Gaussian Component Based Index for GMMs

In many modern applications such as biometric identification systems, sensor networks, medical imaging, geology, and multimedia databases, the data objects are not described exactly. Therefore, recent solutions propose to model data objects by probability density functions(pdf). Since a pdf describing an uncertain object is often not explicitly known, approximation techniques like Gaussian mixture models(GMM) need to be employed. In this paper, we introduce a method for efficiently indexing and querying GMMs allowing fast object retrieval for arbitrary shaped pdf. We consider probability ranking queries which are very important for probabilistic similarity search. Our method stores the components and weighting functions of each GMM in an index structure. During query processing the mixture models are dynamically reconstructed whenever necessary. In an extensive experimental evaluation, we demonstrate that GMMs yield a compact and descriptive representation of video clips. Additionally, we show that our new query algorithm outperforms competitive approaches when answering the given probabilistic queries on a database of GMMs comprising about 100.000 single Gaussians.

This article proposes the distribution similarity measure–based Gaussian mixtures model for the contact-state (CS) modelling in force-guided robotic assembly processes of flexible rubber parts. The wrench (Cartesian force and torque) signals of the manipulated object are captured for different states of the given assembly process. The distribution similarity measure–based Gaussian mixtures model CS modelling scheme is employed in modelling the captured wrench signals for different CSs. The proposed distribution similarity measure–based Gaussian mixtures model CS modelling scheme uses the Gaussian mixtures model in modelling the captured signals. The parameters of the Gaussian mixtures models are computed using expectation maximisation. The optimal number of Gaussian mixtures model components for each CS model is determined by considering the classification success rate as an index for the similarity measure between the distribution of the captured signals and the developed models. The optimal number of Gaussian mixtures model components corresponds to the highest classification success rate; hence, object elasticity variation would be accommodated by properly choosing the optimal number of Gaussian mixtures model components. The performance of the proposed distribution similarity measure–based Gaussian mixtures model CS modelling strategy is evaluated by a test stand composed of a KUKA lightweight robot doing peg-in-hole assembly processes for flexible rubber objects. Two rubber objects with different elasticity are considered for two experiments; in the first experiment, an elastic peg of 30 Shore A hardness is considered and that of the second experiment has hardness of 6 Shore A which is even softer than the one used in experiment 1. Employing the proposed distribution similarity measure–based Gaussian mixtures model CS modelling strategy excellent classification success rate was obtained for both experiments. However, more Gaussian mixtures model components are required for the softer one that gives a strong impression of the non-stationarity behaviour increment for softer materials. Comparison is performed with the available CS modelling schemes and the distribution similarity measure–based Gaussian mixtures model is shown to provide the best classification success rate performance with a reduced computational time.

In rarefied gas flows, discontinuity phenomena such as velocity slip and temperature jump commonly appear in the gas layer adjacent to a solid boundary. Due to the physical complexity of the interactions at the gas-solid interface, particularly in the case of systems with local nonequilibrium state, boundary models with limited number of parameters cannot completely describe the reflection of gas molecules at the boundary. In this work, the Gaussian mixture (GM) model, which is an unsupervised machine learning technique, is employed to construct a statistical gas-solid surface scattering model based on the collisional data obtained from molecular dynamics (MD) simulations. The GM model is applied to study Couette flow for different inert gases (Ar and He) confined between two parallel infinite gold walls at different temperatures. A direct comparison between the results obtained from the GM model and the Cercignani-Lampis-Lord (CLL) scattering kernel against the MD collisional data in terms of the distribution of the predicted postcollisional velocities, and accommodation coefficients has shown that the results from the GM model are an excellent match with the MD results outperforming the CLL scattering kernel. As an example, for He gas, while the predicted energy accommodation coefficient by the CLL model is more than two times higher than the MD predictions, the value computed by the GM model is in excellent agreement with the MD results. This superior performance of the GM model confirms its high potential to derive a generalized boundary condition in systems encountered with highly nonequilibrium and complex gas flow conditions.

