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Conventional chance-constrained programming methods suffer from the inexactness of the estimated probability distribution of the underlying uncertainty from data. To this end, a distributionally robust approach to the problem allows for a level of ambiguity considered around a reference distribution. In this work, we propose a novel formulation for the distributionally robust chance-constrained programming problem using an ambiguity set constructed from a variant of optimal transport distance that was developed for Gaussian Mixture Models. We show that for multimodal process uncertainty, our proposed method provides an effective way to incorporate statistical moment information into the ambiguity set construction step, thus leading to improved optimal solutions. We illustrate the performance of our method on a numerical example as well as a chemical process case study. We show that our proposed methodology leverages the multimodal characteristics from the uncertainty data to give superior performance over the traditional Wasserstein distance-based method. • Ambiguity set constructed from optimal transport between Gaussian Mixture Models. • Hedging against the right family of candidate distributions to avoid unnecessary conservatism. • A tractable distributionally robust chance constrained optimization formulation. • Applicability to more generate type of uncertain constraints. • Better objective-constraint satisfaction trade-off performance than classical Wasserstein DRCCP model. [ABSTRACT FROM AUTHOR]

Zinc oxide nanoparticles (ZnO) possess unique features that mak them a common matter among different industries. Nevertheless, traditional models of synthesizing ZnO-NPs are related with health and environmental and risks due to harmful chemicals. The biosynthesis of zinc oxide nanoparticles was achieved using the hot water extract of Sargassum wightii (SW) , which serves as a reducing agent. This extract is mixed with zinc precursors, initiating a bio-reduction process. UV–vis , FTIR , XRD , Raman , DLS , SEM , EDX , TEM imaging, and XPS analysis are used. The novelty of this research lies in utilizing a bio-reduction process involving hot water extract of SW to synthesize zinc oxide nanoparticles, providing a safer and eco-friendly alternative to traditional chemical methods. Here, the zinc oxide nanoparticles produced through the biosynthesis process effectively addressed oral infections (Streptococcus mutans) due to their ability to disrupt the integrity of bacterial cell membranes, interfere with cellular processes, and inhibit the growth and proliferation of bacteria responsible for oral infections. Gaussian Mixture Models (GMMs) uncover intricate patterns within medical data, enabling enhanced diagnostics, treatment personalization, and patient outcomes. This study aims to apply Gaussian Mixture Models (GMMs) to medical data for subpopulation identification and disease subtyping, contributing to personalized treatment strategies and improved patient care. With a dataset comprising 300 samples, the application of GMM showed lower BIC and AIC values (2500, 3200), a high Silhouette Score (0.65 from −1 to 1) reflecting well-defined clusters, Calinski-Harabasz (120) and Davies-Bouldin Indices (0.45). These metrics collectively underscored the model's success in revealing distinct patterns within the data. ZnO -nanocoated aligners were effective against Streptococcus mutans , with the maximum antibacterial effect observed for 2 days and lasting for 7 days. • Enhanced Green Synthesis: Sargassum wightii-Derived ZnO NPs. • Extensive ZnO NPs Characterization: In-depth Analysis of Properties. • Broad-Spectrum Antibacterial: ZnO NPs Active Against Various Strains. • ZnO NPs' Anticancer Efficacy: Demonstrated Action on MCF-7 Cells. • Sustainable and Versatile: Eco-Conscious Synthesis and Varied Uses. [ABSTRACT FROM AUTHOR]

In this letter, we proposed a novel optimal view generation framework based on the genetic algorithm (GA) and Gaussian mixture models (GMMs) to improve multiview active learning (MV-AL). AL methods enlarge training data sets, by iteratively selecting the most informative samples, in order to improve the classification performance. By using multiple views to build multiple classifiers, the information content of each unlabeled samples can be more accurately estimated. The MV-AL methods are more inherently suitable for high-dimensional data such as hyperspectral images. This hybrid framework simultaneously constructs the optimal number of diverse and sufficient views. The proposed algorithm has two main steps. In the first step, by applying a cluster distortion function-based GMMs, the actual number of available independent views is determined. In the next step, a hybrid GA approach selects the optimal combination of views using two different criteria. The experiments were conducted on two benchmark hyperspectral data sets, namely, Kennedy Space Center (KSC) and Indian Pines AVIRIS. The results demonstrated an increase in diversity and sufficiency of the views compared to the traditional view generation methods. Furthermore, the performance of MV-AL has also been significantly improved. [ABSTRACT FROM AUTHOR]

