fast planar oriented ripple search algorithm for hyperspace vq codebook this paper presents a fast codebook search method for improving the quantization complexity of full search vector quantization vq the proposed method is built on the planar voronoi diagram to label a ripple search domain then the appropriate codeword can easily be found just by searching the local region instead of global exploration in order to take a step further and obtain the close result full search vq would we equip the proposed method with a duplication mechanism that helps to bring down the possible quantizing distortion to its lowest level according to the experimental results the proposed method is indeed capable of providing better outcome at a faster quantization speed than the existing partial search methods moreover the proposed method only requires a little extra storage for duplication

fast full search equivalent encoding algorithms for image compression using vector quantization three fast search routines to be used in the encoding phase of vector quantization vq image compression systems are presented these routines which are based on geometric considerations provide the same results as an exhaustive or full search examples show that the proposed algorithms need only 3 20 of the number of mathematical operations required by a full search and fewer than 50 of the operations required by recently proposed alternatives

a comparison of several vector quantization codebook generation approaches a review and a performance comparison of several often used vector quantization vq codebook generation algorithms are presented the codebook generation algorithms discussed include the linde buzo gray lbg binary splitting algorithm the pairwise nearest neighbor algorithm the simulated annealing algorithm and the fuzzy c means clustering analysis algorithm a new directed search binary splitting method which reduces the complexity of the lbg algorithm is presented also a new initial codebook selection method which can obtain a good initial codebook is presented by using this initial codebook selection algorithm the overall lbg codebook generation time can be reduced by a factor of 1 5 2

a hybrid method for calculation of ruelle pollicott resonances we present a numerical method for calculation of ruelle pollicott resonances of dynamical systems it constructs an effective coarse grained propagator by considering the correlations of multiple observables over multiple time steps the method is compared to the usual approaches to the example of the perturbed cat map and is shown to be numerically efficient and robust

a fast mmse encoding technique for vector quantization the authors present a very efficient minimum mean squared error mmse encoding method useful for vector quantization using this method results in a considerable reduction in the number of multiplications and additions the increase in the number of comparisons is moderate and therefore the overall saving in the number of operations is still considerable very little precomputation and extra storage is required

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

optimization of partition based weighted sum filters and their application to image denoising partition based weighted sum p ws filtering is an effective method for processing nonstationary signals especially those with regularly occurring structures such as images p ws filters were originally formulated as hard partition weighted sum hp ws filters and were successfully applied to image denoising this formulation relied on intuitive arguments to generate the filter class here we present a statistical analysis that justifies the use of weighted sum filters after observation space partitioning unfortunately the hp ws filters are nondifferentiable and an analytical solution for their global optimization is therefore difficult to obtain a two stage suboptimal training procedure has been reported in the literature but prior to this research no evaluation on the optimality of this approach has been reported here a genetic algorithm ga hp ws optimization procedure is developed that in simulations shows that the simpler two stage training procedure yields near optimal results also developed in this paper are soft partition weighted sum sp ws filters the sp ws filters utilize soft or fuzzy partitions that yield a differentiable filtering operation enabling the development of gradient based optimization procedures image denoising simulation results are presented comparing hp ws and sp ws filters their optimization procedures and wavelet based image denoising these results show that p ws filters in general outperform traditional and wavelet based image filters and sp ws filters utilizing soft partitioning not only allow for simple optimization but also yields improved performance

i k means an iterative clustering algorithm based on an enhanced version of the k means abstract the k means tries to minimize the sum of the squared euclidean distance from the mean ssedm of each cluster as its objective function although this algorithm is effective it is too sensitive to initial centers so many approaches in the literature have focused on determining suitable initial centers however selecting suitable initial centers is not always possible especially when the number of clusters is increased this paper proposes an iterative approach to improve quality of the solution produced by the k means this approach tries to iteratively improve the quality of solution of the k means by removing one cluster minus dividing another one plus and applying re clustering again in each iteration this method called iterative k means minus plus i k means the i k means is speeded up using some methods to determine which cluster should be removed which one should be divided and how to accelerate the re clustering process results of experiments show that i k means can outperform k means to be known one of the accurate version of the k means in terms of minimizing ssedm for some instances the accuracy of i k means is about 2 times higher than both the k means and k means while it is faster than k means and has the reasonable runtime in comparison with the k means

