Gaussian Mixture Density Research Articles

Channel identification and signal spectrum estimation for robust automatic speech recognition

A feature estimation technique is proposed for speech signals that are corrupted by both additive and convolutive noises via combining channel identification with power spectrum estimation. A correlation-matching algorithm is developed for channel identification, and a Gaussian mixture density model of speech DFT spectra is formulated for estimation of speech power spectra. Cepstral features of speech are calculated from the estimated power spectra. Using the proposed method, significantly improved accuracy was achieved on speaker-independent continuous speech recognition where the speech data were corrupted by a simulated linear distortion channel and additive white noise.

Feature selection using genetic algorithmand its application to speaker verification

It is shown that a reduction of the set that contains 24 parameters (i.e. the base set) to one that contains only 5, 6, 7, 8 or 10 parameters using a genetic algorithm increases the recognition rate by /spl sim/4.5%. Also, a 0.8% increase in the recognition rate is obtained when a mixture of Gaussian densities are used instead of a single Gaussian density to represent a speaker.

Training mixture density HMMs with SOM and LVQ

The objective of this paper is to present experiments and discussions of how some neural network algorithms can help to improve phoneme recognition using mixture density hidden Markov models (MDHMMs). In MDHMMs, the modelling of the stochastic observation processes associated with the states is based on the estimation of the probability density function of the short-time observations in each state as a mixture of Gaussian densities. The Learning Vector Quantization (LVQ) is used to increase the discrimination between different phoneme models both during the initialization of the Gaussian codebooks and during the actual MDHMM training. The Self-Organizing Map (SOM) is applied to provide a suitably smoothed mapping of the training vectors to accelerate the convergence of the actual training. The codebook topology which is obtained can also be exploited in the recognition phase to speed up the calculations to approximate the observation probabilities. The experiments with LVQ and SOMs show reductions both in the average phoneme recognition error rate and in the computational load compared to the maximum likelihood training and the Generalized Probabilistic Descent (GPD). The lowest final error rate, however, is obtained by using several training algorithms successively. Additional reductions from the online system of about 40% in the error rate are obtained by using the same training methods, but with advanced and higher dimensional feature vectors.

An MLP/HMM hybrid model using nonlinear predictors

In this paper, we propose an MLP/HMM hybrid model in which the input feature vectors are transformed by nonlinear predictors using multilayer perceptrons (MLPs) assigned to each state of a Hidden Markov Model (HMM). The prediction error vectors in the states are modeled by Gaussian mixture densities. The use of a hybrid model is motivated from the need to model the prediction errors in the conventional neural prediction model (NPM) where the prediction errors are variable due to the effect of varying contexts and speaker identity. The MLP/HMM hybrid model is advantageous because frame-correlation in the input speech signal is exploited by employing the MLP predictors, and the variabilities in the prediction error signals are explicitly modeled. We present the training algorithms based on the maximum likelihood (ML) criterion and discriminative criterion for minimum error classification. Experiments were done on speaker-independent continuous speech recognition. By ML training of the hybrid model, we obtained a much better performance than a conventional NPM which does not explicitly model the prediction error signals. By training with the discriminative criterion, confusion among different models was significantly reduced and word error rate was reduced by 56% compared with the ML training.

Implicit models of Gaussian mixture densities and locally optimum detectors

In the classical kernel approximation of a probability density function, a fixed zero-mean smooth approximation of the Dirac delta function is translated to each sample value of the random variable to form a family of density functions. The sample values are the means of the density functions in the corresponding family. The kernel approximation is the average over all members of this family. In certain applications, there may be too few sample values to give a good approximation. In this paper, we propose an approach that utilizes the sample values as the variances of a family of density functions. This approach works particularly well with a Gaussian mixture density.

Feature selection for pattern classification with Gaussian mixture models: A new objective criterion

The selection of a feature set is an important aspect of the pattern classification process. The Fisher ratio is commonly used to rank features with respect to their effectiveness for a given classification task. The procedure used implicitly assumes a symmetric and unimodal probability density for each class. In this paper, we propose a generalized definition of the Fisher ratio as applicable to Gaussian mixture densities, which can represent multi-modal or skewed distributions. The validity and usefulness of the proposed definition is tested by a Monte Carlo simulation experiment. The correlation between the classification results and the proposed objective criterion is found to be better than that attained with the conventional uni-modal measure.