Deep belief networks (DBNs) have shown impressive improvements over the Gaussian mixture models whilst are employed inside the Hidden Markov Model (HMM)-based automatic speech recognition systems. In this study, the benefits of the DBNs to be used in audiovisual speech recognition systems are investigated. First, the DBN-HMMs are explored in speech recognition and lip-reading tasks, separately. Next, the challenge of appropriately integrating the audio and visual information is studied; for this purpose, the application of the fused feature in an audiovisual (AV) DBN-HMM based speech recognition task is studied. With regard to the integration of information, those layers that provide generalities and details with together, so that in overall a completion is made, are selected. A modified technique is proposed based on the entropy of different layers of the used DBNs, to measure the amount of information. The best audio layer representation is found to have the highest entropy, with the highest power of providing information details in the fusion scheme. In contrast, the best visual layer representation is found to have the lowest entropy, which could best provide sufficient generalities. Over the CUAVE database, on English digit recognition task, the conducted experiments show that the AV DBN-HMM, with proposed feature fusion method, can reduce phone error rate by as much as 4% and 1.5%, and word error rate by about 3.49% and 1.89%, over the baseline conventional HMM and audio DBN-HMM, respectively. [ABSTRACT FROM AUTHOR]

The Kullback–Leibler (KL) divergence between two mixture models is a fundamental primitive in many signal processing tasks. Since the KL divergence of mixtures does not admit a closed-form formula, it is in practice either estimated using costly Monte-Carlo stochastic integration or approximated. We present a fast and generic method that builds algorithmically closed-form lower and upper bounds on the entropy, the cross-entropy and the KL divergence of univariate mixtures. We illustrate the versatile method by reporting on our experiments for approximating the KL divergence between Gaussian mixture models. [ABSTRACT FROM PUBLISHER]

We propose an efficient method for image/video figure-ground segmentation using feature relevance (FR) and active contours. Given a set of positive and negative examples of a specific foreground (an object of interest (OOI) in an image or a tracked objet in a video), we first learn the foreground distribution model and its characteristic features that best discriminate it from its contextual background. For this goal, an objective function based on feature likelihood ratio is proposed for supervised FR computation. FR is then incorporated in foreground segmentation of new images and videos using level sets and energy minimization. We show the effectiveness of our approach on several examples of image/video figure-ground segmentation. [ABSTRACT FROM AUTHOR]

Video object segmentation is a challenging problem. Without human annotation or other prior information, it is hard to select a meaningful primary object from a single video, so extracting the primary object across videos is a more promising approach. However, existing algorithms consider the problem as foreground/background segmentation. Therefore, we propose an algorithm that learns the model of the primary object by representing the frames/videos as a graphical model. The probabilistic graphical model is built across a set of videos based on an object proposal algorithm. Our approach considers appearance , spatial, and temporal consistency of the primary objects. A new dataset is created to evaluate the proposed method and to compare it to the state-of-the-art on video object co-segmentation. The experiments show that our method obtains state-of-the-art results, outperforming other algorithms by 1.5% (pixel accuracy) on the MOViCS dataset and 9.6% (pixel accuracy ) on the new dataset. [ABSTRACT FROM PUBLISHER]

We propose a new method for a supervised online estimation of probabilistic discriminative models for classification tasks. The method estimates the class distributions from a stream of data in the form of Gaussian mixture models (GMMs). The reconstructive updates of the distributions are based on the recently proposed online kernel density estimator (oKDE). We maintain the number of components in the model low by compressing the GMMs from time to time. We propose a new cost function that measures loss of interclass discrimination during compression, thus guiding the compression toward simpler models that still retain discriminative properties. The resulting classifier thus independently updates the GMM of each class, but these GMMs interact during their compression through the proposed cost function. We call the proposed method the online discriminative kernel density estimator (odKDE). We compare the odKDE to oKDE, batch state-of-the-art kernel density estimators (KDEs), and batch/incremental support vector machines (SVM) on the publicly available datasets. The odKDE achieves comparable classification performance to that of best batch KDEs and SVM, while allowing online adaptation from large datasets, and produces models of lower complexity than the oKDE. [ABSTRACT FROM PUBLISHER]