fast kalman like optimal unbiased fir filtering with applications in this paper an optimal unbiased finite impulse response oufir filter is proposed as a linking solution between the unbiased fir ufir filter and the kalman filter kf we first derive the batch oufir estimator to minimize the mean square error mse subject to the unbiasedness constraint and then find its fast iterative form it is shown that the oufir filter is full horizon fh and that its estimate converges to the kf estimate by increasing the horizon length n as a special feature we note that the fh oufir filter operates almost as fast as the kf several other critical properties of the oufir filter are illustrated based on simulations and practical applications similar to the ufir filter and contrary to the kf the oufir filter is highly insensitive to the initial conditions it has much better robustness than kf against temporary model uncertainties finally the oufir filter allows for ignoring system noise which is typically not well known to the engineer

rough clustering using generalized fuzzy clustering algorithm in this paper we present a rough k means clustering algorithm based on minimizing the dissimilarity which is defined in terms of the squared euclidean distances between data points and their closest cluster centers this approach is referred to as generalized rough fuzzy k means grfkm algorithm the proposed method solves the divergence problem of available approaches where the cluster centers may not be converged to their final positions and reduces the number of user defined parameters the presented method is shown to be converged experimentally compared to available rough k means clustering algorithms the proposed method provides less computing time unlike available approaches the convergence of the proposed method is independent of the used threshold value moreover it yields better clustering results than rfkm for the handwritten digits data set landsat satellite data set and synthetic data set in terms of validity indices compared to mrkm and rfkm grfkm can reduce the value of xie beni index using the handwritten digits data set where a lower xie beni index value implies the better clustering quality the proposed method can be applied to handle real life situations needing reasoning with uncertainty

an agglomerative clustering algorithm using a dynamic k nearest neighbor list in this paper a new algorithm is developed to reduce the computational complexity of ward s method the proposed approach uses a dynamic k nearest neighbor list to avoid the determination of a cluster s nearest neighbor at some steps of the cluster merge double linked algorithm dla can significantly reduce the computing time of the fast pairwise nearest neighbor fpnn algorithm by obtaining an approximate solution of hierarchical agglomerative clustering in this paper we propose a method to resolve the problem of a non optimal solution for dla while keeping the corresponding advantage of low computational complexity the computational complexity of the proposed method dknna fs dynamic k nearest neighbor algorithm with a fast search in terms of the number of distance calculations is o n 2 where n is the number of data points compared to fpnn with a fast search fpnn fs the proposed method using the same fast search algorithm dknna fs can reduce the computing time by a factor of 1 90 2 18 for the data set from a real image in comparison with fpnn fs dknna fs can reduce the computing time by a factor of 1 92 2 02 using the data set generated from three images compared to dla with a fast search dla fs dknna fs can decrease the average mean square error by 1 26 for the same data set

improvement of the k means clustering filtering algorithm in this paper we present a modified filtering algorithm mfa by making use of center variations to speed up clustering process our method first divides clusters into static and active groups we use the information of cluster displacements to reject unlikely cluster centers for all nodes in the kd tree we reduce the computational complexity of filtering algorithm fa through finding candidates for each node mainly from the set of active cluster centers two conditions for determining the set of candidate cluster centers for each node from active clusters are developed our approach is different from the major available algorithm which passes no information from one stage of iteration to the next theoretical analysis shows that our method can reduce the computational complexity in terms of the number of distance calculations of fa at each stage of iteration by a factor of fc ac where fc and ac are the numbers of total clusters and active clusters respectively compared with the fa our algorithm can effectively reduce the computing time and number of distance calculations it is noted that our proposed algorithm can generate the same clusters as that produced by hard k means clustering the superiority of our method is more remarkable when a larger data set with higher dimension is used

additive vector decoding of transform coded images in a standard transform coding scheme of images or video the decoder can be implemented by a table lookup technique without the explicit use of an inverse transformation in this new decoding method each received code index of a transform coefficient addresses a particular codebook to fetch a component code vector that resembles the basis vector of the linear transformation the output image is then reconstructed by summing a small number of nonzero component code vectors with a set of well designed codebooks this new decoder can exploit the correlation among the quantized transform coefficients to achieve better rate distortion performance than the conventional decoding method an iterative algorithm for designing a set of locally optimal codebooks from a training set of images is presented we demonstrate that this new idea can be applied to decode improved quality pictures from the bitstream generated from a standard encoding scheme of still images or video while the complexity is low enough to justify practical implementation

