mode detection by relaxation a relaxation process is described and applied to the detection of the modes of the underlying probability density function for clustering multidimensional data when the process is iterated the label probabilities become very high in the modal region and very low in the valleys so that mode detection becomes trivial

quantization of memoryless and gauss markov sources over binary markov channels joint source channel coding for stationary memoryless and gauss markov sources and binary markov channels is considered the channel is an additive noise channel where the noise process is an mth order markov chain two joint source channel coding schemes are considered the first is a channel optimized vector quantizer optimized for both source and channel the second scheme consists of a scalar quantizer and a maximum a posteriori detector in this scheme it is assumed that the scalar quantizer output has residual redundancy that can be exploited by the maximum a posteriori detector to combat the correlated channel noise these two schemes are then compared against two schemes which use channel interleaving numerical results show that the proposed schemes outperform the interleaving schemes for very noisy channels with high noise correlation gains of 4 5 db in signal to noise ratio are possible

cluster analysis by binary morphology an approach to unsupervised pattern classification that is based on the use of mathematical morphology operations is developed the way a set of multidimensional observations can be represented as a mathematical discrete binary set is shown clusters are then detected as well separated subsets by means of binary morphological transformations

estimation of the parameters of a gaussian mixture using the method of moments given a general n dimensional bimodal gaussian mixture this paper shows how unknown parameters may be found by the method of moments three cases are considered equal modal probabilities known but not necessarily equal probabilities and all parameters unknown the solution involves sample moments no higher than fourth order for gaussian mixtures where the number of modes is unknown fourth order moments can be used to count them provided all modes have the same covariance matrix and their multiplicity is not greater than data dimensionality examples of mode counting and the determination of bimodal parameters are included

the design of joint source and channel trellis waveform coders the generalized lloyd algorithm is applied to the design of joint source and channel trellis waveform coders to encode discrete time continuous amplitude stationary and ergodic sources operating over discrete memoryless noisy channels experimental results are provided for independent and autoregressive gaussian sources binary symmetric channels and absolute error and squared error distortion measures performance of the joint codes is compared with the tandem combination of a trellis source code and a trellis channel code on the independent gaussian source using the squared error distortion measure operating over an additive white gaussian noise channel it is observed that the jointly optimized codes achieve performance close to or better than that of separately optimized tandem codes of the same constraint length performance improvement via a predictive joint source and channel trellis code is demonstrated for the autoregressive gaussian source using the squared error distortion measure

convexity dependent morphological transformations for mode detection in cluster analysis abstract an approach to unsupervised pattern classification is discussed based on both the mathematical morphology and convexity analysis of the underlying probability density function the density function which is estimated from the input data is dilated when it is concave and eroded when it is convex iterations of these convexity dependent morphological transformations tend to enhance the modes and to enlarge the valleys of the underlying p d f so that mode detection becomes trivial examples of the performance of the clustering scheme based on the so detected modes are given using artificially generated data sets

an exact prediction of n 4 supersymmetric yang mills theory for string theory we propose that the expectation value of a circular bps wilson loop in script n 4 supersymmetric yang mills can be calculated exactly to all orders in a 1 n expansion and to all orders in g2n using the ads cft duality this result yields a prediction of the value of the string amplitude with a circular boundary to all orders in alpha prime and to all orders in gs we then compare this result with string theory we find that the gauge theory calculation for large g2n and to all orders in the 1 n2 expansion does agree with the leading string theory calculation to all orders in gs and to lowest order in alpha prime we also find a relation between the expectation value of any closed smooth wilson loop and the loop related to it by an inversion that takes a point along the loop to infinity and compare this result again successfully with string theory

a fast algorithm for nonparametric probability density estimation a fast algorithm for the well known parzen window method to estimate density functions from the samples is described the computational efforts required by the conventional and straightforward implementation of this estimation procedure limit its practical application to data of low dimensionality the proposed algorithm makes the computation of the same density estimates with a substantial reduction of computer time possible especially for data of high dimensionality some simulation experiments are presented which demonstrate the efficiency of the method they indicate the computational savings that may be achieved through the use of this fast algorithm for artificially generated sets of data

mode finding for mixtures of gaussian distributions gradient quadratic and fixed point iteration algorithms and appropriate values for their control parameters are derived for finding all modes of a gaussian mixture a problem with applications in clustering and regression the significance of the modes found is quantified locally by hessian based error bars and globally by the entropy as sparseness measure

on the performance and complexity of channel optimized vector quantizers the performance and complexity of channel optimized vector quantizers are studied for the gauss markov source observations on the geometric structure of these quantizers are made which have an important implication on the encoding complexity for the squared error distortion measure it is shown that an operation equivalent to a euclidean distance measurement with respect to an appropriately defined set of points used to identify the encoding regions can be used to perform the encoding this implies that the encoding complexity is proportional to the number of encoding regions it is then demonstrated that for very noisy channels and a heavily correlated source when the codebook size is large the number of encoding regions is considerably smaller than the codebook size implying a reduction in encoding complexity

