equilibrium time correlation functions for one dimensional hard point systems as recently proposed the long time behavior of equilibrium time correlation functions for one dimensional systems are expected to be captured by a nonlinear extension of fluctuating hydrodynamics we outline the predictions from the theory aimed at the comparison with molecular dynamics we report on numerical simulations of a fluid with a hard shoulder potential and of a hard point gas with alternating masses these models have in common that the collision time is zero and their dynamics amounts to iterating collision by collision the theory is well confirmed with the twist that the nonuniversal coefficients are still changing at longest accessible times

high rate vector quantization for detection we investigate high rate quantization for various detection and reconstruction loss criteria a new distortion measure is introduced which accounts for global loss in best attainable binary hypothesis testing performance the distortion criterion is related to the area under the receiver operating characteristic roc curve specifically motivated by sanov s theorem we define a performance curve as the trajectory of the pair of optimal asymptotic type i and type ii error rates of the most powerful neyman pearson test of the hypotheses the distortion measure is then defined as the difference between the area under the curve auc of the optimal pre encoded hypothesis test and the auc of the optimal post encoded hypothesis test as compared to many previously introduced distortion measures for decision making this distortion measure has the advantage of being independent of any detection thresholds or priors on the hypotheses which are generally difficult to specify in the code design process a high resolution zador gersho type of analysis is applied to characterize the point density and the inertial profile associated with the optimal high rate vector quantizer the analysis applies to a restricted class of high rate quantizers that have bounded cells with vanishing volumes the optimal point density is used to specify a lloyd type algorithm which allocates its finest resolution to regions where the gradient of the pre encoded likelihood ratio has greatest magnitude

classified vector quantization of images vector quantization vq provides many attractive features for image coding with high compression ratios however initial studies of image coding with vq have revealed several difficulties most notably edge degradation and high computational complexity we address these two problems and propose a new coding method classified vector quantization cvq which is based on a composite source model blocks with distinct perceptual features such as edges are generated from different subsources i e belong to different classes in cvq a classifier determines the class for each block and the block is then coded with a vector quantizer designed specifically for that class we obtain better perceptual quality with significantly lower complexity with cvq when compared to ordinary vq we demonstrate with cvq visual quality which is comparable to that produced by existing coders of similar complexity for rates in the range 0 6 1 0 bits pixel

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

searching for the tracy widom distribution in nonequilibrium processes while originally discovered in the context of the gaussian unitary ensemble the tracy widom distribution also rules the height fluctuations of growth processes this suggests that there might be other nonequilibrium processes in which the tracy widom distribution plays an important role in our contribution we study one dimensional systems with domain wall initial conditions for an appropriate choice of parameters the profile develops a rarefaction wave while maintaining the initial equilibrium states far to the left and right which thus serve as infinitely extended thermal reservoirs for a fermi pasta ulam type anharmonic chain we will demonstrate that the time integrated current has a deterministic contribution linear in time t and fluctuations of size t 1 3 with a tracy widom distributed random amplitude

a greedy tree growing algorithm for the design of variable rate vector quantizers image compression a technique for directly designing a variable rate tree structured vector quantizer by growing the tree one node at a time rather than one layer at time is presented the technique is a natural extension of a tree growing method for decision trees when the tree is pruned with a generalized algorithm for optimally pruning trees improvement is measured in the signal to noise ratio at high rates over pruning a fixed rate tree structured vector quantizer of the same initial rate the growing algorithm can be interpreted as a constrained inverse of the pruning algorithm

high rate vector quantization for the neyman pearson detection of correlated processes this paper investigates the effect of quantization on the performance of the neyman pearson test it is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process each sample is passed through an n point quantizer and transmitted to a decision device which performs a binary hypothesis test for any false alarm level it is shown that the miss probability of the neyman pearson test converges to zero exponentially as the number of samples tends to infinity assuming that the observed process satisfies certain mixing conditions the main contribution of this paper is to provide a compact closed form expression of the error exponent in the high rate regime i e when the number n of quantization levels tends to infinity generalizing previous results of gupta and hero to the case of nonindependent observations if d represents the dimension of one sample it is proved that the error exponent converges at rate n2 d to the one obtained in the absence of quantization as an application relevant high rate quantization strategies which lead to a large error exponent are determined numerical results indicate that the proposed quantization rule can yield better performance than existing ones in terms of detection error

