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Despite its potentials benefits, using prediction targets generated based on latent variable (LV) modeling is not a common practice in supervised learning, a dominating framework for developing prediction models. In supervised learning, it is typically assumed that the outcome to be predicted is clear and readily available, and therefore validating outcomes before predicting them is a foreign concept and an unnecessary step. The usual goal of LV modeling is inference, and therefore using it in supervised learning and in the prediction context requires a major conceptual shift. This study lays out methodological adjustments and conceptual shifts necessary for integrating LV modeling into supervised learning. It is shown that such integration is possible by combining the traditions of LV modeling, psychometrics, and supervised learning. In this interdisciplinary learning framework, generating practical outcomes using LV modeling and systematically validating them based on clinical validators are the two main strategies. In the example using the data from the Longitudinal Assessment of Manic Symptoms (LAMS) Study, a large pool of candidate outcomes is generated by flexible LV modeling. It is demonstrated that this exploratory situation can be used as an opportunity to tailor desirable prediction targets taking advantage of contemporary science and clinical insights. [ABSTRACT FROM AUTHOR]

The human microbiome plays an important role in human health and disease status. Next-generating sequencing technologies allow for quantifying the composition of the human microbiome. Clustering these microbiome data can provide valuable information by identifying underlying patterns across samples. Recently, Fang and Subedi (2023) proposed a logistic normal multinomial mixture model (LNM-MM) for clustering microbiome data. As microbiome data tends to be high dimensional, here, we develop a family of logistic normal multinomial factor analyzers (LNM-FA) by incorporating a factor analyzer structure in the LNM-MM. This family of models is more suitable for high-dimensional data as the number of free parameters in LNM-FA can be greatly reduced by assuming that the number of latent factors is small. Parameter estimation is done using a computationally efficient variant of the alternating expectation conditional maximization algorithm that utilizes variational Gaussian approximations. The proposed method is illustrated using simulated and real datasets. [ABSTRACT FROM AUTHOR]

In this study we present the model-based clustering in order to overcome the problem of mixed pixels for satellite imagery. The mixed pixel problem is one of the major reasons that affect the classification accuracy in the classification of remotely sensed images. Mixed pixels are usually the prime reason for degrading the success in image classification and object recognition. A modified model-based clustering algorithm is developed by modifying membership function and compared with the traditional model-based clustering algorithm in terms of classification error and brier score. Results on classification of satellite images reveal that the suggestive algorithms are robust and effective. [ABSTRACT FROM AUTHOR]

Powerline communication (PLC) channels are known to exhibit multipath propagation behaviour. The authors present a model-based framework to address the challenge of clustering multipath propagation components (MPCs) in PLC channels for indoor low-voltage (LV) environments. The framework employs a range of finite-mixture models (FMMs), including the gamma mixture model, the inverse gamma mixture model, the Gaussian mixture model, the inverse Gaussian mixture model, the Nakagami mixture model, the inverse Nakagami mixture model (INMM) and the Rayleigh mixture model, to identify clusters of MPCs. A measurement campaign of an unknown indoor LV PLC channel is conducted to obtain a channel response. From the channel response, the delay and magnitude parameters of the MPCs are extracted using the space-alternating generalised expectation maximisation algorithm adopted only for these parameters. A maximum likelihood approach and the expectation–maximisation algorithm are employed to fit the FMMs to the MPC delay-magnitude dataset to cluster MPCs in the delay domain. The results of the model-fitting process are then evaluated using the corrected Akaike information criterion (AICc), which enables a fair comparison of the candidate models over the feasible and finite range of clusters. A novel algorithm is introduced for estimating the feasible and finite range of clusters using the extracted delay and magnitude MPC parameters. The AICc's ranking results show that the INMM model provides the best fit. Davies–Bouldin (DB) and Calinski–Harabasz (CH) indexes are used to compare the model-based clustering approach to the conventional distance-based clustering methods. Validation results show that CH and DB indexes closely agree in the optimal number of MPC clusters for model-based clustering, which corresponds to the most within-cluster compactness of MPCs and to the most between-cluster separation in the delay domain. [ABSTRACT FROM AUTHOR]

