Components Of Gaussian Mixture Model Research Articles

Local compressed convex spectral embedding for bird species identification.

This paper proposes a multi-layer alternating sparse-dense framework for bird species identification. The framework takes audio recordings of bird vocalizations and produces compressed convex spectral embeddings (CCSE). Temporal and frequency modulations in bird vocalizations are ensnared by concatenating frames of the spectrogram, resulting in a high dimensional and highly sparse super-frame-based representation. Random projections are then used to compress these super-frames. Class-specific archetypal analysis is employed on the compressed super-frames for acoustic modeling, obtaining the convex-sparse CCSE representation. This representation efficiently captures species-specific discriminative information. However, many bird species exhibit high intra-species variations in their vocalizations, making it hard to appropriately model the whole repertoire of vocalizations using only one dictionary of archetypes. To overcome this, each class is clustered using Gaussian mixture models (GMM), and for each cluster, one dictionary of archetypes is learned. To calculate CCSE for any compressed super-frame, one dictionary from each class is chosen using the responsibilities of individual GMM components. The CCSE obtained using this GMM-archetypal analysis framework is referred to as local CCSE. Experimental results corroborate that local CCSE either outperforms or exhibits comparable performances to existing methods including support vector machine powered by dynamic kernels and deep neural networks.

Multiple-Speaker Localization Based on Direct-Path Features and Likelihood Maximization With Spatial Sparsity Regularization

This paper addresses the problem of multiple-speaker localization in noisy and reverberant environments, using binaural recordings of an acoustic scene. A Gaussian mixture model (GMM) is adopted, whose components correspond to all the possible candidate source locations defined on a grid. After optimizing the GMM-based objective function, given an observed set of binaural features, both the number of sources and their locations are estimated by selecting the GMM components with the largest priors. This is achieved by enforcing a sparse solution, thus favoring a small number of speakers with respect to the large number of initial candidate source locations. An entropy-based penalty term is added to the likelihood, thus imposing sparsity over the set of GMM priors. In addition, the direct-path relative transfer function (DP-RTF) is used to build robust binaural features. The DP-RTF, recently proposed for single-source localization, was shown to be robust to reverberations, since it encodes inter-channel information corresponding to the direct-path of sound propagation. In this paper, we extend the DP-RTF estimation to the case of multiple sources. In the short-time Fourier transform domain, a consistency test is proposed to check whether a set of consecutive frames is associated to the same source or not. Reliable DP-RTF features are selected from the frames that pass the consistency test to be used for source localization. Experiments carried out using both simulation data and real data gathered with a robotic head confirm the efficiency of the proposed multi-source localization method.

Discriminant Analysis on Riemannian Manifold of Gaussian Distributions for Face Recognition With Image Sets.

To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as the Gaussian mixture model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. Since in the light of information geometry, the Gaussians lie on a specific Riemannian manifold, this paper presents a method named discriminant analysis on Riemannian manifold of Gaussian distributions (DARG). We investigate several distance metrics between Gaussians and accordingly two discriminative learning frameworks are presented to meet the geometric and statistical characteristics of the specific manifold. The first framework derives a series of provably positive definite probabilistic kernels to embed the manifold to a high-dimensional Hilbert space, where conventional discriminant analysis methods developed in Euclidean space can be applied, and a weighted Kernel discriminant analysis is devised which learns discriminative representation of the Gaussian components in GMMs with their prior probabilities as sample weights. Alternatively, the other framework extends the classical graph embedding method to the manifold by utilizing the distance metrics between Gaussians to construct the adjacency graph, and hence the original manifold is embedded to a lower-dimensional and discriminative target manifold with the geometric structure preserved and the interclass separability maximized. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB, and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as the Gaussian mixture model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. Since in the light of information geometry, the Gaussians lie on a specific Riemannian manifold, this paper presents a method named discriminant analysis on Riemannian manifold of Gaussian distributions (DARG). We investigate several distance metrics between Gaussians and accordingly two discriminative learning frameworks are presented to meet the geometric and statistical characteristics of the specific manifold. The first framework derives a series of provably positive definite probabilistic kernels to embed the manifold to a high-dimensional Hilbert space, where conventional discriminant analysis methods developed in Euclidean space can be applied, and a weighted Kernel discriminant analysis is devised which learns discriminative representation of the Gaussian components in GMMs with their prior probabilities as sample weights. Alternatively, the other framework extends the classical graph embedding method to the manifold by utilizing the distance metrics between Gaussians to construct the adjacency graph, and hence the original manifold is embedded to a lower-dimensional and discriminative target manifold with the geometric structure preserved and the interclass separability maximized. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB, and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.

