Lawrence Buckingham, Shlomo Geva · QUT ePrints (Queensland University of Technology) · 2000
In this paper we describe the Large Margin Vector Quantization algorithm (LMVQ), which uses gradient ascent to maximise the margin of a radial basis function classifier. We present a derivation of the algorithm, which proceeds from an estimate of the class-conditional probability densities. We show that the key behaviour of Kohonen's well-known LVQ2 and LVQ3 algorithms emerge as natural consequences of our formulation. We compare the performance of LMVQ with that of Kohonen's LVQ algorithms on an artificial classification problem and several well known benchmark classification tasks. We find that the classifiers produced by LMVQ attain a level of accuracy that compares well with those obtained via LVQ1, LVQ2 and LVQ3, with reduced storage complexity. We indicate future directions of enquiry based on the large margin approach to Learning Vector Quantization.
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Fabio Matera · Substance Use & Misuse · 1998
(1998). Learning Vector Quantization Networks. Substance Use & Misuse: Vol. 33, No. 2, pp. 271-282.
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Mário A. T. Figueiredo · 2008
Quantization is the process of mapping a continuous or discrete scalar or vector, produced by a source, into a set of digital symbols that can be transmitted or stored using a finite number of bits. In the case of continuous sources (with values in R or R n) quantization must necessarily be used if the output of the source is to be communicated over a digital channel. In this case, it is, in general, impossible to exactly reproduce the original source output, so we’re in the context of lossy coding/compression. In this lecture notes, we will review the main concepts and results of scalar and vector quantization. For more details, see the book by Gersho and Gray [2], the accessible tutorial by Gray [3], or the comprehensive review by Gray and Neuhoff [4]
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Veen, Rick van, Biehl, Michael, de Vries, Gert-Jan · University of Groningen research database (University of Groningen / Centre for Information Technology) · 2021
Cited by 1Open access
A. Gersho · 1984
Abstract : The second year of AFOSR support at the University of California, Santa Barbara has allowed us to make significant strides in exploring the potential of vector quantization for source coding. Some of this work is described in the attached list of references. Some of the studies were completed, including predictive vector quantization and rate distortion modeling of speech using a composite source model to obtain rate distortion bounds on performance of vector quantization. Particularly important results in the second year include the development of a new family of fast search algorithms for pattern matching and the development of Hierarchical Vector Quantization. Several other promising studies, including compandor/lattice coding, were still in progress when the grant terminated. (Author)
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Rey R. Furner, R.W. Christiansen, Douglas M. Chabries · 2005
Two algorithms combining vector quantization with motion compensation for data reduction are presented. The vector quantization technique used in the algorithms is a mean residual vector quantizer (MRVQ) with 8-bit mean, and the motion compensation technique is a simple block matching algorithm. Both VQ and motion compensation are based on squared error performance criterion. The algorithms are tested on USC data base sequences and distortions plotted. A comparison is made between motion compensated vector quantization and conventional VQ.
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Ravichandran, Jensun · MOnAMi (Hochschule Mittweida Hochschulbibliothek) · 2021
Learning Vector Quantization (LVQ) methods have been popular choices of classification models ever since its introduction by T. Kohonen in the 90s. These days, LVQ is combined with Deep Learning methods to provide powerful yet interpretable machine-learning solutions to some of the most challenging computational problems. However, techniques to model recurrent relationships in the data using prototype methods still remain quite unsophisticated. In particular, we are not aware of any modification of LVQ that allows the input data to have different lengths. Needless to say, such data is abundant in today's digital world and demands new processing techniques to extract useful information. In this paper, we propose the use of the Siamese architecture to not only model recurrent relationships within the prototypes but also the ability to handle prototypes of various dimensions simultaneously.