We present a framework for the estimation of driver behavior at intersections, with applications to autonomous driving and vehicle safety. The framework is based on modeling the driver behavior and vehicle dynamics as a hybrid-state system (HSS), with driver decisions being modeled as a discrete-state system and the vehicle dynamics modeled as a continuous-state system. The proposed estimation method uses observable parameters to track the instantaneous continuous state and estimates the most likely behavior of a driver given these observations. This paper describes a framework that encompasses the hybrid structure of vehicle–driver coupling and uses hidden Markov models (HMMs) to estimate driver behavior from filtered continuous observations. Such a method is suitable for scenarios that involve unknown decisions of other vehicles, such as lane changes or intersection access. Such a framework requires extensive data collection, and the authors describe the procedure used in collecting and analyzing vehicle driving data. For illustration, the proposed hybrid architecture and driver behavior estimation techniques are trained and tested near intersections with exemplary results provided. Comparison is made between the proposed framework, simple classifiers, and naturalistic driver estimation. Obtained results show promise for using the HSS–HMM framework. [ABSTRACT FROM PUBLISHER]

We present a novel approach for the detection of severe obstructive sleep apnea (OSA) based on patients’ voices introducing nonlinear measures to describe sustained speech dynamics. Nonlinear features were combined with state-of-the-art speech recognition systems using statistical modeling techniques (Gaussian mixture models, GMMs) over cepstral parameterization (MFCC) for both continuous and sustained speech. Tests were performed on a database including speech records from both severe OSA and control speakers. A 10 % relative reduction in classification error was obtained for sustained speech when combining MFCC-GMM and nonlinear features, and 33 % when fusing nonlinear features with both sustained and continuous MFCC-GMM. Accuracy reached 88.5 % allowing the system to be used in OSA early detection. Tests showed that nonlinear features and MFCCs are lightly correlated on sustained speech, but uncorrelated on continuous speech. Results also suggest the existence of nonlinear effects in OSA patients’ voices, which should be found in continuous speech. [ABSTRACT FROM AUTHOR]

A robust method to monitor the operating conditions of induction motors is presented. This method utilizes the data analysis of the air-gap torque profile in conjunction with a Bayesian classifier to determine the operating condition of an induction motor as either healthy or faulty. This method is trained offline with datasets generated either from an induction motor modeled by a time-stepping finite-element (TSFE) method or experimental data. This method can effectively monitor the operating conditions of induction motors that are different in frame/class, ratings, or design from the motor used in the training stage. Such differences can include the level of load torque and operating frequency. This is due to a novel air-gap torque normalization method introduced here, which leads to a motor fault classification process independent of these parameters and with no need for prior information about the motor being monitored. The experimental results given in this paper validate the robustness and efficacy of this method. Additionally, this method relies exclusively on data analysis of motor terminal operating voltages and currents, without relying on complex motor modeling or internal performance parameters not readily available. [ABSTRACT FROM PUBLISHER]