Gaussian Mixture models is one of the most popular statistical methods in speaker recognition. The purpose of this research is to perform experiments of speaker recognition using various feature vectors: four formants, four formants with fundamental frequency and mel cepstrum coefficients. Gaussian mixture models using mel cepstrum coefficients is baseline in speaker recognition and gives one of the best results in text independent speaker recognition. After implementing experiments of speaker recognition and comparing experimental results we can affirm that mel scale cepstral coefficients and four formants with fundamental frequency gives quite the same recognition accuracy, but creating of Gaussian mixture speaker models and recognition process continues a few times longer using mel scale cepstral coefficients, because count of calculations is few times greater in that case. Using only four formants gives the worst results of recognition accuracy. Ill. 7, bibl. 12 (in English; summaries in English, Russian and Lithuanian).

In order to have a reliable estimate of wind energy potential of a site, high frequency wind speed and direction data recorded for an extended period of time is required. Weibull distribution function is commonly used to approximate the recorded data distribution for estimation of wind energy. In the present study a comparison of Weibull function and Gaussian mixture model (GMM) as theoretical functions are used. The data set used for the study consists of hourly wind speeds and wind directions of 54 years duration recorded at Ijmuiden wind site located in north of Holland. The entire hourly data set of 54 years is reduced to 12 sets of hourly averaged data corresponding to 12 months. Authenticity of data is assessed by computing descriptive statistics on the entire data set without average and on monthly 12 data sets. Additionally, descriptive statistics show that wind speeds are positively skewed and most of the wind data points are observed to be blowing in south-west direction. Cumulative distribution and probability density function for all data sets are determined for both Weibull function and GMM. Wind power densities on monthly as well as for the entire set are determined from both models using probability density functions of Weibull function and GMM. In order to assess the goodness-of-fit of the fitted Weibull function and GMM, coefficient of determination (R2) and Kolmogorov-Smirnov (K-S) tests are also determined. Although R2 test values for Weibull function are much closer to ‘1’ compared to its values for GMM. Nevertheless, overall performance of GMM is superior to Weibull function in terms of estimated wind power densities using GMM which are in good agreement with the power densities estimated using wind data for the same duration. It is reported that wind power densities for the entire wind data set are 307 W/m2 and 403.96 W/m2 estimated using GMM and Weibull function, respectively.

In the biometrics community, face and speaker recognition are mature fields in which several systems have been proposed over the past twenty years. While existing systems perform well under controlled recording conditions, mismatch caused by the use of different sensors or a lack of cooperation from the subject still significantly affects performance, especially in challenging scenarios such as in forensics. Furthermore, existing methods suffer from scalability issues, which prevents them from taking advantage of increasingly large amounts of training data. This is otherwise a promising approach to improve accuracy in such challenging scenarios. In this thesis we address these problems of mismatch and complexity by developing scalable probabilistic models that we apply to face, speaker and bimodal recognition. Our contributions are four-fold. First, we propose a unified framework for session variability modeling techniques based on Gaussian mixture models (GMM), that encompasses inter-session variability (ISV) modeling, joint factor analysis (JFA) and total variability (TV) modeling. Second, we propose a novel exact and scalable formulation of probabilistic linear discriminant analysis (PLDA), which is a probabilistic and generative framework that models between-class and within-class variations. This formulation solves a major scalability issue, by improving both the time complexity of the training procedure from cubic to linear with respect to the number of samples per class, and the complexity of the scoring procedure. Furthermore, the implementations of all the proposed techniques are integrated into a novel collaborative open source software library called Bob 1 that enforces fair evaluations and encourages reproducible research. Fourth and finally, large-scale experiments are conducted with all of the above machine learning algorithms on several databases such as FRGC for face recognition, NIST SRE12 for speaker recognition and MOBIO for bimodal recognition, showing competitive performances.

