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Showing papers on "Mixture model published in 2014"


Book
14 Apr 2014
TL;DR: In this article, the basics of Bayesian analysis are discussed, and a WinBUGS-based approach is presented to get started with WinBUGs, which is based on the SIMPLE model of memory.
Abstract: Part I. Getting Started: 1. The basics of Bayesian analysis 2. Getting started with WinBUGS Part II. Parameter Estimation: 3. Inferences with binomials 4. Inferences with Gaussians 5. Some examples of data analysis 6. Latent mixture models Part III. Model Selection: 7. Bayesian model comparison 8. Comparing Gaussian means 9. Comparing binomial rates Part IV. Case Studies: 10. Memory retention 11. Signal detection theory 12. Psychophysical functions 13. Extrasensory perception 14. Multinomial processing trees 15. The SIMPLE model of memory 16. The BART model of risk taking 17. The GCM model of categorization 18. Heuristic decision-making 19. Number concept development.

1,192 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider a wide class of latent variable models, including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation, which exploit a certain tensor structure in their low-order observable moments (typically, of second and third-order).
Abstract: This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models--including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation--which exploits a certain tensor structure in their low-order observable moments (typically, of second- and third-order). Specifically, parameter estimation is reduced to the problem of extracting a certain (orthogonal) decomposition of a symmetric tensor derived from the moments; this decomposition can be viewed as a natural generalization of the singular value decomposition for matrices. Although tensor decompositions are generally intractable to compute, the decomposition of these specially structured tensors can be efficiently obtained by a variety of approaches, including power iterations and maximization approaches (similar to the case of matrices). A detailed analysis of a robust tensor power method is provided, establishing an analogue of Wedin's perturbation theorem for the singular vectors of matrices. This implies a robust and computationally tractable estimation approach for several popular latent variable models.

789 citations


Posted Content
TL;DR: This work specifies a graphical model for human pose which exploits the fact the local image measurements can be used both to detect parts (or joints) and also to predict the spatial relationships between them (Image Dependent Pairwise Relations).
Abstract: We present a method for estimating articulated human pose from a single static image based on a graphical model with novel pairwise relations that make adaptive use of local image measurements. More precisely, we specify a graphical model for human pose which exploits the fact the local image measurements can be used both to detect parts (or joints) and also to predict the spatial relationships between them (Image Dependent Pairwise Relations). These spatial relationships are represented by a mixture model. We use Deep Convolutional Neural Networks (DCNNs) to learn conditional probabilities for the presence of parts and their spatial relationships within image patches. Hence our model combines the representational flexibility of graphical models with the efficiency and statistical power of DCNNs. Our method significantly outperforms the state of the art methods on the LSP and FLIC datasets and also performs very well on the Buffy dataset without any training.

474 citations


Journal ArticleDOI
TL;DR: Step-by-step pediatric psychology examples of latent growth curve modeling, latent class growth analysis, and growth mixture modeling using the Early Childhood Longitudinal Study-Kindergarten Class of 1998-1999 data file are provided.
Abstract: Objective — Pediatric psychologists are often interested in finding patterns in heterogeneous longitudinal data. Latent Variable Mixture Modeling is an emerging statistical approach that models such heterogeneity by classifying individuals into unobserved groupings (latent classes) with similar (more homogenous) patterns. The purpose of the second of a two article set is to offer a nontechnical introduction to longitudinal latent variable mixture modeling. Methods — 3 latent variable approaches to modeling longitudinal data are reviewed and distinguished. Results — Step-by-step pediatric psychology examples of latent growth curve modeling, latent class growth analysis, and growth mixture modeling are provided using the Early Childhood Longitudinal Study-Kindergarten Class of 1998–99 data file. Conclusions — Latent variable mixture modeling is a technique that is useful to pediatric psychologists who wish to find groupings of individuals who share similar longitudinal data patterns to determine the extent to which these patterns may relate to variables of interest.