In this paper, we present a new algorithm for pixel labeling and image segmentation based on the standard Gaussian mixture model (GMM). Unlike the standard GMM where pixels themselves are considered independent of each other and the spatial relationship between neighboring pixels is not taken into account, the proposed method incorporates this spatial relationship into the standard GMM. Moreover, the proposed model requires fewer parameters compared with the models based on Markov random fields. In order to estimate model parameters from observations, instead of utilizing an expectation–maximization algorithm, we employ gradient method to minimize a higher bound on the data negative log-likelihood. The performance of the proposed model is compared with methods based on both standard GMM and Markov random fields, demonstrating the robustness, accuracy, and effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the use of a Gaussian Mixture Model (GMM)-based quantizer for quantization of the Line Spectral Frequencies (LSFs) in the Adaptive Multi-Rate (AMR) speech codec. We estimate the parametric GMM model of the probability density function (pdf) for the prediction error (residual) of mean-removed LSF parameters that are used in the AMR codec for speech spectral envelope representation. The studied GMM-based quantizer is based on transform coding using Karhunen-Loève transform (KLT) and transform domain scalar quantizers (SQ) individually designed for each Gaussian mixture. We have investigated the applicability of such a quantization scheme in the existing AMR codec by solely replacing the AMR LSF quantization algorithm segment. The main novelty in this paper lies in applying and adapting the entropy constrained (EC) coding for fixed-rate scalar quantization of transformed residuals thereby allowing for better adaptation to the local statistics of the source. We study and evaluate the compression efficiency, computational complexity and memory requirements of the proposed algorithm. Experimental results show that the GMM-based EC quantizer provides better rate/distortion performance than the quantization schemes used in the referent AMR codec by saving up to 7.32 bits/frame at much lower rate-independent computational complexity and memory requirements. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach to improve the amount of information extracted from the speech aiming to increase the accuracy of a system developed for the automatic detection of pathological voices. The paper addresses the discrimination capabilities of 11 features extracted using nonlinear analysis of time series. Two of these features are based on conventional nonlinear statistics (largest Lyapunov exponent and correlation dimension), two are based on recurrence and fractal-scaling analysis, and the remaining are based on different estimations of the entropy. Moreover, this paper uses a strategy based on combining classifiers for fusing the nonlinear analysis with the information provided by classic parameterization approaches found in the literature (noise parameters and mel-frequency cepstral coefficients). The classification was carried out in two steps using, first, a generative and, later, a discriminative approach. Combining both classifiers, the best accuracy obtained is 98.23% ± 0.001. [ABSTRACT FROM AUTHOR]

Any modification applied to speech signals has an impact on their perceptual quality. In particular, voice conversion to modify a source voice so that it is perceived as a specific target voice involves prosodic and spectral transformations that produce significant quality degradation. Choosing among the current voice conversion methods represents a trade-off between the similarity of the converted voice to the target voice and the quality of the resulting converted speech, both rated by listeners. This paper presents a new voice conversion method termed Weighted Frequency Warping that has a good balance between similarity and quality. This method uses a time-varying piecewise-linear frequency warping function and an energy correction filter, and it combines typical probabilistic techniques and frequency warping transformations. Compared to standard probabilistic systems, Weighted Frequency Warping results in a significant increase in quality scores, whereas the conversion scores remain almost unaltered. This paper carefully discusses the theoretical aspects of the method and the details of its implementation, and the results of an international evaluation of the new system are also included. [ABSTRACT FROM AUTHOR]

Query-by-semantic-description (QBSD) is a natural way for searching/annotating music in a large database. To improve QBSD, we propose the use of anti-words for each annotation word based on the concept of supervised multiclass labeling (SML). More specifically, words that are highly associated with the opposite semantic meaning of a word constitute its anti-word set. By modeling both a word and its anti-word set, our annotation system can achieve 31.1% of equal mean per-word precision and recall, while the original SML model achieves 27.8%. Moreover, by constructing the models of the anti-word explicitly, the performance is also significantly improved for the retrieval system, especially when the query keyword is the antonym of an existing annotation word. [ABSTRACT FROM AUTHOR]

A Bayesian data fusion approach for seabed classification using multiview synthetic aperture sonar (SAS) imagery is proposed. The principled approach exploits all available information and results in probabilistic predictions. Each data point, corresponding to a unique 10 m × 10 m area of seabed, is represented by a vector of wavelet-based features. For each seabed type. the distribution of these features is then modeled by a unique Gaussian mixture model. When multiple views of the same data point (i.e., area of seabed) are available, the views are combined via a joint likelihood calculation. The end result of this Bayesian formulation is the posterior probability that a given data point belongs to each seabed type. It is also shown how these posterior probabilities can be exploited in a form of entropy-based active-learning to determine the most useful additional data to acquire. Experimental results of the proposed multiview classification framework are shown on a large data set of real, multiview SAN imagery spanning more than 2 km2 of seabed. [ABSTRACT FROM AUTHOR]

Gaussian mixture model (GMM)-based predictive coding of line spectral frequencies (LSFs) has gained wide acceptance. In such coders, each mixture of a GMM can be interpreted as defining a linear predictive transform coder. In this paper, we use Kalman filtering principles to model each of these linear predictive transform coders to present GMM Kalman predictive coding. In particular, we show how suitable modeling of quantization noise leads to an adaptive a posteriori GMM that defines a signal-adaptive predictive coder that provides improved coding of LSFs in comparison with the baseline recursive GMM predictive coder. Moreover, we show how running the GMM Kalman predictive coders to convergence can be used to design a stationary GMM Kaiman predictive coding system which again provides improved coding of LSFs but now with only a modest increase in run-time complexity over the baseline. In packet loss conditions, this stationary GMM Kalman predictive coder provides much better performance than the recursive GMM predictive coder, and in fact has comparable mean performance to a memoryless GMM coder. Finally, we illustrate how one can utilize Kalman filtering principles to design a postfilter which enhances decoded vectors from a recursive GMM predictive coder without any modifications to the encoding process. [ABSTRACT FROM AUTHOR]