Speech applications, which operate a system by voice commands, facilitate web access for disabled and visually impaired users. Human-computer interactions, such as speaking and listening to web applications, provide options for developing a multimodal interaction tool in the accessible design of an intelligent web. Speaker identification and verification are essential functionalities for intelligent web programs with speech applications. This paper proposes an enhanced Gaussian mixture model (GMM) method by incorporating the information derived from the support vector machine (SVM), called EGMM-SVM, for web-based applications with speaker recognition. The EGMM-SVM improves the accuracy of the estimated likelihood scores between the speech frame and the GMM. In EGMM-SVM, SVM plays a crucial role in transmitting the quality information of the utterances from a test speaker, through the GMM when performing GMM likelihood calculations. The experimental results show that speaker recognition by using the developed EGMM-SVM with an accurate operation mechanism for Gaussian distribution derivations yields a higher recognition rate than does a conventional GMM without any considerations on the quality of test speech utterances.

Relevance factor of maximum a posteriori adaptation for GMM–NAP–SVM in speaker and language recognition

Purpose:Xerostomia (dry mouth), secondary to parotid‐gland injury, is a distressing side‐effect in head‐and‐neck radiotherapy (RT). This study's purpose is to develop a novel ultrasound technique to quantitatively evaluate post‐RT parotid‐gland injury.Methods:Recent ultrasound studies have shown that healthy parotid glands exhibit homogeneous echotexture, whereas post‐RT parotid glands are often heterogeneous, with multiple hypoechoic (inflammation) or hyperechoic (fibrosis) regions. We propose to use a Gaussian mixture model to analyze the ultrasonic echo‐histogram of the parotid glands. An IRB‐approved clinical study was conducted: (1) control‐group: 13 healthy‐volunteers, served as the control; (2) acutetoxicity group − 20 patients (mean age: 62.5 ± 8.9 years, follow‐up: 2.0±0.8 months); and (3) late‐toxicity group − 18 patients (mean age: 60.7 ± 7.3 years, follow‐up: 20.1±10.4 months). All patients experienced RTOG grade 1 or 2 salivary‐gland toxicity. Each participant underwent an ultrasound scan (10 MHz) of the bilateral parotid glands. An echo‐intensity histogram was derived for each parotid and a Gaussian mixture model was used to fit the histogram using expectation maximization (EM) algorithm. The quality of the fitting was evaluated with the R‐squared value.Results:(1) Controlgroup: all parotid glands fitted well with one Gaussian component, with a mean intensity of 79.8±4.9 (R‐squared>0.96). (2) Acute‐toxicity group: 37 of the 40 post‐RT parotid glands fitted well with two Gaussian components, with a mean intensity of 42.9±7.4, 73.3±12.2 (R‐squared>0.95). (3) Latetoxicity group: 32 of the 36 post‐RT parotid fitted well with 3 Gaussian components, with mean intensities of 49.7±7.6, 77.2±8.7, and 118.6±11.8 (R‐squared>0.98).Conclusion:RT‐associated parotid‐gland injury is common in head‐and‐neck RT, but challenging to assess. This work has demonstrated that the Gaussian mixture model of the echo‐histogram could quantify acute and late toxicity of the parotid glands. This study provides meaningful preliminary data from future observational and interventional clinical research.

In this paper, we propose a novel method to measure the distance between two Gaussian Mixture Models. The proposed distance measure is based on the minimum cost that must paid to transform from one Gaussian Mixture Model into the other. We parameterize the components of a Gaussian Mixture Model which are Gaussian probability density functions (pdf) as positive definite lower triangular transformation matrices. Then we identify that Gaussian pdfs form a Lie group. Based on Lie group theory, the geodesic length can be used to measure the minimum cost that must paid to transform from one Gaussian pdf into the other. Combining geodesic length with the earth mover's distance, we propose the Lie group earth mover's distance for Gaussian Mixture Models. We test our distance measure in image retrieval. The experimental results indicate that our distance measure is more effective than other measures including the Kullback-Liebler divergence.