The Mallows model (MM) occupies a central role in parametric modelling of ranking data to learn preferences of a population of judges. Despite the wide range of metrics for rankings that can be considered in the model specification, the choice is typically limited to the Kendall, Cayley or Hamming distances, due to the closed-form expression of the related model normalizing constant. This work instead focuses on the Mallows model with Spearman distance (MMS). A novel approximation of the normalizing constant is introduced to allow inference even with a large number of items. This allows us to develop and implement an efficient and accurate EM algorithm for estimating finite mixtures of MMS aimed at i) enlarging the applicability to samples drawn from heterogeneous populations, and ii) dealing with partial rankings affected by diverse forms of censoring. These novelties encompass the critical inferential steps that traditionally limited the use of this distance in practice, and render the MMS comparable (or even preferable) to the MMs with other metrics in terms of computational burden. The inferential ability of the EM scheme and the effectiveness of the approximation are assessed by extensive simulation studies. Finally, we show that the application to three real-world datasets endorses our proposals also in the comparison with competing mixtures of ranking models. [ABSTRACT FROM AUTHOR]

Many studies have shown successful applications of the Dirichlet process mixture model (DPMM) for clustering continuous data. Beyond continuous data, in practice, one can expect to see different data types, including ordinal and nominal data. Existing DPMMs for clustering mixed-type data assume a strict covariance matrix structure, resulting in an overfit model. This article explores a DPMM for mixed-type data that allows the covariance matrix to differ from one cluster to another. We assume an underlying latent variable framework for ordinal and nominal data, which is then modeled jointly with the continuous data. The identifiability issue on the covariance matrix poses computational challenges, thus requiring a nonstandard inferential algorithm. The applicability and flexibility of the proposed model are illustrated through simulation examples and real data applications.

The identification of unlabeled neuronal electric signals is one of the most challenging open problems in neuroscience, widely known as Spike Sorting. Motivated to solve this problem, we propose a model-based approach within the mixture modeling framework for clustering oscillatory functional data called MixFMM. The core of the approach is the FMM (Frequency Modulated Möbius) waves, which are non-linear parametric time functions, flexible enough to describe different oscillatory patterns and simple enough to be estimated efficiently. In particular, specific model parameters describe the phase, amplitude and shape of the waveforms. A mixture model is defined using FMM waves as basic functions and gaussian errors, and an EM algorithm is proposed for estimating the parameters. Spike Sorting (SS) has received considerable attention in the literature, and different functional clustering approaches have been considered. We have conducted a fair comparative analysis of the MixFMM with three competitors. Two of them are traditional methods in functional clustering and widely used in Spike Sorting. The third is an approach that has proven superior to many others solving Spike Sorting problems. The datasets used for validation include benchmarking simulated and real cases. The internal and external validation indexes confirm a better performance of the MixFMM on real data sets against the three competitors and an outstanding performance in simulated data against traditional approaches.

Abstract Graphical mixture models provide a powerful tool to visually depict conditional independencies or dependencies between heterogeneous high-dimensional data. When the random variables corresponding to the vertices are continuous, mixture component densities are assumed to be multivariate normal with different covariance matrices, leading to introduction of the Gaussian graphical mixture model (GGMM). The nonparanormal graphical mixture model (NGMM) replaces the restrictive normal assumption with a semiparametric Gaussian copula, which extends the nonparanormal graphical model and mixture models. Such an extension allows us to simultaneously estimate cluster assignments and cluster-specific graphical model structure. To enable such analyses, we propose a regularized estimation scheme with two forms of ℓ 1 penalty function (conventional and unconventional) via the expectation-maximization algorithm to learn a finite mixture of nonparanormal graphical models. We illustrate the performance of our method through a simulation study under both ideal and noisy settings. We also apply the proposed methodology to a breast cancer data set to diagnose malignant or benign tumors in patients. The results showed that the combination of NGMM together with unconventional penalty, which was named as NGMM1 during this study, provides the most efficient approach in clustering and estimating the graphical model structure. [ABSTRACT FROM AUTHOR]