This paper presents a method for automatic classification of birds into different species based on the audio recordings of their sounds. Each individualsyllable segmented from continuous recordings is regarded as the basic recognition unit. To represent the temporal variations as well as sharp transitions within a syllable, a feature set derived from static and dynamic two-dimensional Mel-frequency cepstral coefficients are calculated for the classification of each syllable. Since a bird might generate several types of sounds with variant characteristics, a number of representative prototype vectors are used to model different syllables of identical bird species. For each bird species, a model selection method is developed to determine the optimal mode between Gaussian mixture models (GMM) and vector quantization (VQ) when the amount of training data is different for each species. In addition, a component number selection algorithm is employed to find the most appropriate number of components of GMM or the cluster number of VQ for each species. The mean vectors of GMM or the cluster centroids of VQ will form the prototype vectors of a certain bird species. In the experiments, the best classification accuracy is 84.06% for the classification of 28 bird species. [ABSTRACT FROM AUTHOR]

In this paper, the expectation-maximization (EM) algorithm for Gaussian mixture modeling is improved via three statistical tests. The first test is a multivariate normality criterion based on the Mahalanobis distance of a sample measurement vector from a certain Gaussian component center. The first test is used in order to derive a decision whether to split a component into another two or not. The second test is a central tendency criterion based on the observation that multivariate kurtosis becomes large if the component to be split is a mixture of two or more underlying Gaussian sources with common centers. If the common center hypothesis is true, the component is split into two new components and their centers are initialized by the center of the (old) component candidate for splitting. Otherwise, the splitting is accomplished by a discriminant derived by the third test. This test is based on marginal cumulative distribution functions. Experimental results are presented against seven other EM variants both on artificially generated data-sets and real ones. The experimental results demonstrate that the proposed EM variant has an increased capability to find the underlying model, while maintaining a low execution time. [ABSTRACT FROM PUBLISHER]

Motion trajectories provide rich spatiotemporal information about an object's activity. This paper presents novel classification algorithms for recognizing object activity using object motion trajectory. In the proposed classification system, trajectories are segmented at points of change in curvature, and the subtrajectories are represented by their principal component analysis (PCA) coefficients. We first present a framework to robustly estimate the multivariate probability density function based on PCA coefficients of the subtrajectories using Gaussian mixture models (GMMs). We show that GMM-based modeling alone cannot capture the temporal relations and ordering between underlying entities. To address this issue, we use hidden Markov models (HMMs) with a data-driven design in terms of number of states and topology (e.g., left-right versus ergodic). Experiments using a database of over 5700 complex trajectories (obtained from UCI-KDD data archives and Columbia University Multimedia Group) subdivided into 85 different classes demonstrate the superiority of our proposed 11MM-based scheme using PCA coefficients of subtrajectories in comparison with other techniques in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a set of feature vector normalization methods based on the minimum mean square error (MMSE) criterion and stereo data is presented. They include multi-environment model-based linear normalization (MEMLIN), polynomial MEMLIN (P-MEMLIN), multi-environment model-based histogram normalization (MEMHIN), and phoneme-dependent MEMLIN (PD-MEMLIN). Those methods model clean and noisy feature vector spaces using Gaussian mixture models (GMMs). The objective of the methods is to learn a transformation between clean and noisy feature vectors associated with each pair of clean and noisy model Gaussians. The direct approach to learn the transformation is by using stereo data; that is, noisy feature vectors and the corresponding clean feature vectors. In this paper, however, a nonstereo data based training procedure, is presented. The transformations can be modeled just like a bias vector (MEMLIN), or by using a first-order polynomial (P-MEMLIN) or a nonlinear function based on histogram equalization (MEMHIN). Further improvements are obtained by using phoneme-dependent bias vector transformation (PD-MEMLIN). In PD-MEMLIN, the clean and noisy feature vector spaces are split into several phonemes, and each of them is modeled as a GMM. Those methods achieve significant word error rate improvements over others that are based on similar targets. The experimental results using the SpeechDat Car database show an average improvement in word error rate greater than 68% in all cases compared to the baseline when using the original clean acoustic models, and up to 83% when training acoustic models on the new normalized feature space. [ABSTRACT FROM AUTHOR]