GMMs similarity measure based on LPP-like projection of the parameter space

The need for a comparison between two Gaussian Mixture Models (GMMs) plays a crucial role in various pattern recognition tasks and is involved as a key components in many expert and artificial intelligence (AI) systems dealing with real-life problems. As those system often operate on large data-sets and use high dimensional features, it is crucial for their recognition component to be computationally efficient in addition to its good recognition accuracy. In this work we deliver the novel similarity measure between GMMs, by LPP-like projecting the components of a particular GMM, from the high dimensional original parameter space, to a much lower dimensional space. Thus, finding the distance between two GMMs in the original space is reduced to finding the distance between sets of lower dimensional Euclidian vectors, pondered by corresponding weights. By doing so, we manage to obtain much better trade-off between the recognition accuracy and the computational complexity, in comparison to the measures between GMMs utilizing distances between Gaussian components evaluated in the original parameter space. Thus, the GMM measure that we propose is suitable for applications in AI systems that use GMMs in their recognition tasks and operate on large data sets, as the required number of overall Gaussian components involved in such systems is always large. We evaluate the proposed GMM measure on artificial, as well as real-world experimental data obtaining a much better trade-off between recognition accuracy and the computational complexity, in comparison to all baseline GMM similarity measures tested.

Estimating number of components in Gaussian mixture model using combination of greedy and merging algorithm

The brain must deal with a massive flow of sensory information without receiving any prior information. Therefore, when creating cognitive models, it is important to acquire as much information as possible from the data itself. Moreover, the brain has to deal with an unknown number of components (concepts) contained in a dataset without any prior knowledge. Most of the algorithms in use today are not able to effectively copy this strategy. We propose a novel approach based on neural modelling fields theory (NMF) to overcome this problem. The algorithm combines NMF and greedy Gaussian mixture models. The novelty lies in the combination of information criterion with the merging algorithm. The performance of the algorithm was compared with other well-known algorithms and tested both on artificial and real-world datasets.

Evaluation of ground distances and features in EMD-based GMM matching for texture classification

Recently, the Earth Mover׳s Distance (EMD) has demonstrated its superiority in Gaussian mixture models (GMMs) based texture classification. The ground distances between Gaussian components of GMMs have great influences on performance of GMM matching, which however, has not been fully studied yet. Meanwhile, image features play a key role in image classification task, and often greatly impact classification performance. In this paper, we present a comprehensive study of ground distances and image features in texture classification task. We divide existing ground distances into statistics based ones and Riemannian manifold based ones. We make a theoretical analysis of the differences and relationships among these ground distances. Inspired by Gaussian embedding distance and product of Lie Groups distance, we propose an improved Gaussian embedding distance to compare Gaussians. We also evaluate for the first time the image features for GMM matching, including the handcrafted features such as Gabor filter, Local Binary Pattern (LBP) descriptor, SIFT, covariance descriptor and high-level features extracted by deep convolution networks. The experiments are conducted on three texture databases, i.e., KTH-TIPS-2b, FMD and UIUC. Based on experimental results, we show that the uses of geometrical structure and balance strategy are critical to ground distances. The experimental results show that GMM with the proposed ground distance can achieve state-of-the-art performance when high-level features are exploited.

RB Particle Filter Time Synchronization Algorithm Based on the DPM Model.

Time synchronization is essential for node localization, target tracking, data fusion, and various other Wireless Sensor Network (WSN) applications. To improve the estimation accuracy of continuous clock offset and skew of mobile nodes in WSNs, we propose a novel time synchronization algorithm, the Rao-Blackwellised (RB) particle filter time synchronization algorithm based on the Dirichlet process mixture (DPM) model. In a state-space equation with a linear substructure, state variables are divided into linear and non-linear variables by the RB particle filter algorithm. These two variables can be estimated using Kalman filter and particle filter, respectively, which improves the computational efficiency more so than if only the particle filter was used. In addition, the DPM model is used to describe the distribution of non-deterministic delays and to automatically adjust the number of Gaussian mixture model components based on the observational data. This improves the estimation accuracy of clock offset and skew, which allows achieving the time synchronization. The time synchronization performance of this algorithm is also validated by computer simulations and experimental measurements. The results show that the proposed algorithm has a higher time synchronization precision than traditional time synchronization algorithms.