a fast vq codebook generation algorithm using codeword displacement in this paper we present a fast codebook generation algorithm called cgaucd codebook generation algorithm using codeword displacement by making use of the codeword displacement between successive partition processes by implementing a fast search algorithm named mfaupi modified fast algorithm using projection and inequality for vq encoding in the partition step of cgaucd the codebook generation time can be further reduced significantly using mfaupi the computing time of cgaucd can be reduced by a factor of 4 7 7 6 compared to generalized lloyd algorithm gla our proposed method can reduce the codebook generation time by a factor of 35 9 121 2 compared to the best codebook generation algorithm to our knowledge our approach can further reduce the corresponding computing time by 26 0 32 8 it is noted that our proposed algorithm can generate the same codebook as that produced by the gla the superiority of our method is more remarkable when a larger codebook is generated

fast k nearest neighbor search based on projection and triangular inequality in this paper a novel algorithm for finding k points that are closest to a query point is presented some inequalities are used to delete impossible data points and reduce distance computations our algorithm makes use of a data point s feature to reject unlikely candidates for a query point and can eliminate many of the unlikely data points which cannot be rejected by other available algorithms experimental results show that our algorithm is superior to other methods in terms of computing time and the number of distance calculations in most cases and is more remarkable if a larger data set with higher dimension is used compared with available approaches our method can reduce the computing time and number of distance calculations significantly

a fast search algorithm for vector quantization using mean pyramids of codewords one of the most serious problems for vector quantization especially for high dimensional vectors is the high computational complexity of searching for the closest codeword in the codebook design and encoding phases although quantizing high dimensional vectors rather than low dimensional vectors results in better performance the computation time needed for vector quantization grows exponentially with the vector dimension this makes high dimensional vectors unsuitable for vector quantization to overcome this problem a fast search algorithm under the assumption that the distortion is measured by the squared euclidean distance is proposed using the mean pyramids of codewords the algorithm ran reject many codewords that are impossible matches and hence save a great deal of computation time the algorithm is efficient for high dimensional codeword searches experimental results confirm the effectiveness of the proposed method

projection based spatially adaptive reconstruction of block transform compressed images at the present time block transform coding is probably the most popular approach for image compression for this approach the compressed images are decoded using only the transmitted transform data we formulate image decoding as an image recovery problem according to this approach the decoded image is reconstructed using not only the transmitted data but in addition the prior knowledge that images before compression do not display between block discontinuities a spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets apart from the data constraint set this algorithm uses another new constraint set that enforces between block smoothness the novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics a simplified spatially adaptive recovery algorithm is also proposed and the analysis of its computational complexity is presented numerical experiments are shown that demonstrate that the proposed algorithms work better than both the jpeg deblocking recommendation and our previous projection based image decoding approach

quantization based clustering algorithm in this paper a quantization based clustering algorithm qbca is proposed to cluster a large number of data points efficiently unlike previous clustering algorithms qbca places more emphasis on the computation time of the algorithm specifically qbca first assigns the data points to a set of histogram bins by a quantization function then it determines the initial centers of the clusters according to this point distribution finally qbca performs clustering at the histogram bin level rather than the data point level we also propose two approaches to improve the performance of qbca further i a shrinking process is performed on the histogram bins to reduce the number of distance computations and ii a hierarchical structure is constructed to perform efficient indexing on the histogram bins finally we analyze the performance of qbca theoretically and experimentally and show that the approach 1 can be easily implemented 2 identifies the clusters effectively and 3 outperforms most of the current state of the art clustering approaches in terms of efficiency

locating pollicott ruelle resonances in chaotic dynamical systems a class of numerical schemes a class of numerical methods to determine pollicott ruelle resonances in chaotic dynamical systems is proposed this is achieved by relating some existing procedures that make use of the pade approximants and interpolating exponentials to both the memory function techniques used in the theory of relaxation and the filter diagonalization method used in the harmonic inversion of time correlation functions this relationship leads to a theoretical framework in which all these methods become equivalent and which allows for new and improved numerical schemes

a fast exact gla based on code vector activity detection this paper introduces a new method for reducing the number of distance calculations in the generalized lloyd algorithm gla which is a widely used method to construct a codebook in vector quantization reduced comparison search detects the activity of the code vectors and utilizes it on the classification of the training vectors for training vectors whose current code vector has not been modified we calculate distances only to the active code vectors a large proportion of the distance calculations can be omitted without sacrificing the optimality of the partition the new method is included in several fast gla variants reducing their running times over 50 on average