285 citations


Journal ArticleDOI
TL;DR: Practical effect size measures and power curves that can be used to predict power for the BLRT in LCA given a proposed sample size and a set of hypothesized population parameters are provided.
Abstract: Selecting the number of different classes which will be assumed to exist in the population is an important step in latent class analysis (LCA). The bootstrap likelihood ratio test (BLRT) provides a data-driven way to evaluate the relative adequacy of a (K -1)-class model compared to a K-class model. However, very little is known about how to predict the power or the required sample size for the BLRT in LCA. Based on extensive Monte Carlo simulations, we provide practical effect size measures and power curves which can be used to predict power for the BLRT in LCA given a proposed sample size and a set of hypothesized population parameters. Estimated power curves and tables provide guidance for researchers wishing to size a study to have sufficient power to detect hypothesized underlying latent classes.

270 citations


Proceedings ArticleDOI
23 Jun 2014
TL;DR: A new generative algorithm is devised to effectively pretrain the SDN and then fine-tune it with back-propagation to achieve the state-of-the-art detection performance.
Abstract: In this paper, we propose a Switchable Deep Network (SDN) for pedestrian detection. The SDN automatically learns hierarchical features, salience maps, and mixture representations of different body parts. Pedestrian detection faces the challenges of background clutter and large variations of pedestrian appearance due to pose and viewpoint changes and other factors. One of our key contributions is to propose a Switchable Restricted Boltzmann Machine (SRBM) to explicitly model the complex mixture of visual variations at multiple levels. At the feature levels, it automatically estimates saliency maps for each test sample in order to separate background clutters from discriminative regions for pedestrian detection. At the part and body levels, it is able to infer the most appropriate template for the mixture models of each part and the whole body. We have devised a new generative algorithm to effectively pretrain the SDN and then fine-tune it with back-propagation. Our approach is evaluated on the Caltech and ETH datasets and achieves the state-of-the-art detection performance.

256 citations


Journal ArticleDOI
TL;DR: A DNN is used to construct a global non-linear mapping relationship between the spectral envelopes of two speakers to significantly improve the performance in terms of both similarity and naturalness compared to conventional methods.
Abstract: This paper presents a new spectral envelope conversion method using deep neural networks (DNNs). The conventional joint density Gaussian mixture model (JDGMM) based spectral conversion methods perform stably and effectively. However, the speech generated by these methods suffer severe quality degradation due to the following two factors: 1) inadequacy of JDGMM in modeling the distribution of spectral features as well as the non-linear mapping relationship between the source and target speakers, 2) spectral detail loss caused by the use of high-level spectral features such as mel-cepstra. Previously, we have proposed to use the mixture of restricted Boltzmann machines (MoRBM) and the mixture of Gaussian bidirectional associative memories (MoGBAM) to cope with these problems. In this paper, we propose to use a DNN to construct a global non-linear mapping relationship between the spectral envelopes of two speakers. The proposed DNN is generatively trained by cascading two RBMs, which model the distributions of spectral envelopes of source and target speakers respectively, using a Bernoulli BAM (BBAM). Therefore, the proposed training method takes the advantage of the strong modeling ability of RBMs in modeling the distribution of spectral envelopes and the superiority of BAMs in deriving the conditional distributions for conversion. Careful comparisons and analysis among the proposed method and some conventional methods are presented in this paper. The subjective results show that the proposed method can significantly improve the performance in terms of both similarity and naturalness compared to conventional methods.

246 citations


Journal ArticleDOI
TL;DR: In this paper, a 3-step method for estimating the effects of auxiliary variables (i.e., covariates and distal outcome) in mixture modeling provides a useful way to specify complex mixture models.
Abstract: The 3-step method for estimating the effects of auxiliary variables (i.e., covariates and distal outcome) in mixture modeling provides a useful way to specify complex mixture models. One of the benefits of this method is that the measurement parameters of the mixture model are not influenced by the auxiliary variable(s). In addition, it allows for models that involve multiple latent class variables to be specified without each part of the model influencing the others. This article describes a unique latent transition analysis model where the measurement models are a latent class analysis model and a growth mixture model. We highlight the application of this model to study kindergarten readiness profiles and link it to elementary students’ reading trajectories. Mplus syntax for the 3-step specification is provided.