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

exact scaling functions for one dimensional stationary kpz growth we determine the stationary two point correlation function of the one dimensional kpz equation through the scaling limit of a solvable microscopic model the polynuclear growth model the equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a riemann hilbert problem related to the painleve ii equation we solve these equations numerically with very high precision and compare our up to numerical rounding exact result with the prediction of colaiori and moore 1 obtained from the mode coupling approximation

termination and continuity of greedy growing for tree structured vector quantizers tree structured vector quantizers tsvq provide a computationally efficient variable rate method of compressing vector valued data in applications the problem of designing a tsvq from empirical training data is critical greedy growing algorithms are a common and effective approach to the design problem they are recursive procedures that produce a tsvq one node at a time by optimizing a simple splitting criterion at each step while unsupervised greedy growing algorithms are well understood from an experimental point of view there has been little theory to support their use or to examine their behavior on large training sets the authors present a rigorous analysis of a greedy growing algorithm proposed by riskin 1990 riskin and gray 1991 and balakrishnan 1991 the first part of the paper is a description of the algorithm and an examination of its asymptotic behavior as it applies to a fixed absolutely continuous distribution the second part of the paper establishes the structural consistency of the algorithm with respect to a convergent sequence of distributions as an application the authors obtain results concerning the large sample empirical behavior of the algorithm when it is applied to stationary ergodic training vectors

hierarchies of n point functions for nonlinear conservation laws with random initial data abstract nonlinear conservation laws subject to random initial conditions pose fundamental problems in the evolution and interactions of shocks and rarefactions using a discrete set of values for the solution we derive a hierarchy of equations in terms of the states in two different methods this hierarchy involves the n point function the probability that the solution takes on various values at different positions in terms of the n 1 point function in the first approach these equations can be closed but the resulting solutions do not persist through shock interactions in our second approach the n point function is expressed in terms of the n 1 point functions and remains valid through collisions of shocks

combining image compression and classification using vector quantization we describe a method of combining classification and compression into a single vector quantizer by incorporating a bayes risk term into the distortion measure used in the quantizer design algorithm once trained the quantizer can operate to minimize the bayes risk weighted distortion measure if there is a model providing the required posterior probabilities or it can operate in a suboptimal fashion by minimizing the squared error only comparisons are made with other vector quantizer based classifiers including the independent design of quantization and minimum bayes risk classification and kohonen s lvq a variety of examples demonstrate that the proposed method can provide classification ability close to or superior to learning vq while simultaneously providing superior compression performance

global convergence and empirical consistency of the generalized lloyd algorithm the generalized lloyd algorithm for vector quantizer design is analyzed as a descent algorithm for nonlinear programming a broad class of convex distortion functions is considered and any input distribution that has no singular continuous part is allowed a well known convergence theorem is applied to show that iterative applications of the algorithm produce a sequence of quantizers that approaches the set of fixed point quantizers the methods of the theorem are extended to sequences of algorithms yielding results on the behavior of the algorithm when an unknown distribution is approximated by a training sequence of observations it is shown that as the length of the training sequence grows large that 1 fixed point quantizers for the training sequence approach the set of fixed point quantizers for the true distribution and 2 limiting quantizers produced by the algorithm with the training sequence distribution perform no worse than limiting quantizers produced by the algorithm with the true distribution

vector quantization technique for nonparametric classifier design an effective data reduction technique based on vector quantization is introduced for nonparametric classifier design two new nonparametric classifiers are developed and their performance is evaluated using various examples the new methods maintain a classification accuracy that is competitive with that of classical methods but at the same time yields very high data reduction rates

consistency of data driven histogram methods for density estimation and classification we present general sufficient conditions for the almost surel1 consistency of histogram density estimates based on data dependent partitions analogous conditions guarantee the almost sure risk consistency of histogram classification schemes based on data dependent partitions multivariate data is considered throughout in each case the desired consistency requires shrinking cells subexponential growth of a combinatorial complexity measure and sub linear growth of the number of cells it is not required that the cells of every partition be rectangles with sides paralles to the coordinate axis or that each cell contain a minimum number of points no assumptions are made concerning the common distribution of the training vectors we apply the results to establish the consistency of several known partitioning estimates including the kn spacing density estimate classifiers based on statistically equivalent blocks and classifiers based on multivariate clustering schemes