Speaker adaptation using combined transformation and Bayesian methods

Adapting the parameters of a statistical speaker independent continuous-speech recognizer to the speaker and the channel can significantly improve the recognition performance and robustness of the system. In continuous mixture-density hidden Markov models the number of component densities is typically very large, and it may not be feasible to acquire a sufficient amount of adaptation data for robust maximum-likelihood estimates. To solve this problem, we have recently proposed a constrained estimation technique for Gaussian mixture densities. To improve the behavior of our adaptation scheme for large amounts of adaptation data, we combine it here with Bayesian techniques. We evaluate our algorithms on the large-vocabulary Wall Street Journal corpus for nonnative speakers of American English. The recognition error rate is approximately halved with only a small amount of adaptation data, and it approaches the speaker-independent accuracy achieved for native speakers.

A speech recognition method based on the sequential multi-layer perceptrons

A novel multi-layer perceptrons (MLP)-based speech recognition method is proposed in this study. In this method, the dynamic time warping capability of hidden Markov models (HMM) is directly combined with the discriminant based learning of MLP for the sake of employing a sequence of MLPs (SMLP) as a word recognizer. Each MLP is regarded as a state recognizer to distinguish an acoustic event. Next, the word recognizer is formed by serially cascading all state recognizers. Advantages of both HMM and MLP methods are attained in this system through training the SMLP with an algorithm which combines a dynamic programming (DP) procedure with a generalized probabilistic descent (GPD) algorithm. Additionally, two sub-syllable SMLP-based schemes are studied through application of this method toward the recognition of isolated Mandarin digits. Simulation results confirm that the performance of the method is comparable to a well modeled continuous Gaussian mixture density HMM trained with the minimum error criterion. Not only does the SMLP require less trainable parameters than the HMM system, but the former is more convenient for analysing internal features. With the aid of internal feature selection, discarding the least useful parameters of SMLP without affecting its performance is relatively easy.

Gaussian mixture density modeling, decomposition, and applications

We present a new approach to the modeling and decomposition of Gaussian mixtures by using robust statistical methods. The mixture distribution is viewed as a contaminated Gaussian density. Using this model and the model-fitting (MF) estimator, we propose a recursive algorithm called the Gaussian mixture density decomposition (GMDD) algorithm for successively identifying each Gaussian component in the mixture. The proposed decomposition scheme has advantages that are desirable but lacking in most existing techniques. In the GMDD algorithm the number of components does not need to be specified a priori, the proportion of noisy data in the mixture can be large, the parameter estimation of each component is virtually initial independent, and the variability in the shape and size of the component densities in the mixture is taken into account. Gaussian mixture density modeling and decomposition has been widely applied in a variety of disciplines that require signal or waveform characterization for classification and recognition. We apply the proposed GMDD algorithm to the identification and extraction of clusters, and the estimation of unknown probability densities. Probability density estimation by identifying a decomposition using the GMDD algorithm, that is, a superposition of normal distributions, is successfully applied to automated cell classification. Computer experiments using both real data and simulated data demonstrate the validity and power of the GMDD algorithm for various models and different noise assumptions.

Training module for estimating mixture Gaussian densities for speech unit models in speech recognition systems

Training module for estimating mixture Gaussian densities for speech unit models in speech recognition systems

Self-learning speaker and channel adaptation based on spectral variation source decomposition

A self-learning speaker and channel adaptation technique based on the separation of speech spectral variation sources is developed for improving speaker-independent continuous speech recognition. Statistical methods are formulated to remove spectral biases at the acoustic level and to adapt parameters of Gaussian mixture densities at the phone unit level. The spectral bias is estimated in two steps using unsupervised maximum likelihood estimation: the probability distributions of the speech spectral features are first assumed uniform for severely mismatched channels, and the spectral bias is then reestimated using Gaussian phone models. Unsupervised sequential phone model adaptation (USPA) is performed via Bayesian estimation from the on-line, bias-removed speech data, and iterative phone model adaptation (IPA) is further performed for dictation applications. The task vocabulary size was 853; the grammar perplexity was 105; the test speech data were collected under mismatched recording conditions with each test set containing 198 sentences. Depending on the speakers and channel conditions, the two-step spectral bias removal yielded relative error reductions (RER) of 3% to 11% compared to the conventional cepstral mean removal; the USPA yielded RER of 12% to 26% after the two-step bias removal; the IPA further yielded RER of 8% to 19% after the USPA.