joint source and noisy channel trellis encoding corresp in a trellis encoding communication system the decoder is a time invariant nonlinear filter with finite memory sliding block code and the encoder is a trellis search algorithm matched to the decoder a coding theorem is established for a trellis encoding of a stationary and ergodic source over a discrete memoryless noisy channel which shows that such communication systems can perform arbitrarily close to the source distortion rate function evaluated at the channel capacity

design of channel optimized vector quantizers in the presence of channel mismatch we study the design of channel optimized vector quantizers in the presence of channel mismatch we show that when the statistics of the channel bit error rate ber are not known a minimax solution is the one obtained by designing for the worst possible channel then we consider the case when the probability density function of channel ber is known and propose an algorithm that provides a minimum average distortion also by using an estimate of the channel ber at the decoder we develop a decoder adaptive scheme that further improves the performance in all cases we have limited ourselves to table lookup decoders which amount to very small computational complexities finally the utilization of lookup tables at the encoder and the effects of imperfect estimation of channel bers are considered

efficient source decoding over memoryless noisy channels using higher order markov models exploiting the residual redundancy in a source coder output stream during the decoding process has been proven to be a bandwidth efficient way to combat noisy channel degradations this redundancy can be employed to either assist the channel decoder for improved performance or design better source decoders in this work a family of solutions for the asymptotically optimum minimum mean squared error mmse reconstruction of a source over memoryless noisy channels is presented when the redundancy in the source encoder output stream is exploited in the form of a spl gamma order markov model spl gamma spl ges 1 and a delay of spl delta spl delta 0 is allowed in the decoding process it is demonstrated that the proposed solutions provide a wealth of tradeoffs between computational complexity and the memory requirements a simplified mmse decoder which is optimized to minimize the computational complexity is also presented considering the same problem setup several other maximum a posteriori probability map symbol and sequence decoders are presented as well numerical results are presented which demonstrate the efficiency of the proposed algorithms

estimating components of univariate gaussian mixtures using prony s method a new technique for estimating the component parameters of a mixture of univariate gaussian distributions using the method of moments is presented the method of moments basically involves equating the sample moments to the corresponding mixture moments expressed in terms of component parameters and solving these equations for the unknown parameters these moment equations however are nonlinear in the unknown parameters and heretofore an analytic solution of these equations has been obtained only for two component mixtures 2 numerical solutions also tend to be unreliable for more than two components due to the large number of nonlinear equations and parameters to be solved for in this correspondence under the condition that the component distributions have equal variances or equal means the nonlinear moment equations are transformed into a set of linear equations using prony s method the solution of these equations for the unknown parameters is analytically feasible and numerically reliable for mixtures with several components numerous examples using the proposed technique for two three and four component mixtures are presented

cluster analysis by adaptive rank order filters abstract an adaptive filter is proposed for detecting the modes of underlying probability density function of the data the adaptive procedure is based on the selection of an appropriate rank order according to the local measurements of the entropy of the density function the approach requires no a priori information about the structure of the data set but it is governed by the sampling parameter experiments demonstrate the usefulness of the filter

some nonabelian toy models in the large n limit schwinger dyson equations are used to study the largen limit ofu n gauge theory on several small lattices explicit solutions are found which are beyond the reach of existing steepest descent technique they show a phase transition in a three placquette model at couplingg2n 3 resembling the known transition in the one placquette model and lending support to expectations of a similar transition in the four dimensional lattice theory

a clustering method based on multidimensional texture analysis considering the analogy between image segmentation and cluster analysis the aim of this paper is to adapt statistical texture measures to describe the spatial distribution of multidimensional observations the main idea is to consider the cluster cores as domains characterized by their specific textures in the data space the distribution of the data points is first described as a multidimensional histogram defined on a multidimensional regular array of sampling points in order to evaluate locally a multidimensional texture a co occurrence matrix is introduced which characterizes the local distribution of the data points in the multidimensional data space several local texture features can be computed from this co occurrence matrix which accumulates spatial and statistical information on the data distribution in the neighborhoods of the sampling points texture features are selected according to their ability to discriminate different distributions of data points the sampling points where the local underlying texture is evaluated are categorized into different texture classes the points assigned to these classes tend to form connected components in the data space which are considered as the cores of the clusters

unitary matrix models as exactly solvable string theories models of unitary matrices are solved exactly in a double scaling limit using orthogonal polynomials on a circle exact differential equations are found for the scaling functions of these models for the simplest model k 1 the painlev e ii equation with constant 0 is obtained there are possible nonperturbative phase transitions in these models the scaling function is of the form mathit n mathrm ensuremath 1 2 mathit k 1 ifmmode times else texttimes fi f mathit n 2 mathit k 2 mathit k 1 ensuremath lambda mathit x ensuremath lambda for the kth multicritical point the specific heat is mathit f 2 and is therefore manifestly positive equations are given for k 2 and 3 with a discussion of asymptotic behavior