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

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 comparison of different finite fields for use in elliptic curve cryptosystems we examine the relative efficiency of four methods for finite field representation in the context of elliptic curve cryptography ecc we conclude that a set of fields called the optimized extension fields oefs give greater performance even when used with affine coordinates when compared against the type of fields recommended in the emerging ecc standards although this performance advantage is only marginal and hence there is probably no need to change the current standards to allow oef fields in standards compliant implementations

bayes risk weighted vector quantization with posterior estimation for image compression and classification classification and compression play important roles in communicating digital information their combination is useful in many applications including the detection of abnormalities in compressed medical images in view of the similarities of compression and low level classification it is not surprising that there are many similar methods for their design because some of these methods are useful for designing vector quantizers it seems natural that vector quantization vq is explored for the combined goal we investigate several vq based algorithms that seek to minimize both the distortion of compressed images and errors in classifying their pixel blocks these algorithms are investigated with both full search and tree structured codes we emphasize a nonparametric technique that minimizes both error measures simultaneously by incorporating a bayes risk component into the distortion measure used for the design and encoding we introduce a tree structured posterior estimator to produce the class posterior probabilities required for the bayes risk computation in this design for two different image sources we demonstrate that this system provides superior classification while maintaining compression close or superior to that of several other vq based designs including kohonen s 1992 learning vector quantizer and a sequential quantizer classifier design

automatic image orientation detection we present an algorithm for automatic image orientation estimation using a bayesian learning framework we demonstrate that a small codebook the optimal size of codebook is selected using a modified mdl criterion extracted from a learning vector quantizer lvq can be used to estimate the class conditional densities of the observed features needed for the bayesian methodology we further show how principal component analysis pca and linear discriminant analysis lda can be used as a feature extraction mechanism to remove redundancies in the high dimensional feature vectors used for classification the proposed method is compared with four different commonly used classifiers namely k nearest neighbor support vector machine svm a mixture of gaussians and hierarchical discriminating regression hdr tree experiments on a database of 16 344 images have shown that our proposed algorithm achieves an accuracy of approximately 98 on the training set and over 97 on an independent test set a slight improvement in classification accuracy is achieved by employing classifier combination techniques

image classification by a two dimensional hidden markov model for block based classification an image is divided into blocks and a feature vector is formed for each block by grouping statistics extracted from the block conventional block based classification algorithms decide the class of a block by examining only the feature vector of this block and ignoring context information in order to improve classification by context an algorithm is proposed that models images by two dimensional 2 d hidden markov models hmms the hmm considers feature vectors statistically dependent through an underlying state process assumed to be a markov mesh which has transition probabilities conditioned on the states of neighboring blocks from both horizontal and vertical directions thus the dependency in two dimensions is reflected simultaneously the hmm parameters are estimated by the em algorithm to classify an image the classes with maximum a posteriori probability are searched jointly for all the blocks applications of the hmm algorithm to document and aerial image segmentation show that the algorithm outperforms cart sup tm lvq and bayes vq

histogram regression estimation using data dependent partitions we establish general sufficient conditions for the l 2 conoistency of multivariate histogram regression estimates based on data dependent partitions these same conditions insure the consistency of partitioning regression estimates based on local polynomial fits and with an additional regularity assumption the consistency of histogram estimates for conditional medians our conditions require shrinking cells subexponential growth of a combinatorial complexity measure and sublinear growth of restricted cell counts it is not assumed that the cells of every partition be rectangles with sides parallel to the coordinate axis or that each cell contain a minimum number of points response variables are assumed to be bounded throughout our results may be applied to a variety of partitioning schemes we established the consistency of histograms regression estimates based on cubic partitions with data dependent offsets k thresholding in one dimension and empirically optimal nearest neighbor clustering schemes in addition it is shown that empirically optimal regression trees are consistent when the size of the trees grows with the number of samples at an appropriate rate

recursive partitioning to reduce distortion adaptive partitioning of a multidimensional feature space plays a fundamental role in the design of data compression schemes most partition based design methods operate in an iterative fashion seeking to reduce distortion at each stage of their operation by implementing a linear split of a selected cell the operation and eventual outcome of such methods is easily described in terms of binary tree structured vector quantizers this paper considers a class of simple growing procedures for tree structured vector quantizers of primary interest is the asymptotic distortion of quantizers produced by the unsupervised implementation of the procedures it is shown that application of the procedures to a convergent sequence of distributions with a suitable limit yields quantizers whose distortion tends to zero analogous results are established for tree structured vector quantizers produced from stationary ergodic training data the analysis is applicable to procedures employing both axis parallel and oblique splitting and a variety of distortion measures the results of the paper apply directly to unsupervised procedures that may be efficiently implemented on a digital computer

nonlinear fluctuating hydrodynamics in one dimension the case of two conserved fields we study the bs model which is a one dimensional lattice field theory taking real values its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges the bs model has two locally conserved fields the peak structure of their steady state space time correlations is determined through numerical simulations and compared with nonlinear fluctuating hydrodynamics which predicts a traveling peak with kpz scaling function and a standing peak with a scaling function given by the maximally asymmetric levy distribution with parameter alpha 5 3 as a by product we completely classify the universality classes for two coupled stochastic burgers equations with arbitrary coupling coefficients