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A. Gersho, Robert M. Gray · 1992
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K.L. Oehler, Pamela C. Cosman, Robert M. Gray et al. · 2002
The authors describe a simple technique for combining vector quantization and low level classification of images. The goal is to classify automatically certain simple features in an image as part of the compression process to enhance their appearance in the reconstructed image. Images in the training sequence are divided into blocks and each block is classified into a particular class by a human observer. This knowledge is used when designing the code-book so that both small average distortion and accurate implicit classification are achieved. The codebook can also be designed to have different average distortions for the different classes. The technique is a variation on a variable rate tree-structured vector quantizer which is grown by splitting a single terminal node at each iteration. The splitting criterion selection allows tradeoffs among compression rate, distortion, and misclassification rate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Thomas Villmann, Sven Haase · Neural Computation · 2011
Supervised and unsupervised vector quantization methods for classification and clustering traditionally use dissimilarities, frequently taken as Euclidean distances. In this article, we investigate the applicability of divergences instead, focusing on online learning. We deduce the mathematical fundamentals for its utilization in gradient-based online vector quantization algorithms. It bears on the generalized derivatives of the divergences known as Fréchet derivatives in functional analysis, which reduces in finite-dimensional problems to partial derivatives in a natural way. We demonstrate the application of this methodology for widely applied supervised and unsupervised online vector quantization schemes, including self-organizing maps, neural gas, and learning vector quantization. Additionally, principles for hyperparameter optimization and relevance learning for parameterized divergences in the case of supervised vector quantization are given to achieve improved classification accuracy.
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Pasquale Romano, F Pasquale Romano, Stephen A. Benton et al. · 1990
This thesis investigates image coding using a combination of sub-band analysis/synthesis techniques and vector quantization. The design of a vector quantizer for image sub-bands is investigated, and the interplay between multi-rate filter banks and the vector coder is examined. The goal is twofold, first, a vector quantizer that is bounded by a distortion criterion versus an apriori fixed limit is essential to more optimally allocate bits in a sub-band coding system. This is due to the dynamic nature of the energy distribution in the sub-bands. Second, parameters for the vector quantizer that are psychophysically and statistically well matched to the characteristics of image sub-bands must be determined. Chrominance information is treated independantly due to reduced acuity in humans to chroma information. Ultimately a moving picture coding system is proposed which affords significant bit rate reductions while maintaining a high degree of flexibility with respect to the feature set required in an interactive multi-media environment. Wherever applicable, the tradeoffs between coding efficiency and flexibility are discussed. Issues involving source material and
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Timo Kaukoranta · 2003
Abstract Scalar quantization is a basic technique for analog‐to‐digital signal transformation. It has an extensive theoretical background in addition to the practical usefulness. Vector quantization offers very good possibilities for lossy signal compression. The method has the great advance that its decoding runs extremely fast. Unfortunately, it includes other complexity problems such as the construction of the codebook, the search of the nearest reproduction vector, and the storage of the codebook. This work describes the basic properties of quantization and introduces several vector quantization structures briefly. Most common methods for codebook construction are described also.
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The MIT Press eBooks · 1999
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Peter F. Swaszek, John B. Thomas · Defense Technical Information Center (DTIC) · 1983
In this report, the authors consider the quantization of random sources. The problem of signal quantizer design under an incomplete statistical description of the source is first considered. It is assumed that a histogram of the source on a finite domain is known. The compandor model for a non-uniform quantizer with a large number of output levels is employed. Both minimum mean and minimaz error criteria are investigated leading to the design of piecewise linear compressors. Topics on the partitioning of the histogram are included. For vector quantization, the design of a spherical coordinates quantizer in k dimensions is discussed. Exact and compandor model solutions are derived as is the factorization of the quantization levels to each quantizer. Numerical examples are presented along with asymptotic results. Also investigated is the optimality of polar quantizers with the subsequent development of optimal circularly symmertric quantizers. Examples of these Dirichlet polar quantizers for the bivariate Gaussian source are included and their performance is compared to optimum error rates. The topic of implementation is considered. (Author)
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King Ngi Ngan, H.C. Koh · IEEE Transactions on Image Processing · 1992
A vector quantization scheme based on the classified vector quantization (CVQ) concept, called predictive classified vector quantization (PCVQ), is presented. Unlike CVQ where the classification information has to be transmitted, PCVQ predicts it, thus saving valuable bit rate. Two classifiers, one operating in the Hadamard domain and the other in the spatial domain, were designed and tested. The classification information was predicted in the spatial domain. The PCVQ schemes achieved bit rate reductions over the CVQ ranging from 20 to 32% for two commonly used color test images while maintaining the same acceptable image quality. Bit rates of 0.70-0.93 bits per pixel (bpp) were obtained depending on the image and PCVQ scheme used.