Spectral representation of speech is complete when both the Fourier transform magnitude and phase spectra are specified. In conventional speech recognition systems, features are generally derived from the short-time magnitude spectrum. Although the importance of Fourier transform phase in speech perception has been realized, few attempts have been made to extract features from it. This is primarily because the resonances of the speech signal which manifest as transitions in the phase spectrum are completely masked by the wrapping of the phase spectrum. Hence, an alternative to processing the Fourier transform phase, for extracting speech features, is to process the group delay function which can be directly computed from the speech signal. The group delay function has been used in earlier efforts, to extract pitch and formant information from the speech signal. In all these efforts, no attempt was made to extract features from the speech signal and use them for speech recognition applications. This is primarily because the group delay function fails to capture the short-time spectral structure of speech owing to zeros that are close to the unit circle in the z-plane and also due to pitch periodicity effects. In this paper, the group delay function is modified to overcome these effects. Cepstral features are extracted from the modified group delay function and are called the modified group delay feature (MODGDF). The MODGDF is used for three speech recognition tasks namely, speaker, language, and continuous-speech recognition. Based on the results of feature and performance evaluation, the significance of the MODGDF as a new feature for speech recognition is discussed. [ABSTRACT FROM AUTHOR]

Gaussian mixture models (GMMs) have proven extremely successful for text-independent speaker recognition. The standard training method for GMM models is to use MAP adaptation of the means of the mixture components based on speech from a target speaker. Recent methods in compensation for speaker and channel variability have proposed the idea of stacking the means of the GMM model to form a GMM mean supervector. We examine the idea of using the GMM supervector in a support vector machine (SVM) classifier. We propose two new SVM kernels based on distance metrics between GMM models. We show that these SVM kernels produce excellent classification accuracy in a NIST speaker recognition evaluation task. [ABSTRACT FROM AUTHOR]

It has been previously demonstrated that systems based on local features and relatively complex statistical models, namely, one-dimensional (1-D) hidden Markov models (HMMs) and pseudo-two-dimensional (2-D) HMMs, are suitable for face recognition. Recently, a simpler statistical model, namely, the Gaussian mixture model (GMM), was also shown to perform well. In much of the literature devoted to these models, the experiments were performed with controlled images (manual face localization, controlled lighting, background, pose, etc). However, a practical recognition system has to be robust to more challenging conditions. In this article we evaluate, on the relatively difficult BANCA database, the performance, robustness and complexity of GMM and HMM-based approaches, using both manual and automatic face localization. We extend the GMM approach through the use of local features with embedded positional information, increasing performance without sacrificing its low complexity. Furthermore, we show that the traditionally used maximum likelihood (ML) training approach has problems estimating robust model parameters when there is only a few training images available. Considerably more precise models can be obtained through the use of Maximum a posteriori probability (MAP) training. We also show that face recognition techniques which obtain good performance on manually located faces do not necessarily obtain good performance on automatically located faces, indicating that recognition techniques must be designed from the ground up to handle imperfect localization. Finally, we show that while the pseudo-2-D HMM approach has the best overall performance, authentication time on current hardware makes it impractical. The best tradeoff in terms of authentication time, robustness and discrimination performance is achieved by the extended GMM approach. [ABSTRACT FROM AUTHOR]

An algorithm for multiple description coding (MDC) based on Gaussian mixture models (GMMs) is presented. Based on the parameters of the GMM, the algorithm combines MDC scalar quantizers, yielding a source-optimized vector MDC system. The performance is evaluated on a speech spectrum source in terms of mean-squared error and log spectral distortion. It is demonstrated experimentally that the proposed system outperforms single description coding and repetition coding over a wide range of channel failure probabilities. The proposed algorithm has a complexity that is linear in rate and dimension while retaining a near optimal vector quantizer point density. [ABSTRACT FROM AUTHOR]