and change detection in the approach presented the spatial nonstationarity is handled by an underlying quadtree segmentation structure a maximum likelihood criterion and a simpler minimum variance criterion are discussed as detection and segmentation rules the results of this research indicate that a constrained joint process model involving only a single gain parameter and a shift parameter is the best tradeoff between performance and computational complexity

a multiple hyper ellipsoidal subclass model for an evolutionary classifier abstract a pattern classification scheme in which the classifier is able to grow and evolve during the operation process is presented the evolutionary property of the classifier is made possible by modeling the pattern vectors in multiple hyper ellipsoidal subclass distributions learning of the classifier takes place at the subclass levels only this property allows the classifier to retain its previously learned patterns while accepting and learning new pattern classes the classifier is suitable to operate in dynamical environments where continuous updating of the pattern class distributions is needed

in defense of one vs all classification we consider the problem of multiclass classification our main thesis is that a simple one vs all scheme is as accurate as any other approach assuming that the underlying binary classifiers are well tuned regularized classifiers such as support vector machines this thesis is interesting in that it disagrees with a large body of recent published work on multiclass classification we support our position by means of a critical review of the existing literature a substantial collection of carefully controlled experimental work and theoretical arguments

template matching in rotated images a rotationally invariant template matching using normalized invariant moments is described it is shown that if normalized invariant moments in circular windows are used then template matching in rotated images becomes similar to template matching in translated images a speedup technique based on the idea of two stage template matching is also described in this technique the zeroth order moment is used in the first stage to determine the likely match positions and the second and third order moments are used in the second stage to determine the best match position among the likely ones

moment preserving pattern matching abstract an accurate template matching algorithm of low computational complexity that facilitates low cost hardware design and vlsi implementation is highly desired by many image processing applications this paper describes a template matching method called moment preserving pattern matching mppm which reduces the computational complexity of template matching significantly and provides several advantages in hardware implementation the methodology is based on the concepts of pairing function and moment preserving quantization the experimental results show that it is computationally fast and accurate in locating the template if noise corruption is not too severe for obtaining a template matching algorithm of high accuracy and robustness against noise and low computational cost mppm is applied to a two stage matching scheme a statistical model for estimating the correlation threshold is also given

maximin projection learning for optimal treatment decision with heterogeneous individualized treatment effects a saline feature of data from clinical trials and medical studies is inhomogeneity patients not only differ in baseline characteristics but also the way they respond to treatment optimal individualized treatment regimes are developed to select effective treatments based on patient s heterogeneity however the optimal treatment regime might also vary for patients across different subgroups in this paper we mainly consider patient s heterogeneity caused by groupwise individualized treatment effects assuming the same marginal treatment effects for all groups we propose a new maximin projection learning for estimating a single treatment decision rule that works reliably for a group of future patients from a possibly new subpopulation based on estimated optimal treatment regimes for all subgroups the proposed maximin treatment regime is obtained by solving a quadratically constrained linear programming qclp problem which can be efficiently computed by interior point methods consistency and asymptotic normality of the estimator is established numerical examples show the reliability of the proposed methodology

strong averaging principle for two time scale non autonomous stochastic fitzhugh nagumo system with jumps in this paper we study an averaging principle for stochastic fitzhugh nagumo system with different time scales driven by cylindrical wiener processes and poisson jumps where the slow equation is non autonomous and the fast equation is autonomous case under suitable assumptions we show that the slow component mean square strongly converges to the solution of the corresponding averaging equation and the rate of the convergence as a by product is also affirmed finally we give some open problems which are derived from this paper

multiple subclass pattern recognition a maximin correlation approach this paper addresses a correlation based nearest neighbor pattern recognition problem where each class is given as a collection of subclass templates the recognition is performed in two stages in the first stage the class is determined templates for this stage are created using the subclass templates assignment into subclasses occurs in the second stage this two stage approach may be used to accelerate template matching in particular the second stage may be omitted when only the class needs to be determined the authors present a method for optimal aggregation of subclass templates into class templates for each class the new template is optimal in that it maximizes the worst case i e minimum correlation with its subclass templates an algorithm which solves this maximin optimization problem is presented and its correctness is proved in addition test results are provided indicating that the algorithm s execution time is polynomial in the number of subclass templates the authors show tight bounds on the maximin correlation the bounds are functions only of the number of original subclass templates and the minimum element in their correlation matrix the algorithm is demonstrated on a multifont optical character recognition problem

an improved path integration method for nonlinear systems under poisson white noise excitation abstract in order to overcome some unsatisfactory trends and limitations of the traditional path integration pi method for poisson white noise a novel pi method is proposed in this paper which includes two improved schemes the first one is a new transition probability density function tpdf approximation which considers the randomness of the impulse happening time during each time intervals the second one is a transformation of chapman kolmogorov ck equation by a variable substitution instead of directly using it whose numerical calculation is based on the back stepping runge kutta scheme and the triangulation based interpolation monte carlo simulations mcs are utilized to measure the accuracy of the improved algorithm with three illustrative nonlinear systems the results show that compared with the traditional pi method the improved pi method can give a more accurate description of the tpdf values and provide more precise stationary probability density function pdf results whenever the mean arrival rate is large or small the improved algorithm has a wider range of choices in time interval values to maintain the accuracy of stationary pdf results besides it is discovered that cubic interpolation deserves to be applied in the improved pi method more than linear and natural interpolations

a two stage cross correlation approach to template matching two stage template matching with sum of absolute differences as the similarity measure has been developed by vanderburg and rosenfeld 1 2 this correspondence shows the development of two stage template matching with cross correlation as the similarity measure the threshold value of the first stage is derived analytically and its validity is verified experimentally considerable speed up over the one stage process can be obtained by introducing only a small false dismissal probability

stochastic averaging of quasi partially integrable hamiltonian systems under combined gaussian and poisson white noise excitations abstract a stochastic averaging method for predicting the response of quasi partially integrable and non resonant hamiltonian systems to combined gaussian and poisson white noise excitations is proposed for the case with r 1 r n independent first integrals which are in involution an r dimensional averaged generalized fokker planck kolmogorov gfpk equation for the transition probability density of r independent first integrals is derived from the stochastic integro differential equations sides of the original quasi partially integrable and non resonant hamiltonian systems by using the stochastic jump diffusion chain rule and the stochastic averaging theorem an example is given to illustrate the applications of the proposed stochastic averaging method and a combination of the finite difference method and the successive over relaxation method is used to solve the reduced gfpk equation to obtain the stationary probability density of the system the results are well verified by a monte carlo simulation

a new approach for imbalanced data classification based on data gravitation imbalanced classification is an important machine learning research topic that troubles most general classification models because of the imbalanced class distribution a newly developed physical inspired classification method i e the data gravitation based classification dgc model performs well in many general classification problems however like other general classifiers the performance of dgc suffers in imbalanced tasks in this study we develop a specific dgc model namely imbalanced dgc idgc model for imbalanced problems the amplified gravitation coefficient agc is introduced for gravitation computing agc is a type of coefficient that contains class imbalance information which can strengthen and weaken the gravitational field of the minority and majority classes we also design a fitness evaluation function in the weight optimization procedure of the data distribution to ensure that the model parameters adapt to the imbalanced class distributions a total of 44 binary class data sets and 15 multiclass imbalanced data sets are used to test the performance of the proposed method experimental results show that the adapted dgc model is effective for imbalanced problems