In this paper, we develop a mixture of autoregressive (MoAR) process model with time varying and freely indexed covariates under the flexible class of two–piece distributions using the scale mixtures of normal (TP-SMN) family. This novel family of time series (TP-SMN-MoAR) models was used to examine flexible and robust clustering of reported cases of Covid-19 across 313 counties in the U.S. The TP-SMN distributions allow for symmetrical/ asymmetrical distributions as well as heavy-tailed distributions providing for flexibility to handle outliers and complex data. Developing a suitable hierarchical representation of the TP-SMN family enabled the construction of a pseudo-likelihood function to derive the maximum pseudo-likelihood estimates via an EM-type algorithm. [ABSTRACT FROM AUTHOR]

Climate change has become increasingly important in recent years. It is the outcome of the burning of fossil fuels that increased the concentration of atmospheric carbon dioxide (CO 2 ), over the last century. Mitigating the impacts of climate change requires a better understanding and assessment of the countries' economic decisions on the amount of CO 2 emissions. This paper assesses the variability between the different countries in the trends of CO 2 emissions and electricity consumption from 1975 to 2014, while identifying clusters of countries of similar trends over time. The novel methodology applied in this paper enables us to assess long-debated issues in climate literature. The temporal dynamic effects of electricity consumption and economic growth on CO 2 emissions across countries are studied using functional data analysis (FDA) methods. The latter have proven to be useful tools for visualising similarities and differences in the non-linear trends of CO 2 emissions without forcing linear trends and stationary relationships which can be unrealistic and misleading. The results indicate the possibility of identifying changes in the trends of CO 2 emissions and electricity consumption for a wide range of heterogeneous countries over the study period. The findings also reveal that economic growth puts a strain on the environment, where many high-income countries are still away from attaining economic-energy sustainability. [ABSTRACT FROM AUTHOR]

One of the challenges in clustering categorical data is the curse of dimensionality caused by the inherent sparsity of high-dimensional data, the records of which include a large number of attributes. The latent class model (LCM) assumes local independence between the variables in clusters, and is a parsimonious model-based clustering approach that has been used to circumvent the problem. The mixture of a log-linear model is more flexible but requires more parameters to be estimated. In this research, we recognize that each categorical observation can be conceived as a network with pairwise linked nodes, which are the response levels of the observation attributes. Therefore, the categorical data for clustering is considered a finite mixture of different component layer networks with distinct patterns. We apply a penalized composite likelihood approach to a finite mixture of networks for sparse multivariate categorical data to reduce the number of parameters, implement the EM algorithm to estimate the model parameters, and show that the estimates are consistent and satisfy asymptotic normality. The performance of the proposed approach is shown to be better in comparison with the conventional methods for both synthetic and real datasets. [ABSTRACT FROM AUTHOR]

The Cluster Weighted Robust Model (CWRM) is a recently introduced methodology to robustly estimate mixtures of regressions with random covariates. The CWRM allows users to flexibly perform regression clustering, safeguarding it against data contamination and spurious solutions. Nonetheless, the resulting solution depends on the chosen number of components in the mixture, the percentage of impartial trimming, the degree of heteroscedasticity of the errors around the regression lines and of the clusters in the explanatory variables. Therefore, an appropriate model selection is crucially required. Such a complex modeling task may generate several "legitimate" solutions: each one derived from a distinct hyperparameters specification. The present article introduces a two step-monitoring procedure to help users effectively explore such a vast model space. The first phase uncovers the most appropriate percentages of trimming, whilst the second phase explores the whole set of solutions, conditioning on the outcome derived from the previous step. The final output singles out a set of "top" solutions, whose optimality, stability and validity is assessed. Novel graphical and computational tools—specifically tailored for the CWRM framework—will help the user make an educated choice among the optimal solutions. Three examples on real datasets showcase our proposal in action. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

Clustering analysis is a prevalent statistical method which divides populations into several subgroups of similar units. However, most existing clustering methods require complete data. One general method that addresses incomplete data is multiple imputation (MI) which avoids many limitations found in other single imputation-based methods and complete case analyses. Nevertheless, adopting MI framework to clustering analysis can be challenging since each imputed data might consist of a different number of clusters and there is not a unique parameter for clustering analysis. In response to this problem, we have developed MICA: Multiply Imputed Cluster Analysis. MICA is a framework for clustering incomplete data consisting of two clustering stages. We assess the properties of MICA and its superiority over other existing incomplete clustering strategies based on a simulation study under various data structures. In addition, we demonstrate the usage of MICA by applying it to the Youth Risk Behavior Surveillance System (YRBSS) 2019 data. [ABSTRACT FROM AUTHOR]