240 citations


Journal ArticleDOI
TL;DR: This article aims at giving an overview of joint latent class modelling, especially in the prediction context, by introducing the model, discussing estimation and goodness-of-fit, and comparing it with the shared random-effect model.
Abstract: Most statistical developments in the joint modelling area have focused on the shared random-effect models that include characteristics of the longitudinal marker as predictors in the model for the time-to-event. A less well-known approach is the joint latent class model which consists in assuming that a latent class structure entirely captures the correlation between the longitudinal marker trajectory and the risk of the event. Owing to its flexibility in modelling the dependency between the longitudinal marker and the event time, as well as its ability to include covariates, the joint latent class model may be particularly suited for prediction problems. This article aims at giving an overview of joint latent class modelling, especially in the prediction context. The authors introduce the model, discuss estimation and goodness-of-fit, and compare it with the shared random-effect model. Then, dynamic predictive tools derived from joint latent class models, as well as measures to evaluate their dynamic pre...

240 citations


Journal ArticleDOI
TL;DR: The first model-based clustering algorithm for multivariate functional data is proposed, based on the assumption of normality of the principal component scores, and it ability to take into account the dependence among curves.

239 citations


Journal ArticleDOI
TL;DR: Comparisons are presented to illustrate the relative performance of the restricted and unrestricted models, and demonstrate the usefulness of the recently proposed methodology for the unrestricted MST mixture, by some applications to three real datasets.
Abstract: Finite mixtures of multivariate skew t (MST) distributions have proven to be useful in modelling heterogeneous data with asymmetric and heavy tail behaviour. Recently, they have been exploited as an effective tool for modelling flow cytometric data. A number of algorithms for the computation of the maximum likelihood (ML) estimates for the model parameters of mixtures of MST distributions have been put forward in recent years. These implementations use various characterizations of the MST distribution, which are similar but not identical. While exact implementation of the expectation-maximization (EM) algorithm can be achieved for `restricted' characterizations of the component skew t-distributions, Monte Carlo (MC) methods have been used to fit the `unrestricted' models. In this paper, we review several recent fitting algorithms for finite mixtures of multivariate skew t-distributions, at the same time clarifying some of the connections between the various existing proposals. In particular, recent results have shown that the EM algorithm can be implemented exactly for faster computation of ML estimates for mixtures with unrestricted MST components. The gain in computational time is effected by noting that the semi-infinite integrals on the E-step of the EM algorithm can be put in the form of moments of the truncated multivariate non-central t-distribution, similar to the restricted case, which subsequently can be expressed in terms of the non-truncated form of the central t-distribution function for which fast algorithms are available. We present comparisons to illustrate the relative performance of the restricted and unrestricted models, and demonstrate the usefulness of the recently proposed methodology for the unrestricted MST mixture, by some applications to three real datasets.

Proceedings Article
08 Dec 2014
TL;DR: In this paper, a graphical model for human pose estimation from a single static image is proposed, which exploits the fact the local image measurements can be used both to detect parts and also to predict the spatial relationships between them.
Abstract: We present a method for estimating articulated human pose from a single static image based on a graphical model with novel pairwise relations that make adaptive use of local image measurements. More precisely, we specify a graphical model for human pose which exploits the fact the local image measurements can be used both to detect parts (or joints) and also to predict the spatial relationships between them (Image Dependent Pairwise Relations). These spatial relationships are represented by a mixture model. We use Deep Convolutional Neural Networks (DCNNs) to learn conditional probabilities for the presence of parts and their spatial relationships within image patches. Hence our model combines the representational flexibility of graphical models with the efficiency and statistical power of DCNNs. Our method significantly outperforms the state of the art methods on the LSP and FLIC datasets and also performs very well on the Buffy dataset without any training.

Proceedings ArticleDOI
23 Jun 2014
TL;DR: It is shown that better action recognition using skeletal features can be achieved by replacing gaussian mixture models by deep neural networks that contain many layers of features to predict probability distributions over states of hidden Markov models.
Abstract: Over the last few years, with the immense popularity of the Kinect, there has been renewed interest in developing methods for human gesture and action recognition from 3D skeletal data. A number of approaches have been proposed to extract representative features from 3D skeletal data, most commonly hard wired geometric or bio-inspired shape context features. We propose a hierarchial dynamic framework that first extracts high level skeletal joints features and then uses the learned representation for estimating emission probability to infer action sequences. Currently gaussian mixture models are the dominant technique for modeling the emission distribution of hidden Markov models. We show that better action recognition using skeletal features can be achieved by replacing gaussian mixture models by deep neural networks that contain many layers of features to predict probability distributions over states of hidden Markov models. The framework can be easily extended to include a ergodic state to segment and recognize actions simultaneously.