Statistical characteristics of moving acoustic sources in ocean waveguides

The statistical characteristics of the response of an array of hydrophones to a moving narrow-band acoustic source in an ocean waveguide are investigated. The discrete Fourier transform of a solution of the wave equation with a moving source is calculated, and the sequence of the amplitudes of the Fourier coefficients at particular frequencies are shown to contain oscillatory terms that depend upon the environment, the source frequency, position and velocity, and the resolution of the DFT. This analysis suggests that Gaussian mixture densities may apply to time series of Fourier coefficients of data received from a moving source. This is verified by analyzing data from a deep water Navy experiment. Simulations are then carried out which show that the fluctuations caused by source motion are sufficient to favor Gaussian mixture densities over Gaussian densities and that the applicability of the Gaussian model, but not the Gaussian mixture model, depends upon the velocity and position of the source.

Gaussian mixture density modeling of non-Gaussian source for autoregressive process

A new approach is taken to model non-Gaussian sources of AR processes using Gaussian mixture densities that are known to be effective for approximating wide varieties of probability distributions. A maximum likelihood estimation algorithm is derived for estimating the AR parameters by solving a generalized normal equation, and a clustering algorithm is used for estimating the parameters of Gaussian mixture density of the source signals. The correlation matrix of the generalized normal equation is not Toeplitz but is symmetric and in general positive definite. Higher order statistics of skewness and kurtosis are used for identifying the source distribution as being Gaussian or non-Gaussian and, consequently, determining the parameter estimation technique between the conventional method and the proposed method. Experiments on non-Gaussian source AR processes demonstrate that under high SNR conditions (SNR/spl ges/20 dB), the proposed algorithm outperforms the conventional AR estimation algorithm and the cumulant-based algorithm by an order-of-magnitude reduction of average estimation errors. The proposed algorithm also has very low estimation errors with short data records. Finally, a maximum likelihood prediction method is formulated for non-Gaussian source AR processes that has shown potential in achieving higher efficiency signal coding than linear predictive coding. >

Speaker adaptation using constrained estimation of Gaussian mixtures

A trend in automatic speech recognition systems is the use of continuous mixture-density hidden Markov models (HMMs). Despite the good recognition performance that these systems achieve on average in large vocabulary applications, there is a large variability in performance across speakers. Performance degrades dramatically when the user is radically different from the training population. A popular technique that can improve the performance and robustness of a speech recognition system is adapting speech models to the speaker, and more generally to the channel and the task. In continuous mixture-density HMMs the number of component densities is typically very large, and it may not be feasible to acquire a sufficient amount of adaptation data for robust maximum-likelihood estimates. To solve this problem, the authors propose a constrained estimation technique for Gaussian mixture densities. The algorithm is evaluated on the large-vocabulary Wall Street Journal corpus for both native and nonnative speakers of American English. For nonnative speakers, the recognition error rate is approximately halved with only a small amount of adaptation data, and it approaches the speaker-independent accuracy achieved for native speakers. For native speakers, the recognition performance after adaptation improves to the accuracy of speaker-dependent systems that use six times as much training data. >

An acoustic-phonetic-based speaker adaptation technique for improving speaker-independent continuous speech recognition

A new speaker adaptation technique is proposed for improving speaker-independent continuous speech recognition based on a decomposition of spectral variation sources. In this technique, the spectral variations are separated into two categories, one acoustic and the other phone-specific, where each variation source is modeled by a linear transformation system. The technique consists of two sequential steps: first, acoustic normalization is performed, and second, phone model parameters are adapted. Experiments of speaker adaptation on the TIMIT database using short calibration speech (5 s per speaker) have shown significant performance improvement over the baseline speaker-independent continuous speech recognition, where the recognition system uses Gaussian mixture density based hidden Markov models of phone units. For a vocabulary size of 853 and test set perplexity of 104, the recognition word accuracy has been improved from 86.9% for the baseline system to 90.5% after adaptation, corresponding to an error reduction of 27.5%. On a more difficult test set that contains an additional variation source due to recording channel mismatch, a more significant performance improvement has been obtained: for the same vocabulary and a test set perplexity of 101, the recognition word accuracy has been improved from 65.4% for the baseline to 86.0% after adaptation, corresponding to an error reduction of 59.5%.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Training module for estimating mixture Gaussian densities for speech-unit models in speech recognition systems