Generalized I-vector Representation with Phonetic Tokenizations and Tandem Features for both Text Independent and Text Dependent Speaker Verification

This paper presents a generalized i-vector representation framework with phonetic tokenization and tandem features for text independent as well as text dependent speaker verification. In the conventional i-vector framework, the tokens for calculating the zero-order and first-order Baum-Welch statistics are Gaussian Mixture Model (GMM) components trained from acoustic level MFCC features. Yet besides MFCC, we believe that phonetic information makes another direction that can benefit the system performance. Our contribution in this paper lies in integrating phonetic information into the i-vector representation by several extensions, forming a more generalized i-vector framework. First, the tokens for calculating the zero-order statistics is extended from the MFCC trained GMM components to phonetic phonemes, trigrams and tandem feature trained GMM components, using phoneme posterior probabilities. Second, given the zero-order statistics (posterior probabilities on tokens), the feature used to calculate the first-order statistics is also extended from MFCC to tandem feature, and is not necessarily the same feature employed by the tokenizer. Third, the zero-order and first-order statistics vectors are then concatenated and represented by the simplified supervised i-vector approach followed by the standard Probabilistic Linear Discriminant Analysis (PLDA) back-end. We study different token and feature combinations, and we show that the feature level fusion of acoustic level MFCC features and phonetic level tandem features with GMM based i-vector representation achieves the best performance for text independent speaker verification. Furthermore, we demonstrate that the phonetic level phoneme constraints introduced by the tandem features help the text dependent speaker verification system to reject wrong password trials and improve the performance dramatically. Experimental results are reported on the NIST SRE 2010 common condition 5 female part task and the RSR 2015 part 1 female part task for text independent and text dependent speaker verification, respectively. For the text independent speaker verification task, the proposed generalized i-vector representation outperforms the i-vector baseline by relatively 53 % in terms of equal error rate (EER) and norm minDCF values. For the text dependent speaker verification task, our proposed approach also reduced the EER significantly from 23 % to 90 % relatively for different types of trials.

Scribble-based object segmentation with modified gaussian mixture models

In this paper, we present an interactive segmentation method, designed to help the user to extract an object of interest from an image. The proposed approach adopts the scribble-based segmentation paradigm. The user interaction consists of specifying a set of lines, corresponding to both foreground and background scribbles. The segmentation process is based on color distributions, estimated with Gaussian mixture models (GMM). We show that such a technique presents some limitations when dealing with compressed images, even for relatively high quality compression factors: in this case, blocking artifacts may degrade the segmentation results. In order to overcome such a drawback, a modified GMM model, which re-shapes the Gaussian mixture based on the eigenvalues of the GMM components, is proposed. The experimental evaluation, carried out on a corpus of various images with different characteristics and textures, demonstrates the superiority of the modified GMM model which is able to appropriately take into account compression artifacts.

Image segmentation using spectral clustering of Gaussian mixture models

A novel image segmentation method that combines spectral clustering and Gaussian mixture models is presented in this paper. The new method contains three phases. First, the image is partitioned into small regions modeled by a Gaussian Mixture Model (GMM), and the GMM is solved by an Expectation-Maximization (EM) algorithm with a newly proposed Image Reconstruction Criterion, named EM-IRC. Second, the distances among the GMM components are measured using Kullback-Leibler (KL) divergence, and a revised [email protected]?s algorithm developed from [email protected]?s operations is used to build the similarity matrix based on those distances. Finally, spectral clustering is applied to this improved similarity matrix to merge the GMM components, i.e., the corresponding small image regions, to obtain the final segmentation result. Our contributions include the new EM-IRC algorithm, the revised [email protected]?s algorithm, and the novel overall framework. The experimental evaluation on the IRIS dataset and the real-world image segmentation problem demonstrates the effectiveness of our proposed approach.

A FRAMEWORK FOR MULTILINGUAL TEXT- INDEPENDENT SPEAKER IDENTIFICATION SYSTEM

This article evaluates the performance of Extreme Learning Machine (ELM) and Gaussian Mixture Model (GMM) in the context of text independent Multi lingual speaker identification for recorded and synthesized speeches. The type and number of filters in the filter bank, number of samples in each frame of the speech signal and fusion of model scores play a vital role in speaker identification accuracy and are analyzed in this article. Extreme Learning Machine uses a single hidden layer feed forward neural network for multilingual speaker identification. The individual Gaussian components of GMM best represent speaker-dependent spectral shapes that are effective in speaker identity. Both the modeling techniques make use of Linear Predictive Residual Cepstral Coefficient (LPRCC), Mel Frequency Cepstral Coefficient (MFCC), Modified Mel Frequency Cepstral Coefficient (MMFCC) and Bark Frequency Cepstral Coefficient (BFCC) features to represent the speaker specific attributes of speech signals. Experimental results show that GMM outperforms ELM with speaker identification accuracy of 97.5% with frame size of 256 and frame shift of half of frame size and filter bank size of 40.