Journal ArticleDOI
TL;DR: Experimental results show that the proposed approach outperforms state-of-the-art weakly-supervised image segmentation methods, on five popular segmentation data sets and performs competitively to the fully- supervised segmentation models.
Abstract: Weakly-supervised image segmentation is a challenging problem with multidisciplinary applications in multimedia content analysis and beyond. It aims to segment an image by leveraging its image-level semantics (i.e., tags). This paper presents a weakly-supervised image segmentation algorithm that learns the distribution of spatially structural superpixel sets from image-level labels. More specifically, we first extract graphlets from a given image, which are small-sized graphs consisting of superpixels and encapsulating their spatial structure. Then, an efficient manifold embedding algorithm is proposed to transfer labels from training images into graphlets. It is further observed that there are numerous redundant graphlets that are not discriminative to semantic categories, which are abandoned by a graphlet selection scheme as they make no contribution to the subsequent segmentation. Thereafter, we use a Gaussian mixture model (GMM) to learn the distribution of the selected post-embedding graphlets (i.e., vectors output from the graphlet embedding). Finally, we propose an image segmentation algorithm, termed representative graphlet cut, which leverages the learned GMM prior to measure the structure homogeneity of a test image. Experimental results show that the proposed approach outperforms state-of-the-art weakly-supervised image segmentation methods, on five popular segmentation data sets. Besides, our approach performs competitively to the fully-supervised segmentation models.

Proceedings Article
21 Jun 2014
TL;DR: This work proposes a generative RPCA model under the Bayesian framework by modeling data noise as a mixture of Gaussians (MoG), a universal approximator to continuous distributions and thus the model is able to fit a wide range of noises such as Laplacian, Gaussian, sparse noises and any combinations of them.
Abstract: The research on robust principal component analysis (RPCA) has been attracting much attention recently. The original RPCA model assumes sparse noise, and use the L1-norm to characterize the error term. In practice, however, the noise is much more complex and it is not appropriate to simply use a certain Lp-norm for noise modeling. We propose a generative RPCA model under the Bayesian framework by modeling data noise as a mixture of Gaussians (MoG). The MoG is a universal approximator to continuous distributions and thus our model is able to fit a wide range of noises such as Laplacian, Gaussian, sparse noises and any combinations of them. A variational Bayes algorithm is presented to infer the posterior of the proposed model. All involved parameters can be recursively updated in closed form. The advantage of our method is demonstrated by extensive experiments on synthetic data, face modeling and background subtraction.

Journal ArticleDOI
TL;DR: The efficacy of the proposed Gaussian mixture model (GMM)-based inversion method is demonstrated with videos reconstructed from simulated compressive video measurements, and from a realCompressive video camera.
Abstract: A Gaussian mixture model (GMM)-based algorithm is proposed for video reconstruction from temporally compressed video measurements. The GMM is used to model spatio-temporal video patches, and the reconstruction can be efficiently computed based on analytic expressions. The GMM-based inversion method benefits from online adaptive learning and parallel computation. We demonstrate the efficacy of the proposed inversion method with videos reconstructed from simulated compressive video measurements, and from a real compressive video camera. We also use the GMM as a tool to investigate adaptive video compressive sensing, i.e., adaptive rate of temporal compression.