A model-training module generates mixture Gaussian density models from speech training data for continuous, or isolated word speech recognition systems. Speech feature sequences are labeled into segments of states of speech units using Viterbi-decoding based optimized segmentation algorithm. Each segment is modeled by a Gaussian density, and the parameters are estimated by sample mean and sample covariance. A mixture Gaussian density is generated for each state of each speech unit by merging the Gaussian densities of all the segments with the same corresponding label. The resulting number of mixture components is proportional to the dispersion and sample size of the training data. A single, fully merged, Gaussian density is also generated for each state of each speech unit. The covariance matrices of the mixture components are selectively smoothed by a measure of relative sharpness of the Gaussian density and the smoothing can also be done blockwise. The weights of the mixture components are set uniformly initially, and are reestimated using a segmental-average procedure. The weighting coefficients, together with the Gaussian densities, then become the models of speech units for use in speech recognition.

Experimental evaluation of features for robust speaker identification

This correspondence presents an experimental evaluation of different features and channel compensation techniques for robust speaker identification. The goal is to keep all processing and classification steps constant and to vary only the features and compensations used to allow a controlled comparison. A general, maximum-likelihood classifier based on Gaussian mixture densities is used as the classifier, and experiments are conducted on the King speech database, a conversational, telephone-speech database. The features examined are mel-frequency and linear-frequency filterbank cepstral coefficients, linear prediction cepstral coefficients, and perceptual linear prediction (PLP) cepstral coefficients. The channel compensation techniques examined are cepstral mean removal, RASTA processing, and a quadratic trend removal technique. It is shown for this database that performance differences between the basic features is small, and the major gains are due to the channel compensation techniques. The best "across-the-divide" recognition accuracy of 92% is obtained for both high-order LPC features and band-limited filterbank features.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonparametric multivariate density estimation: a comparative study

The paper algorithmically and empirically studies two major types of nonparametric multivariate density estimation techniques, where no assumption is made about the data being drawn from any of known parametric families of distribution. The first type is the popular kernel method (and several of its variants) which uses locally tuned radial basis (e.g., Gaussian) functions to interpolate the multidimensional density; the second type is based on an exploratory projection pursuit technique which interprets the multidimensional density through the construction of several 1D densities along highly "interesting" projections of multidimensional data. Performance evaluations using training data from mixture Gaussian and mixture Cauchy densities are presented. The results show that the curse of dimensionality and the sensitivity of control parameters have a much more adverse impact on the kernel density estimators than on the projection pursuit density estimators.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A speaker-independent continuous speech recognition system using continuous mixture Gaussian density HMM of phoneme-sized units

The author describes a large vocabulary, speaker-independent, continuous speech recognition system which is based on hidden Markov modeling (HMM) of phoneme-sized acoustic units using continuous mixture Gaussian densities. A bottom-up merging algorithm is developed for estimating the parameters of the mixture Gaussian densities, where the resultant number of mixture components is proportional to both the sample size and dispersion of training data. A compression procedure is developed to construct a word transcription dictionary from the acoustic-phonetic labels of sentence utterances. A modified word-pair grammar using context-sensitive grammatical parts is incorporated to constrain task difficulty. The Viterbi beam search is used for decoding. The segmental K-means algorithm is implemented as a baseline for evaluating the bottom-up merging technique. The system has been evaluated on the TIMIT database (1990) for a vocabulary size of 853. For test set perplexities of 24, 104, and 853, the decoding word accuracies are 90.9%, 86.0%, and 62.9%, respectively. For the perplexity of 104, the decoding accuracy achieved by using the merging algorithm is 4.1% higher than that using the segmental K-means (22.8% error reduction), and the decoding accuracy using the compressed dictionary is 3.0% higher than that using a standard dictionary (18.1% error reduction). >

Bayesian learning for hidden Markov model with Gaussian mixture state observation densities

An investigation into the use of Bayesian learning of the parameters of a multivariate Gaussian mixture density has been carried out. In a framework of continuous density hidden Markov model (CDHMM), Bayesian learning serves as a unified approach for parameter smoothing, speaker adaptation, speaker clustering and corrective training. The goal is to enhance model robustness in a CDHMM-based speech recognition system so as to improve performance. Our approach is to use Bayesian learning to incorporate prior knowledge into the training process in the form of prior densities of the HMM parameters. The theoretical basis for this procedure is presented and results applying it to parameter smoothing, speaker adaptation, speaker clustering and corrective training are given.