performance of quantizers on noisy channels using structured families of codes achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers it is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end to end distortion decays to zero exponentially fast as a function of the overall transmission rate and is achieved by choosing a channel code rate that is independent of the overall transmission rate we show that for certain families of practical channel codes and binary lattice vector quantizers the overall distortion can be made to decay to zero exponentially fast as a function of the square root of transmission rate this is achieved by carefully choosing a channel code rate that decays to zero as the transmission rate grows explicit channel code rate schedules are obtained for several well known families of channel codes

noise histogram and cluster validity for gaussian mixtured data abstract in this study a critique of the clustering methodology is carried out for the definition of a cluster determination of the number of clusters and evaluation of heuristic partitional clustering algorithms when the data is a noisy gaussian mixture the effects of noise in determining the number of clusters and the clustering parameters are investigated two cluster validity criteria namely the likelihood information criterion and the sum of squared error are described it is concluded that these criteria can be used as a guide in deciding on the number of valid clusters by using the proposed sum of squared error criterion an improvement algorithm which reduces the effect of noise on the results of heuristic clustering algorithms is described

a sequence based approximate mmse decoder for source coding over noisy channels using discrete hidden markov models in previous work on source coding over noisy channels it was recognized that when the source has memory there is typically residual redundancy between the discrete symbols produced by the encoder which can be capitalized upon by the decoder to improve the overall quantizer performance sayood and borkenhagen 1991 and phamdo and farvardin see ieee trans inform theory vol 40 p 186 93 1994 proposed detectors at the decoder which optimize suitable criteria in order to estimate the sequence of transmitted symbols phamdo and farvardin also proposed an instantaneous approximate minimum mean squared error iammse decoder these methods provide a performance advantage over conventional systems but the maximum a posteriori map structure is suboptimal while the iammse decoder makes limited use of the redundancy alternatively combining aspects of both approaches we propose a sequence based approximate mmse sammse decoder for a markovian sequence of encoder produced symbols and a discrete memoryless channel we approximate the expected distortion at the decoder under the constraint of fixed decoder complexity for this simplified cost the optimal decoder computes expected values based on a discrete hidden markov model using the wellknown forward backward f b algorithm performance gains for this scheme are demonstrated over previous techniques in quantizing gauss markov sources over a range of noisy channel conditions moreover a constrained delay version is also suggested

reconstruction of predictively encoded signals over noisy channels using a sequence mmse decoder in this paper we consider the problem of decoding predictively encoded signal over a noisy channel when there is residual redundancy captured by a spl gamma order markov model in the sequence of transmitted data our objective is to minimize the mean squared error mse in the reconstruction of the original signal input to the predictive source coder the problem is formulated and solved through minimum mean squared error mmse decoding of a sequence of samples over a memoryless noisy channel the related previous works include several maximum a posteriori map and mmse based decoders the map based approaches are suboptimal when the performance criterion is the mse on the other hand the previously known mmse based approaches are suboptimal since they are designed to efficiently reconstruct the data samples received the prediction residues rather than the original signal the proposed scheme is set up by modeling the source coder produced symbols and their redundancy with a trellis structure methods are presented to optimize the solutions in terms of complexity numerical results and comparisons are provided which demonstrate the effectiveness of the proposed techniques

dpcm picture transmission over noisy channels with the aid of a markov model the problem of dpcm picture transmission over noisy channels is considered it is well known that dpcm systems are very sensitive to channel errors the goal in this work is to build robustness against channel errors three methods are proposed in this paper and are obtained by modeling the encoded signal as a markov sequence first an optimum method for decoding correlated sequences is derived and it is shown to require viterbi decoding then a modified map method mmap for markov sequences is described a maximal signal to noise msnr receiver for dpcm systems is also developed that minimizes the distortion power due to channel errors the appropriate cost matrix for this receiver is computed these methods are applied to dpcm picture transmission over noisy channels and are compared with a another method the snr graphs as well as subjective examination of the received pictures demonstrate that the proposed procedures are quite effective and superior to that method among the proposed methods the msnr receiver was found to be more effective than the others for a given order of the markov model it is observed that the proposed methods are most beneficial for low detail pictures

an approximate solution to normal mixture identification with application to unsupervised pattern classification in this paper an approach to unsupervised pattern classifiation is discussed the classification scheme is based on an approximation of the probability densities of each class under the assumption that the input patterns are of a normal mixture the proposed technique for identifying the mixture does not require prior information the description of the mixture in terms of convexity allows to determine from a totally unlabeled set of samples the number of components and for each of them approximate values of the mean vector the covariance matrix and the a priori probability discriminant functions can then be constructed computer simulations show that the procedure yields decision rules whose performances remain close to the optimum bayes minimum error rate while involving only a small amount of computation