ruelle resonances in quantum many body dynamics we define a quantum perron frobenius master operator over a suitable normed space of translationally invariant states adjoint to the quasi local c algebra of quantum lattice gasses e g spin chains whose spectrum determines the exponents of decay of time correlation functions the theoretical ideas are applied to a generic example of kicked ising spin 1 2 chains we show that the chaotic eigenmodes corresponding to leading eigenvalue resonances have fractal structure in the basis of local operators

removal of compression artifacts using projections onto convex sets and line process modeling we present a new image recovery algorithm to remove in addition to blocking ringing artifacts from compressed images and video this new algorithm is based on the theory of projections onto convex sets pocs a new family of directional smoothness constraint sets is defined based on line processes modeling of the image edge structure the definition of these smoothness sets also takes into account the fact that the visibility of compression artifacts in an image is spatially varying to overcome the numerical difficulty in computing the projections onto these sets a divide and conquer dac strategy is introduced according to this strategy new smoothness sets are derived such that their projections are easier to compute the effectiveness of the proposed algorithm is demonstrated through numerical experiments using motion picture expert group based mpeg based coders decoders codecs

a novel encoding algorithm for vector quantization using transformed codebook in this paper a novel encoding algorithm for vector quantization is presented our method uses a set of transformed codewords and partial distortion rejection to determine the reproduction vector of an input vector experimental results show that our algorithm is superior to other methods in terms of the computing time and number of distance calculations compared with available approaches our method can reduce the computing time and number of distance calculations significantly compared with the available best method of reducing the number of distance computations our approach can reduce the number of distance calculations by 32 3 67 1 compared with the best encoding algorithm for vector quantization our method can also further reduce the computing time by 19 7 23 9 the performance of our method is better when a larger codebook is used and is weakly correlated to codebook size

a fast k means clustering algorithm using cluster center displacement in this paper we present a fast k means clustering algorithm fkmcucd using the displacements of cluster centers to reject unlikely candidates for a data point the computing time of our proposed algorithm increases linearly with the data dimension d whereas the computational complexity of major available kd tree based algorithms increases exponentially with the value of d theoretical analysis shows that our method can reduce the computational complexity of full search by a factor of sf and sf is independent of vector dimension the experimental results show that compared to full search our proposed method can reduce computational complexity by a factor of 1 37 4 39 using the data set from six real images compared with the filtering algorithm which is among the available best algorithms of k means clustering our algorithm can effectively reduce the computing time it is noted that our proposed algorithm can generate the same clusters as that produced by hard k means clustering the superiority of our method is more remarkable when a larger data set with higher dimension is used

hierarchy oriented searching algorithms using alternative duplicate codewords for vector quantization mechanism in this paper we will show those algorithms that speed up the search of a closest codeword over a given codebook the mechanism is based on a multilevel concept constructed as a hierarchical organization for a given codebook with size n existing n codewords there are only log email protected levels that need to be constructed in order to find the closest codeword where k is a parameter selection to optimize the comparisons in the course of the searching theoretically the comparisons required to find the closest codeword are on average email protected log email protected which is substantially faster than that of a full search job besides in order to approach the perfect match with the exact one among the codewords a duplicate mechanism is also applied to our algorithm so that the lowest possible distortion is achieved as is observed from the results of the experiments the estimation of comparisons in our execution without codeword duplicate is on average about email protected log email protected n times the full search method it is worth noting that the larger the size of the codebook the more the speed increases in particular there are two classifications non duplicate and duplicate method which are associated with the codewords distribution in the dominated set which were experimented on some tables the duplicate is manipulated by the training set containing six popular image data to demonstrate the efficiency of our scheme also the time requirement to find the closest codeword is effectively reduced especially in the case of a large sized codebook therefore our scheme offers a novel exploration and achieves a faster performance in the closest codeword searching for vector quantization of image data

image restoration of compressed image using classified vector quantization abstract to reduce communication bandwidth or storage space image compression is needed however the subjective quality of compressed images may be unacceptable and the improvement of quality for compressed images may be desirable this paper extends and modifies classified vector quantization cvq to improve the quality of compressed images the process consists of two phases the encoding phase and the decoding phase the encoding procedure needs a codebook for the encoder which transforms a compressed image to a set of codeword indices the decoding phase also requires a different codebook for the decoder which enhances a compressed image from a set of codeword indices using cvq to improve a compressed image s quality is different from the existing algorithm which cannot reconstruct the high frequency components for compressed images the experimental results show that the image quality is improved dramatically for images in the training set the improvement of psnr is about 3 db for images which are outside the training set the improvement of psnr is about 0 57 db which is comparable to the existing method