Journal ArticleDOI
TL;DR: This overview article presents ICA, and then its generalization to multiple data sets, IVA, both using mutual information rate, and presents conditions for the identifiability of the given linear mixing model and derive the performance bounds.
Abstract: Starting with a simple generative model and the assumption of statistical independence of the underlying components, independent component analysis (ICA) decomposes a given set of observations by making use of the diversity in the data, typically in terms of statistical properties of the signal. Most of the ICA algorithms introduced to date have considered one of the two types of diversity: non-Gaussianity?i.e., higher-order statistics (HOS)?or, sample dependence. A recent generalization of ICA, independent vector analysis (IVA), generalizes ICA to multiple data sets and adds the use of one more diversity, dependence across multiple data sets for achieving an independent decomposition, jointly across multiple data sets. Finally, both ICA and IVA, when implemented in the complex domain, enjoy the addition of yet another type of diversity, noncircularity of the sources?underlying components. Mutual information rate provides a unifying framework such that all these statistical properties?types of diversity?can be jointly taken into account for achieving the independent decomposition. Most of the ICA methods developed to date can be cast as special cases under this umbrella, as well as the more recently developed IVA methods. In addition, this formulation allows us to make use of maximum likelihood theory to study large sample properties of the estimator, derive the Cram?r?Rao lower bound (CRLB) and determine the conditions for the identifiability of the ICA and IVA models. In this overview article, we first present ICA, and then its generalization to multiple data sets, IVA, both using mutual information rate, present conditions for the identifiability of the given linear mixing model and derive the performance bounds. We address how various methods fall under this umbrella and give examples of performance for a few sample algorithms compared with the performance bound. We then discuss the importance of approaching the performance bound depending on the goal, and use medical image analysis as the motivating example.

Journal ArticleDOI
TL;DR: This work presents a new method based on Dirichlet process Gaussian mixture models, which is used to estimate per-pixel background distributions, followed by probabilistic regularisation, and develops novel model learning algorithms for continuous update of the model in a principled fashion as the scene changes.
Abstract: Video analysis often begins with background subtraction. This problem is often approached in two steps-a background model followed by a regularisation scheme. A model of the background allows it to be distinguished on a per-pixel basis from the foreground, whilst the regularisation combines information from adjacent pixels. We present a new method based on Dirichlet process Gaussian mixture models, which are used to estimate per-pixel background distributions. It is followed by probabilistic regularisation. Using a non-parametric Bayesian method allows per-pixel mode counts to be automatically inferred, avoiding over-/under- fitting. We also develop novel model learning algorithms for continuous update of the model in a principled fashion as the scene changes. These key advantages enable us to outperform the state-of-the-art alternatives on four benchmarks.

Journal ArticleDOI
TL;DR: The subjective listening tests indicate that the naturalness of the converted speech by the proposed method is comparable with that by the ML-GMM method with global variance constraint, and the results show the superiority of the method over PLS-based methods.
Abstract: We propose a nonparametric framework for voice conversion, that is, exemplar-based sparse representation with residual compensation. In this framework, a spectrogram is reconstructed as a weighted linear combination of speech segments, called exemplars, which span multiple consecutive frames. The linear combination weights are constrained to be sparse to avoid over-smoothing, and high-resolution spectra are employed in the exemplars directly without dimensionality reduction to maintain spectral details. In addition, a spectral compression factor and a residual compensation technique are included in the framework to enhance the conversion performances. We conducted experiments on the VOICES database to compare the proposed method with a large set of state-of-the-art baseline methods, including the maximum likelihood Gaussian mixture model (ML-GMM) with dynamic feature constraint and the partial least squares (PLS) regression based methods. The experimental results show that the objective spectral distortion of ML-GMM is reduced from 5.19 dB to 4.92 dB, and both the subjective mean opinion score and the speaker identification rate are increased from 2.49 and 73.50% to 3.15 and 79.50%, respectively, by the proposed method. The results also show the superiority of our method over PLS-based methods. In addition, the subjective listening tests indicate that the naturalness of the converted speech by our proposed method is comparable with that by the ML-GMM method with global variance constraint.

Proceedings ArticleDOI
23 Jun 2014
TL;DR: This work proposes distributed algorithms for learning large- mixture models that capture long-tail distributions, which are hard to model with current approaches, and introduces a generalized notion of mixtures (or subcategories) that allow for examples to be shared across multiple subc categories.
Abstract: We argue that object subcategories follow a long-tail distribution: a few subcategories are common, while many are rare. We describe distributed algorithms for learning large- mixture models that capture long-tail distributions, which are hard to model with current approaches. We introduce a generalized notion of mixtures (or subcategories) that allow for examples to be shared across multiple subcategories. We optimize our models with a discriminative clustering algorithm that searches over mixtures in a distributed, "brute-force" fashion. We used our scalable system to train tens of thousands of deformable mixtures for VOC objects. We demonstrate significant performance improvements, particularly for object classes that are characterized by large appearance variation.