This paper proposes a data-driven approximation of the Cumulative Distribution Function using the Finite Mixtures of the Cumulative Distribution Function of Logistic distribution. Since it is not possible to solve the logistic mixture model using the Maximum likelihood method, the mixture model is modeled to approximate the empirical cumulative distribution function using the computational intelligence algorithms. The Probability Density Function is obtained by differentiating the estimate of the Cumulative Distribution Function. The proposed technique estimates the Cumulative Distribution Function of different benchmark distributions. Also, the performance of the proposed technique is compared with the state-of-the-art kernel density estimator and the Gaussian Mixture Model. Experimental results on κ−μ distribution show that the proposed technique performs equally well in estimating the probability density function. In contrast, the proposed technique outperforms in estimating the cumulative distribution function. Also, it is evident from the experimental results that the proposed technique outperforms the state-of-the-art Gaussian Mixture model and kernel density estimation techniques with less training data.

Scattering kernels are of paramount importance in modeling gas–surface interactions for rarefied gas flows. However, most existing empirical models need one or several accommodation coefficients (ACs) to be determined before applications. In this paper, an unsupervised machine learning technique, known as the Gaussian mixture (GM) model, is applied to establish a new scattering kernel based on the simulated data collected by molecular dynamics (MD) simulations. The main work is devoted to the scattering of diatomic molecules under thermal non-equilibrium conditions. Correspondingly, different MD simulations on the scattering process of nitrogen molecules from a platinum surface have been performed involving rotational and translational excitation. Here, we evaluate the performance of the GM and Cercignani–Lampis–Lord models against the MD approach by comparing the velocity correlation distributions and the relevant outgoing velocity probability density function as well as the computed ACs. The presented comparisons have demonstrated the superiority of the GM model in matching with MD results. Therefore, in the case of diatomic gases, the GM model can be employed as a promising strategy to derive the generalized boundary conditions.

In this paper we seek a Gaussian mixture model (GMM) of an n-variate probability density function. Usually the parameters of GMMs are determined in the original n-dimensional space by optimizing a maximum likelihood (ML) criterion. A practical deficiency of this method of fitting GMMs is its poor performance when dealing with high-dimensional data since a large sample size is needed to match the accuracy that is possible in low dimensions. We propose a method for fitting the GMM based on the projection pursuit strategy. This GMM is highly constrained and hence its ability to model structure in subspaces is enhanced, compared to a direct ML fitting of a GMM in high dimensions. Our method is closely related to recently developed independent factor analysis (IFA) mixture models. The comparisons with ML fitting of GMM in n-dimensions and IFA mixtures show that the proposed method is an attractive choice for fitting GMMs using small sizes of training sets.

The Gaussian mixture models (GMM) represent an efficient model that was broadly used in most of speaker recognition applications. This study introduces a novel method for speaker verification task. We propose a reduced feature vector employing new information detected from the speaker's voice for performing text-independent speaker verification applications using GMM. We use the power spectrum density of the speech signal to improve the system's performance. Speaker verification experiments were evaluated with the TIMIT dataset. The suggested system performance is evaluated against the baseline systems. The decrease in the error rate is well observed and the results have demonstrated the effectiveness of the new approach which avoids the use of more complex algorithms or the combination of different approaches.

Even though speaker recognition has gained significant progress in recent years, its performance is known to be deteriorated severely with the existence of strong background noises. Inspired by a recently proposed clean-frame selection approach, this work investigates a relatively elegant weighting method when computing the Baum-Welch statistics of Gaussian mixture models (GMMs) in i-vector extraction. By introducing weighting parameters to the frames of enrollment/testing utterances, the optimization problem is redefined and solved. New updating rules are derived by incorporating weights to the computation of posterior probabilities, mean vectors, and covariance matrices of the GMM. The experiments conducted on the Speakers in the Wild (SITW) database show that the proposed algorithm has significantly improved the performance of i-vector-based speaker recognition systems in noisy environments. Compared with the GMM i-vector baseline, the equal error rate is reduced from 5.75 to 4.72 and the minimum value of cost function (C det min ) is reduced from 0.4825 to 0.4505. Slight but significant superiority is also observed over the method with an additional feature enhancement frontend by using deep neural networks.