HMM Based Intermediate Matching Kernel for Classification of Sequential Patterns of Speech Using Support Vector Machines

In this paper, we address the issues in the design of an intermediate matching kernel (IMK) for classification of sequential patterns using support vector machine (SVM) based classifier for tasks such as speech recognition. Specifically, we address the issues in constructing a kernel for matching sequences of feature vectors extracted from the speech signal data of utterances. The codebook based IMK and Gaussian mixture model (GMM) based IMK have been proposed earlier for matching the varying length patterns represented as sets of features vectors for tasks such as image classification and speaker recognition. These methods consider the centers of clusters and the components of GMM as the virtual feature vectors used in the design of IMK. As these methods do not use sequence information in matching the patterns, these methods are not suitable for matching sequential patterns. We propose the hidden Markov model (HMM) based IMK for matching sequential patterns of varying length. We consider two approaches to design the HMM-based IMK. In the first approach, each of the two sequences to be matched is segmented into subsequences with each subsequence aligned to a state of the HMM. Then the HMM-based IMK is constructed as a combination of state-specific GMM-based IMKs that match the subsequences aligned with the particular states of the HMM. In the second approach, the HMM-based IMK is constructed without segmenting sequences, and by matching the local feature vectors selected using the responsibility terms that account for being in a state and generating the feature vectors by a component of the GMM of that state. We study the performance of the SVM based classifiers using the proposed HMM-based IMK for recognition of isolated utterances of E-set in English alphabet and recognition of consonent–vowel segments in Hindi language.

Entropy-Based Approach for Uncertainty Propagation of Nonlinear Dynamical Systems

Uncertainty propagation of dynamical systems is a common need across many domains and disciplines. In nonlinear settings, the extended Kalman filter is the de facto standard propagation tool. Recently, a new class of propagation methods called sigma-point Kalman filters was introduced, which eliminated the need for explicit computation of tangent linear matrices. It has been shown in numerous cases that the actual uncertainty of a dynamical system cannot be accurately described by a Gaussian probability density function. This has motivated work in applying the Gaussian mixture model approach to better approximate the non-Gaussian probability density function. A limitation to existing approaches is that the number of Gaussian components of the Gaussian mixture model is fixed throughout the propagation of uncertainty. This limitation has made previous work ill-suited for nonstationary probability density functions either due to inaccurate representation of the probability density function or computational burden given a large number of Gaussian components that may not be needed. This work examines an improved method implementing a Gaussian mixture model that is adapted online via splitting of the Gaussian mixture model components triggered by an entropy-based detection of nonlinearity during the probability density function evolution. In doing so, the Gaussian mixture model approximation adaptively includes additional components as nonlinearity is encountered and can therefore be used to more accurately approximate the probability density function. This paper introduces this strategy, called adaptive entropy-based Gaussian-mixture information synthesis. The adaptive entropy-based Gaussian-mixture information synthesis method is demonstrated for its ability to accurately perform inference on two cases of uncertain orbital dynamical systems. The impact of this work for orbital dynamical systems is that the improved representation of the uncertainty of the space object can then be used more consistently for identification and tracking.

Regularized mixture density estimation with an analytical setting of shrinkage intensities.

In this paper, we propose a method for P-variate probability density estimation assuming a Gaussian mixture model (GMM). Our method exploits a regularization technique for improving the estimation accuracy of the GMM component covariance matrices. We derive an expectation maximization algorithm for fitting our regularized GMM (RGMM), which exploits an analytical Ledoit-Wolf-type shrinkage estimation of the covariance matrices. Our method is compared with recent model-based and variational Bayes approximation methods using synthetic and real data sets. The obtained results show that the proposed RGMM method achieves a significant improvement in the performance of multivariate probability density estimation with respect to other methods on both the synthetic and the real data sets.