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J. Mihalik, J. Chmúrny · 1990
Vector image quantization allows the maximum efficiency to be achieved for block image encoding. A shortcoming of an optimal vector quantization block (OVQB) is the presence of a large number of operations consisting of squaring, adding, or subtracting (see [1–3]). Using a block for vector quantization with tree encoding (BVQTE), the number of operations can be reduced (see [4-6]), but the required memory capacity is increased. When OVQB and BVQTE are combined, one can obtain a hybrid vector quantization (HVQB) which allows a high efficiency to be ensured without the shortcomings inherent in the quantization processes in the case when OVQB and BVQTE are used separately. The authors have developed a principle of operation and an optimization algorithm for HVQB which has been presented in the present work along with the theoretical results of optimizing certain of its modifications for vector image quantization. Then the quantization efficiency, number of operations, and requirements governing the memory capacity of the device are estimated, and a comparison is made with results obtained for independent use of OVQB and BVQTE.
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Rodríguez Fonollosa, José Adrián, Masgrau Gómez, Enrique José · RECERCAT (Consorci de Serveis Universitaris de Catalunya)
The authors present a novel multiple-stage vector-quantization method that allows the adaptation of the quantizer to the signal to be coded. This adaptation is computationally very simple and is made with no increase in bit rate. The resulting quantizer provides a robust performance across different speakers and environments. It has been applied to the quantization of the LPC parameters, and the results show a significant increase in performance compared to conventional multistage vector quantizers
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Christian Rohlfing, Hauke Krüger, Peter Vary · 2012
In this paper we present Logarithmic Cubic Vector Quantization (LCVQ), a novel type of gain-shape vector quantization (GSVQ). In LCVQ, the vector to be quantized is decomposed into a gain factor and a shape vec- tor which is a normalized version of the input vector. Both components are quantized independently and transmitted to the decoder. Compared to other GSVQ approaches, in LCVQ the input vectors are normalized such that all shape vectors are lo- cated on the surface of the unit hypercube. As a conclusion, the shape vector quantizer can be realized based on uniform scalar quantizers. This yields low computational complexi ty as well as high memory efficiency even in case of very high vector dimensions. In order to demonstrate the coding efficiency of the proposed quantization scheme, LCVQ is compared to existing quanti- zation schemes, the recently proposed logarithmic spheric al vector quantization (LSVQ), logarithmic scalar quantizat ion (LSQ) and adaptive quantization backward (AQB).
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Robert A. Lindsay, D.E. Abercrombie · 2002
This paper presents a technique for reducing the storage requirements needed to implement a vector quantizer, by restricting the orientations of boundaries allowed to partition the vector space into Voronoi regions. A modification to the LBG algorithm optimizes the quantizer within the constraints of the Voronoi boundary restrictions and a binary tree growth encoder.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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R.P. Rao, William A. Pearlman · IEEE Transactions on Information Theory · 1993
Alphabet-constrained rate-distortion theory is extended to coding of sources with memory. Two different cases are considered: when only the size of the codebook is constrained and when the codevector values are also held fixed. For both cases, nth-order constrained-alphabet rate-distortion functions are defined and a convergent algorithm for their evaluation is presented. Specific simulations using AR(1) sources show that performance near the rate-distortion bound is possible using a reproduction alphabet consisting of a small number of codevectors. It is also shown that the additional constraint of holding the codevector values fixed does not degrade performance of the coder in relation to the size-only constrained case. This observation motivates the development of a fixed-codebook vector quantizer, called the alphabet- and entropy-constrained vector quantizer, the performance of which is comparable to the entropy-constrained vector quantizer. A number of examples using an AR(1) and a speech source are presented to corroborate the theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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