Social network data are relational data recorded among a group of actors, interacting in different contexts. Often, the same set of actors can be characterised by multiple social relations, captured by a multidimensional network. A common situation is that of colleagues working in the same institution, whose social interactions can be defined on professional and personal levels. In addition, individuals in a network tend to interact more frequently with similar others, naturally creating communities. Latent space models for network data are useful to recover clustering of the actors, as they allow to represent similarities between them by their positions and relative distances in an interpretable low-dimensional social space. We propose the infinite mixture latent position cluster model for multidimensional network data, which enables model-based clustering of actors interacting across multiple social dimensions. The model is based on a Bayesian non-parametric framework that allows to perform automatic inference on the clustering allocations, the number of clusters, and the latent social space. The method is tested on extensive simulated data experiments. It is also employed to investigate the presence of communities in two multidimensional workplace social networks recording relations of different types among colleagues. [ABSTRACT FROM AUTHOR]

Mixed data refers to a mixture of continuous and categorical variables. The clustering problem with mixed data is a long-standing statistical problem. The latent Gaussian mixture model, a model-based approach for such a problem, has received attention owing to its simplicity and interpretability. However, these approaches are prone to dimensionality problems. Specifically, parameters must be estimated for each group, and the number of covariance parameters is quadratic in the number of variables. To address this, we propose “regClustMD,” a novel model-based clustering method that can address sparse dependence among variables. We consider a sparse latent Gaussian mixture model, assuming that the precision matrix between variables has sparse nonzero elements. We propose maximizing a penalized complete log-likelihood using the Monte Carlo expectation-maximization (MCEM) algorithm. Our numerical experiments and real data analyses demonstrated that our method outperformed a counterpart algorithm in both accuracy and failure rate under the correlated data structure.

We discuss a Bayesian hierarchical copula model for clusters of financial time series. A similar approach has been developed in recent paper. However, the prior distributions proposed there do not always provide a proper posterior. In order to circumvent the problem, we adopt a proper global–local shrinkage prior, which is also able to account for potential dependence structures among different clusters. The performance of the proposed model is presented via simulations and a real data analysis.

Recent advancements in miniaturized fluorescence microscopy have made it possible to investigate neuronal responses to external stimuli in awake behaving animals through the analysis of intracellular calcium signals. An ongoing challenge is deconvolving the temporal signals to extract the spike trains from the noisy calcium signals' time series. In this article, we propose a nested Bayesian finite mixture specification that allows the estimation of spiking activity and, simultaneously, reconstructing the distributions of the calcium transient spikes' amplitudes under different experimental conditions. The proposed model leverages two nested layers of random discrete mixture priors to borrow information between experiments and discover similarities in the distributional patterns of neuronal responses to different stimuli. Furthermore, the spikes' intensity values are also clustered within and between experimental conditions to determine the existence of common (recurring) response amplitudes. Simulation studies and the analysis of a dataset from the Allen Brain Observatory show the effectiveness of the method in clustering and detecting neuronal activities. [ABSTRACT FROM AUTHOR]

We propose a variant of the bootstrap to assess the variability of posterior probabilities arising from Gaussian model-based clustering. The bootstrap variant uses predictions based on out-of-bootstrap-sample observations and then constructs confidence intervals for the posterior probabilities using the percentile method. The methodology outperforms the multivariate Delta method approach when comparing empirical coverage probabilities on simulated data. The proposed and multivariate Delta methods are also illustrated on the well-known Iris data set. [ABSTRACT FROM AUTHOR]

Cluster-weighted models (CWMs) are useful tools for identifying latent functional relationships between response variables and covariates. However, owing to excess distributional assumptions made on the covariates, these models can suffer misspecifications of component distributions, which could also undermine the estimation accuracy and render the model structure complicated for interpretation. To address this issue, we consider CWMs with univariate responses and propose a novel CWM by modelling each cluster as a finite mixture to enhance flexibility while retaining parsimony. We prove that the proposed method can provide more meaningful clusters in the data than those of existing methods. Additionally, we present a procedure to construct such a proposed CWM and a feasible expectation-maximization algorithm to estimate the model parameters. Numerical demonstrations, including simulations and real data analysis, are also provided. [ABSTRACT FROM AUTHOR]