a fast nearest neighbor algorithm based on a principal axis search tree a new fast nearest neighbor algorithm is described that uses principal component analysis to build an efficient search tree at each node in the tree the data set is partitioned along the direction of maximum variance the search algorithm efficiently uses a depth first search and a new elimination criterion the new algorithm was compared to 16 other fast nearest neighbor algorithms on three types of common benchmark data sets including problems from time series prediction and image vector quantization this comparative study illustrates the strengths and weaknesses of all of the leading algorithms the new algorithm performed very well on all of the data sets and was consistently ranked among the top three algorithms

improvement of the fast exact pairwise nearest neighbor algorithm pairwise nearest neighbor pnn is an effective method of data clustering which can always generate good clustering results but with high computational complexity fast exact pnn fpnn algorithm proposed by franti et al is an effective method to speed up pnn and generates the same clustering results as those generated by pnn in this paper we present a novel method to improve the fpnn algorithm our algorithm uses the property that the cluster distance increases as the cluster merge process proceeds and adopts a fast search algorithm to reject impossible candidate clusters experimental results show that our proposed method can effectively reduce the number of distance calculations and computation time of fpnn algorithm compared with fpnn our proposed approach can reduce the computation time and number of distance calculations by a factor of 24 8 and 146 4 respectively for the data set from three real images it is noted that our method generates the same clustering results as those produced by pnn and fpnn

leading pollicott ruelle resonances for chaotic area preserving maps recent investigations in nonlinear sciences show that not only hyperbolic but also mixed dynamical systems may exhibit exponential relaxation in the chaotic regime the relaxation rates which lead the decay of probability distributions and correlation functions are related to the classical evolution resolvent perron frobenius operator pole logarithm the so called pollicott ruelle resonances in this brief report the leading pollicott ruelle resonances are calculated analytically for a general class of area preserving maps besides the leading resonances related to the diffusive modes of momentum dynamics slow rate we also calculate the leading faster rate related to the angular correlations the analytical results are compared to the existing results in the literature

minimum variance unbiased fir filter for discrete time variant systems this paper is concerned with the minimum variance unbiased mvu finite impulse response fir filtering problem for linear system described by discrete time variant state space models an mvu fir filter is derived by minimizing the variance from the unbiased fir ufir filter the relationship between the filter gains of mvu fir ufir and optimal fir ofir filters is derived analytically and the mean square errors mses of different fir filters are compared to provide an insight into the estimation performance simulations provided verify that errors in the mvu fir filter are in between the ufir and ofir filters it is also shown that the mvu fir filter can offer optimal estimates without a prior knowledge of the initial state and exhibits better robustness against temporary modeling uncertainties than the kalman filter

voronoi regions of lattices second moments of polytopes and quantization if a point is picked at random inside a regular simplex octahedron 600 cell or other polytope what is its average squared distance from the centroid in n dimensional space what is the average squared distance of a random point from the closest point of the lattice a n or d n e n a n ast or d n ast the answers are given here together with a description of the voronoi or nearest neighbor regions of these lattices the results have applications to quantization and to the design of signals for the gaussian channel for example a quantizer based on the eight dimensional lattice e8 has a mean squared error per symbol of 0 0717 cdots when applied to uniformly distributed data compared with 0 08333 cdots for the best one dimensional quantizer

classical nonlinear response of a chaotic system ii langevin dynamics and spectral decomposition the spectrum of a strongly chaotic system consists of discrete complex ruelle pollicott rp resonances we interpret the rp resonances as eigenstates and eigenvalues of the fokker planck operator obtained by adding an infinitesimal diffusion term to the first order liouville operator we demonstrate how the deterministic expression for the linear response is reproduced in the limit of vanishing noise for the second order response function we establish an equivalence of the spectral decomposition in the limit of vanishing noise and the long time asymptotic expansion in the deterministic case