Journal ArticleDOI
27 Jul 2014
TL;DR: This work proposes to represent the distributions for sampling scattering directions and light emission by a parametric mixture model trained in an on-line (i.e. progressive) manner from a potentially infinite stream of particles that enables recovering good sampling distributions in scenes with complex lighting.
Abstract: Monte Carlo techniques for light transport simulation rely on importance sampling when constructing light transport paths. Previous work has shown that suitable sampling distributions can be recovered from particles distributed in the scene prior to rendering. We propose to represent the distributions by a parametric mixture model trained in an on-line (i.e. progressive) manner from a potentially infinite stream of particles. This enables recovering good sampling distributions in scenes with complex lighting, where the necessary number of particles may exceed available memory. Using these distributions for sampling scattering directions and light emission significantly improves the performance of state-of-the-art light transport simulation algorithms when dealing with complex lighting.

Proceedings ArticleDOI
23 Jun 2014
TL;DR: A novel real-time algorithm for simultaneous pose and shape estimation for articulated objects, such as human beings and animals, and a novel shape adaptation algorithm based on the same probabilistic model that automatically captures the shape of the subjects during the dynamic pose estimation process.
Abstract: In this paper we present a novel real-time algorithm for simultaneous pose and shape estimation for articulated objects, such as human beings and animals. The key of our pose estimation component is to embed the articulated deformation model with exponential-maps-based parametrization into a Gaussian Mixture Model. Benefiting from the probabilistic measurement model, our algorithm requires no explicit point correspondences as opposed to most existing methods. Consequently, our approach is less sensitive to local minimum and well handles fast and complex motions. Extensive evaluations on publicly available datasets demonstrate that our method outperforms most state-of-art pose estimation algorithms with large margin, especially in the case of challenging motions. Moreover, our novel shape adaptation algorithm based on the same probabilistic model automatically captures the shape of the subjects during the dynamic pose estimation process. Experiments show that our shape estimation method achieves comparable accuracy with state of the arts, yet requires neither parametric model nor extra calibration procedure.

Journal ArticleDOI
TL;DR: It is shown that RBMs can be used to identify networks and their temporal activations with accuracy that is equal or greater than that of factorization models, a significant prospect for future neuroimaging research.

Journal ArticleDOI
TL;DR: A distributed intrusion detection framework, in which a local parameterized detection model is constructed in each node using the online Adaboost algorithm, and an algorithm based on particle swarm optimization (PSO) and support vector machines is used to detect intrusions.
Abstract: Current network intrusion detection systems lack adaptability to the frequently changing network environments. Furthermore, intrusion detection in the new distributed architectures is now a major requirement. In this paper, we propose two online Adaboost-based intrusion detection algorithms. In the first algorithm, a traditional online Adaboost process is used where decision stumps are used as weak classifiers. In the second algorithm, an improved online Adaboost process is proposed, and online Gaussian mixture models (GMMs) are used as weak classifiers. We further propose a distributed intrusion detection framework, in which a local parameterized detection model is constructed in each node using the online Adaboost algorithm. A global detection model is constructed in each node by combining the local parametric models using a small number of samples in the node. This combination is achieved using an algorithm based on particle swarm optimization (PSO) and support vector machines. The global model in each node is used to detect intrusions. Experimental results show that the improved online Adaboost process with GMMs obtains a higher detection rate and a lower false alarm rate than the traditional online Adaboost process that uses decision stumps. Both the algorithms outperform existing intrusion detection algorithms. It is also shown that our PSO, and SVM-based algorithm effectively combines the local detection models into the global model in each node; the global model in a node can handle the intrusion types that are found in other nodes, without sharing the samples of these intrusion types.