Families of mixtures of multivariate power exponential (MPE) distributions have already been introduced and shown to be competitive for cluster analysis in comparison to other mixtures of elliptical distributions, including mixtures of Gaussian distributions. A family of mixtures of multivariate skewed power exponential distributions is proposed that combines the flexibility of the MPE distribution with the ability to model skewness. These mixtures are more robust to variations from normality and can account for skewness, varying tail weight, and peakedness of data. A generalized expectation-maximization approach, which combines minorization-maximization and optimization based on accelerated line search algorithms on the Stiefel manifold, is used for parameter estimation. These mixtures are implemented both in the unsupervised and semi-supervised classification frameworks. Both simulated and real data are used for illustration and comparison to other mixture families. [ABSTRACT FROM AUTHOR]

In this paper, we propose a functional partially linear regression model with latent group structures to accommodate the heterogeneous relationship between a scalar response and functional covariates. The proposed model is motivated by a salinity tolerance study of barley families, whose main objective is to detect salinity tolerant barley plants. Our model is flexible, allowing for heterogeneous functional coefficients while being efficient by pooling information within a group for estimation. We develop an algorithm in the spirit of the K‐means clustering to identify latent groups of the subjects under study. We establish the consistency of the proposed estimator, derive the convergence rate and the asymptotic distribution, and develop inference procedures. We show by simulation studies that the proposed method has higher accuracy for recovering latent groups and for estimating the functional coefficients than existing methods. The analysis of the barley data shows that the proposed method can help identify groups of barley families with different salinity tolerant abilities. [ABSTRACT FROM AUTHOR]

Although basketball is a dynamic process sport, played between two sides of five players each, learning some static information is essential for professional players, coaches, and team managers. In order to have a deep understanding of field goal attempts among different players, we propose a zero‐inflated Poisson model with clustered regression coefficients to learn the shooting habits of different players over the court and the heterogeneity among them. Specifically, the zero‐inflated model captures a large portion of the court with zero field goal attempts, and the mixture of finite mixtures model captures the heterogeneity among different players based on clustered regression coefficients and inflated probabilities. Both theoretical and empirical justification through simulation studies validate our proposed method. We apply our proposed model to data from the National Basketball Association (NBA), for learning players' shooting habits and heterogeneity among different players over the 2017–2018 regular season. This illustrates our model as a way of providing insights from different aspects. [ABSTRACT FROM AUTHOR]

We develop clustering procedures for longitudinal trajectories based on a continuous‐time hidden Markov model (CTHMM) and a generalized linear observation model. Specifically, in this article we carry out finite and infinite mixture model‐based clustering for a CTHMM and achieve inference using Markov chain Monte Carlo (MCMC). For a finite mixture model with a prior on the number of components, we implement reversible‐jump MCMC to facilitate the trans‐dimensional move between models with different numbers of clusters. For a Dirichlet process mixture model, we utilize restricted Gibbs sampling split–merge proposals to improve the performance of the MCMC algorithm. We apply our proposed algorithms to simulated data as well as a real‐data example, and the results demonstrate the desired performance of the new sampler. [ABSTRACT FROM AUTHOR]

Poverty, inequality and climate change are profoundly interconnected issues and represent grave threats to the future of our planet and civilization. Failure in one will result in failure in the other; thus, government responses to such threats must be meticulously coordinated, especially across environmental and welfare state programs. In recent years, a growing body of research has examined the links between these two domains, lauding the eco-welfare state as a viable path forward. As the literature on the eco-welfare state is at an early stage, this study proposes two essential theoretical and empirical contributions. First, it examines the most prominent theoretical interpretations of the concept of eco-welfare state and proposes a refined understanding. Second, using model-based cluster analysis for 42 countries, this study empirically unveils a global shift towards and the existence of an eco-welfare state. [ABSTRACT FROM AUTHOR]