an efficient encoding algorithm for vector quantization based on subvector technique in this paper a new and fast encoding algorithm for vector quantization is presented this algorithm makes full use of two characteristics of a vector the sum and the variance a vector is separated into two subvectors one is composed of the first half of vector components and the other consists of the remaining vector components three inequalities based on the sums and variances of a vector and its two subvectors components are introduced to reject those codewords that are impossible to be the nearest codeword thereby saving a great deal of computational time while introducing no extra distortion compared to the conventional full search algorithm the simulation results show that the proposed algorithm is faster than the equal average nearest neighbor search enns the improved enns the equal average equal variance nearest neighbor search eenns and the improved eenns algorithms comparing with the improved eenns algorithm the proposed algorithm reduces the computational time and the number of distortion calculations by 2 4 to 6 and 20 5 to 26 8 respectively the average improvements of the computational time and the number of distortion calculations are 4 and 24 6 for the codebook sizes of 128 to 1024 respectively

postprocessing of compressed images via sequential denoising in this paper we propose a novel postprocessing technique for compression artifact reduction our approach is based on posing this task as an inverse problem with a regularization that leverages on existing state of the art image denoising algorithms we rely on the recently proposed plug and play prior framework suggesting the solution of general inverse problems via alternating direction method of multipliers leading to a sequence of gaussian denoising steps a key feature in our scheme is a linearization of the compression decompression process so as to get a formulation that can be optimized in addition we supply a thorough analysis of this linear approximation for several basic compression procedures the proposed method is suitable for diverse compression techniques that rely on transform coding in particular we demonstrate impressive gains in image quality for several leading compression methods jpeg jpeg2000 and hevc

an efficient nearest neighbor search method a simple but efficient nearest neighbor search algorithm is proposed and simulation results demonstrating its effectiveness in the case of vector quantization for a given source are presented the simulation results indicate that use of this approach reduces the number of multiplications and additions to as low as 9 percent of those required for the conventional full search method the reduction in the number of subtractions is also considerable the increase in the number of comparisons is moderate and therefore the total number of operations can be as low as 28 percent of those required by the full search method an additional advantage of the described algorithm is the fact that it requires no precomputations and or extra memory

a fast search algorithm for vector quantization using l sub 2 norm pyramid of codewords vector quantization for image compression requires expensive encoding time to find the closest codeword to the input vector this paper presents a fast algorithm to speed up the closest codeword search process in vector quantization encoding by using an appropriate topological structure of the codebook we first derive a condition to eliminate unnecessary matching operations from the search procedure then based on this elimination condition a fast search algorithm is suggested simulation results show that with little preprocessing and memory cost the proposed search algorithm significantly reduces the encoding complexity while maintaining the same encoding quality as that of the full search algorithm it is also found that the proposed algorithm outperforms the existing search algorithms

fast design of 2 d linear phase complex fir digital filters by analytical least squares method two dimensional full plane and half plane filters are more general and much better frequency responses can be obtained than the quarter plane filters in this correspondence the analytical least squares method is generalized and extended for designing 2 d full plane and half plane linear phase complex fir digital filters the 2 d filter s coefficients can be effectively determined by use of a closed form transformation matrix and some simple element functions the unique advantage of this technique is that it is very fast without employing iterative optimization procedures and matrix inversions design examples are presented to illustrate the simplicity and efficiency of the proposed method

fast agglomerative clustering using information of k nearest neighbors in this paper we develop a method to lower the computational complexity of pairwise nearest neighbor pnn algorithm our approach determines a set of candidate clusters being updated after each cluster merge if the updating process is required for some of these clusters k nearest neighbors are found for them the number of distance calculations for our method is o n 2 where n is the number of data points to further reduce the computational complexity of the proposed algorithm some available fast search approaches are used compared to available approaches our proposed algorithm can reduce the computing time and number of distance calculations significantly compared to fpnn our method can reduce the computing time by a factor of about 26 8 for the data set from a real image compared with pmlfpnn our approach can reduce the computing time by a factor of about 3 8 for the same data set

a receding horizon kalman fir filter for discrete time invariant systems a receding horizon kalman fir filter is presented that combines the kalman filter and the receding horizon strategy when the horizon initial state is assumed to be unknown the suggested filter is a fir filter form which has many good inherent properties it can always be defined irrespective of singularity problems caused by unknown information about the horizon initial state the suggested filter can be represented in either an iterative form or a standard fir form it is also shown that the suggested filter possesses the unbiasedness property and the remarkable deadbeat property irrespective of any horizon initial condition the validity of the suggested filter is illustrated by numerical examples