Journal ArticleDOI
TL;DR: This work reviews various methods that have been proposed to answer the question of how many components to include in the normal mixture model and proposes a probabilistic clustering procedure corresponding to the g components in the mixture model.
Abstract: Mixture distributions, in particular normal mixtures, are applied to data with two main purposes in mind. One is to provide an appealing semiparametric framework in which to model unknown distributional shapes, as an alternative to, say, the kernel density method. The other is to use the mixture model to provide a probabilistic clustering of the data into g clusters corresponding to the g components in the mixture model. In both situations, there is the question of how many components to include in the normal mixture model. We review various methods that have been proposed to answer this question. WIREs Data Mining Knowl Discov 2014, 4:341-355. doi: 10.1002/widm.1135

Journal ArticleDOI
TL;DR: The Gaussian mixture model has been incorporated into the placement optimization by means of the so-called Gaussian component combination method and the occurrence of either loss of data or degradation of metrological performance of the measurement devices is also considered.
Abstract: Future active distribution grids are characterized by rapid and significant changes of operation and behavior due to, for example, intermittent power injections from renewable sources and the load-generation characteristic of the so-called prosumers. The design of a robust measurement infrastructure is critical for safe and effective grid control and operation. We had earlier proposed a placement procedure that allows finding an optimal robust measurement location incorporating phasor measurement units and smart metering devices for distribution system state estimation. In this paper, the lack of detailed information on distributed generation is also considered in the optimal meter placement procedure, so that the distributed measurement system can provide accurate estimates even with limited knowledge of the profile of the injected power. Possible non-Gaussian distribution of the distributed power generation has been taken into account. With this aim, the Gaussian mixture model has been incorporated into the placement optimization by means of the so-called Gaussian component combination method. The occurrence of either loss of data or degradation of metrological performance of the measurement devices is also considered. Tests performed on a UKGDS 16-bus distribution network are presented and discussed.

Journal ArticleDOI
TL;DR: In this paper, dimensionality reduction targeting the preservation of multimodal structures is proposed to counter the parameter-space issue, where locality-preserving nonnegative matrix factorization, as well as local Fisher's discriminant analysis, is deployed as preprocessing to reduce the dimensionality of data for the Gaussian-mixture-model classifier.
Abstract: The Gaussian mixture model is a well-known classification tool that captures non-Gaussian statistics of multivariate data. However, the impractically large size of the resulting parameter space has hindered widespread adoption of Gaussian mixture models for hyperspectral imagery. To counter this parameter-space issue, dimensionality reduction targeting the preservation of multimodal structures is proposed. Specifically, locality-preserving nonnegative matrix factorization, as well as local Fisher's discriminant analysis, is deployed as preprocessing to reduce the dimensionality of data for the Gaussian-mixture-model classifier, while preserving multimodal structures within the data. In addition, the pixel-wise classification results from the Gaussian mixture model are combined with spatial-context information resulting from a Markov random field. Experimental results demonstrate that the proposed classification system significantly outperforms other approaches even under limited training data.

Proceedings ArticleDOI
24 Aug 2014
TL;DR: The experimental results indicate that the mixture-KDE method provides a useful and accurate methodology for capturing and predicting individual-level spatial patterns in the presence of noisy and sparse data.
Abstract: Location-based data is increasingly prevalent with the rapid increase and adoption of mobile devices. In this paper we address the problem of learning spatial density models, focusing specifically on individual-level data. Modeling and predicting a spatial distribution for an individual is a challenging problem given both (a) the typical sparsity of data at the individual level and (b) the heterogeneity of spatial mobility patterns across individuals. We investigate the application of kernel density estimation (KDE) to this problem using a mixture model approach that can interpolate between an individual's data and broader patterns in the population as a whole. The mixture-KDE approach is evaluated on two large geolocation/check-in data sets, from Twitter and Gowalla, with comparisons to non-KDE baselines, using both log-likelihood and detection of simulated identity theft as evaluation metrics. Our experimental results indicate that the mixture-KDE method provides a useful and accurate methodology for capturing and predicting individual-level spatial patterns in the presence of noisy and sparse data.

Journal ArticleDOI
TL;DR: The RSCFCM algorithm is proposed, utilizing the negative log-posterior as the dissimilarity function, introducing a novel factor and integrating the bias field estimation model into the fuzzy objective function, which successfully overcomes the drawbacks of existing FCM-type clustering schemes and EM-type mixture models.

Journal ArticleDOI
TL;DR: Mixtures of skew-t factor analyzers are very well-suited for model-based clustering of high-dimensional data, giving superior clustering results when compared to a well-established family of Gaussian mixture models.