Patch Distribution Compatible Semisupervised Dimension Reduction for Face and Human Gait Recognition

We propose a new semisupervised learning algorithm, referred to as patch distribution compatible semisupervised dimension reduction, for face and human gait recognition. Each image (a face image or an average human silhouette image) is first represented as a set of local patch features and it is further characterized as the corresponding patch distribution feature, which can be expressed as an image-specific Gaussian mixture model (GMM) adapted from the universal background model. Assuming that the individual components of the image-specific GMMs from all the training images reside on a submanifold, we assign a component-level prediction label matrix to each individual GMM component and introduce a new regularizer based on a set of local submanifold smoothness assumptions in our objective function. We also constrain each component-level prediction label matrix to be consistent with the image-level prediction label matrix , as well as enforce to be close to the given labels for the labeled samples. We further use a linear regression function to provide embeddings for the training data and the unseen test data. Inspired by the recent work flexible manifold embedding, we additionally integrate the regression residue in our objective function to measure the mismatch between and , such that our method can better cope with the data sampled from a nonlinear manifold. Finally, the optimal solutions of the component-level prediction label matrix , the image-level prediction label matrix , the projection matrix , and the bias term b can be simultaneously obtained. Comprehensive experiments on three benchmark face databases CMU PIE, FERET, and AR as well as the USF HumanID gait database clearly demonstrate the effectiveness of our algorithm over other state-of-the-art semisupervised dimension reduction methods.

Maximum likelihood estimation of Gaussian mixture models using stochastic search

Gaussian mixture models (GMM), commonly used in pattern recognition and machine learning, provide a flexible probabilistic model for the data. The conventional expectation-maximization (EM) algorithm for the maximum likelihood estimation of the parameters of GMMs is very sensitive to initialization and easily gets trapped in local maxima. Stochastic search algorithms have been popular alternatives for global optimization but their uses for GMM estimation have been limited to constrained models using identity or diagonal covariance matrices. Our major contributions in this paper are twofold. First, we present a novel parametrization for arbitrary covariance matrices that allow independent updating of individual parameters while retaining validity of the resultant matrices. Second, we propose an effective parameter matching technique to mitigate the issues related with the existence of multiple candidate solutions that are equivalent under permutations of the GMM components. Experiments on synthetic and real data sets show that the proposed framework has a robust performance and achieves significantly higher likelihood values than the EM algorithm.

Voice Conversion Using Partial Least Squares Regression

Voice conversion can be formulated as finding a mapping function which transforms the features of the source speaker to those of the target speaker. Gaussian mixture model (GMM)-based conversion is commonly used, but it is subject to overfitting. In this paper, we propose to use partial least squares (PLS)-based transforms in voice conversion. To prevent overfitting, the degrees of freedom in the mapping can be controlled by choosing a suitable number of components. We propose a technique to combine PLS with GMMs, enabling the use of multiple local linear mappings. To further improve the perceptual quality of the mapping where rapid transitions between GMM components produce audible artefacts, we propose to low-pass filter the component posterior probabilities. The conducted experiments show that the proposed technique results in better subjective and objective quality than the baseline joint density GMM approach. In speech quality conversion preference tests, the proposed method achieved 67% preference score against the smoothed joint density GMM method and 84% preference score against the unsmoothed joint density GMM method. In objective tests the proposed method produced a lower Mel-cepstral distortion than the reference methods.

Method for unsupervised change detection in satellite images

A Gaussian mixture model (GMM) and Bayesian inferencing (BI) based unsupervised change detection method in satellite images is presented. The data distribution of the difference image, which is computed from satellite images of the same scene acquired at different time instances, is modelled by using GMM. The components of the overall GMM are separated into two classes to model the data distributions of changed and unchanged pixels. The weights of the components in each class are used to estimate the a priori probability of each corresponding class. The final change detection is achieved by applying BI to classify each pixel of the difference image into one or two classes.

Automatic Classification of Bird Species From Their Sounds Using Two-Dimensional Cepstral Coefficients

This paper presents a method for automatic classification of birds into different species based on the audio recordings of their sounds. Each individual syllable 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.

Joint Key-Frame Extraction and Object Segmentation for Content-Based Video Analysis

Key-frame extraction and object segmentation are usually implemented independently and separately due to the fact that they are on different semantic levels and involve different features. In this work, we propose a joint key-frame extraction and object segmentation method by constructing a unified feature space for both processes, where key-frame extraction is formulated as a feature selection process for object segmentation in the context of Gaussian mixture model (GMM)-based video modeling. Specifically, two divergence-based criteria are introduced for key-frame extraction. One recommends key-frame extraction that leads to the maximum pairwise interclass divergence between GMM components. The other aims at maximizing the marginal divergence that shows the intra-frame variation of the mean density. The proposed methods can extract representative key-frames for object segmentation, and some interesting characteristics of key-frames are also discussed. This work provides a unique paradigm for content-based video analysis