an improvement of the minimum distortion encoding algorithm for vector quantization in this note we present a very simple method for improving the efficiency of minimum distortion encoding for vector quantization simulations indicates a reduction of up to 70 percent in the number of multiplications for a full search vector quantizer with a large number of codewords and about 25 40 percent for a tree search vector quantizer similar improvement can be achieved in other vector quantization systems

fast global k means clustering using cluster membership and inequality in this paper we present a fast global k means clustering algorithm by making use of the cluster membership and geometrical information of a data point this algorithm is referred to as mfgkm the algorithm uses a set of inequalities developed in this paper to determine a starting point for the jth cluster center of global k means clustering adopting multiple cluster center selection mcs for mfgkm we also develop another clustering algorithm called mfgkm mcs mcs determines more than one starting point for each step of cluster split while the available fast and modified global k means clustering algorithms select one starting point for each cluster split our proposed method mfgkm can obtain the least distortion while mfgkm mcs may give the least computing time compared to the modified global k means clustering algorithm our method mfgkm can reduce the computing time and number of distance calculations by a factor of 3 78 5 55 and 21 13 31 41 respectively with the average distortion reduction of 5 487 for the statlog data set compared to the fast global k means clustering algorithm our method mfgkm mcs can reduce the computing time by a factor of 5 78 8 70 with the average reduction of distortion of 30 564 using the same data set the performances of our proposed methods are more remarkable when a data set with higher dimension is divided into more clusters

a receding horizon kalman fir filter for linear continuous time systems a receding horizon kalman finite impulse response fir filter is suggested for continuous time systems combining the kalman filter with the receding horizon strategy in the suggested filter the horizon initial state is assumed to be unknown it can always be obtained irrespective of unknown information on the horizon initial state the filter may be the first stochastic fir form for continuous time systems that may have many good inherent properties the suggested filter can be represented in an iterative form and also in a standard fir form the suggested filter turns out to be a remarkable deadbeat observer the validity of the suggested filter is illustrated by numerical examples

fast searching algorithm for vector quantization using projection and triangular inequality in this paper a new and fast searching algorithm for vector quantization is presented two inequalities one used for terminating the searching process and the other used to delete impossible codewords are presented to reduce the distortion computations our algorithm makes use of a vector s features mean value edge strength and texture strength to reject many unlikely codewords that cannot be rejected by other available approaches experimental results show that our algorithm is superior to other algorithms in terms of computing time and the number of distortion calculations compared with available approaches our method can reduce the computing time and the number of distortion computations significantly compared with the best method of reducing distortion computation our algorithm can further reduce the number of distortion calculations by 29 to 58 4 compared with the best encoding algorithm for vector quantization our approach also further reduces the computing time by 8 to 47 7

product code vector quantizers for waveform and voice coding memory and computation requirements imply fundamental limitations on the quality that can be achieved in vector quantization systems used for speech waveform coding and linear predictive voice coding lpc one approach to reducing storage and computation requirements is to organize the set of reproduction vectors as the cartesian product of a vector codebook describing the shape of each reproduction vector and a scalar codebook describing the gain or energy such shape gain vector quantizers can be applied both to waveform coding using a quadratic error distortion measure and to voice coding using an itakura saito distortion measure in each case the minimum distortion reproduction vector can be found by first selecting a shape code word and then based on that choice selecting a gain codeword several algorithms are presented for the design of shape gain vector quantizers based on a traning sequence of data or a probabilistic model the algorithms are used to design shape gain vector quantizers for both the waveform coding and voice coding application the quantizers are simulated and their performance is compared to that of previously reported vector quantization systems

leading ruelle resonances of chaotic maps the leading ruelle resonances of typical chaotic maps the perturbed cat map and the standard map are calculated by variation it is found that excluding the resonance associated with the invariant density the next subleading resonances are approximately the roots of the equation z 4 ensuremath gamma where ensuremath gamma is a positive number that characterizes the amount of stochasticity of the map the results are verified by numerical computations and the implications to the form factor of the corresponding quantum maps are discussed

fast quantizing and decoding and algorithms for lattice quantizers and codes for each of the lattices a n n geq 1 d n n geq 2 e 6 e 7 e 8 and their duals a very fast algorithm is given for finding the closest lattice point to an arbitrary point if these lattices are used for vector quantizing of uniformly distributed data the algorithm finds the minimum distortion lattice point if the lattices are used as codes for a gaussian channel the algorithm performs maximum likelihood decoding