Fisheries governance systems designed to regulate fishing are often described as being highly diverse across countries. However, there is little systematic work that directly examines and describes the (dis)similarities across such systems, and how socio‐political and economic contexts drive such variation at a global scale. In this paper, we use 68 indicators from a novel dataset to examine the fisheries governance systems in place to constrain overfishing in national waters across 142 countries. We found that countries cluster in just two distinct governance groups which display different traits to constrain overfishing. Where one group takes a tougher stance on aspects regarding access to its fisheries resources, the other is more focused on gathering fisheries information and publicizing the data. The 10 greatest differences between groups relate to the gathering of information and monitoring of their fisheries, the effectiveness of compliance systems and the existence of policies around sustainability. On these key differences, one group consistently displays more far‐reaching governance traits. The overall governance capacity of a country and the national socio‐economic importance of fisheries are identified as potential drivers of this variation. Despite their differences, the two groups show substantial overlap for many indicators, particularly those that are inexpensive, but also for certain costly policies. These patterns prompt hypotheses of policy transfer or convergence across fisheries governance systems, most notably regarding 'low‐hanging fruit' policies. [ABSTRACT FROM AUTHOR]

We propose a Bayesian nonparametric matrix clustering approach to analyze the latent heterogeneity structure in the shot selection data collected from professional basketball players in the National Basketball Association (NBA). The proposed method adopts a mixture of finite mixtures framework and fully uses the spatial information via a mixture of matrix normal distribution representation. We propose an efficient Markov chain Monte Carlo algorithm for posterior sampling that allows simultaneous inference on both the number of clusters and the cluster configurations. We also establish large-sample convergence properties for the posterior distribution. The compelling empirical performance of the proposed method is demonstrated via simulation studies and an application to shot chart data from selected players in the NBAs 2017–2018 regular season. for this article are available online. [ABSTRACT FROM AUTHOR]

A classic problem in population genetics is the characterization of discrete population structure in the presence of continuous patterns of genetic differentiation. Especially when sampling is discontinuous, the use of clustering or assignment methods may incorrectly ascribe differentiation due to continuous processes (e.g., geographic isolation by distance) to discrete processes, such as geographic, ecological, or reproductive barriers between populations. This reflects a shortcoming of current methods for inferring and visualizing population structure when applied to genetic data deriving from geographically distributed populations. Here, we present a statistical framework for the simultaneous inference of continuous and discrete patterns of population structure. The method estimates ancestry proportions for each sample from a set of two-dimensional population layers, and, within each layer, estimates a rate at which relatedness decays with distance. This thereby explicitly addresses the "clines versus clusters" problem in modeling population genetic variation, and remedies some of the overfitting to which nonspatial models are prone. The method produces useful descriptions of structure in genetic relatedness in situations where separated, geographically distributed populations interact, as after a range expansion or secondary contact. We demonstrate the utility of this approach using simulations and by applying it to empirical datasets of poplars and black bears in North America.

We discuss a Bayesian hierarchical copula model for clusters of financial time series. A similar approach has been developed in recent paper. However, the prior distributions proposed there do not always provide a proper posterior. In order to circumvent the problem, we adopt a proper global–local shrinkage prior, which is also able to account for potential dependence structures among different clusters. The performance of the proposed model is presented via simulations and a real data analysis. [ABSTRACT FROM AUTHOR]

Parsimonious finite mixture models often require the a priori selection of desired model dimensionality. For example, projection-based parsimonious models demand the dimension of the subspace for projection. Other models ask for their own structural restrictions on parameters. The subspace clustering framework is a projection-based parsimonious model for various finite mixtures, including the Gaussian variant. The existing dimension selection methods for subspace clustering are ad-hoc or potentially computationally prohibitive, creating a need for a principled, yet computationally lightweight, approach. In light of this problem, a hypothesis test-based intrinsic dimension estimation method called the Anderson Relaxation Test (ART) is introduced, and its performance is examined in both simulated and real data settings. [ABSTRACT FROM AUTHOR]

Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where they tend to be over-parameterized. As a consequence, different solutions have been proposed, often relying on matrix decompositions or variable selection strategies. Recently, a methodological link between Gaussian graphical models and finite mixtures has been established, paving the way for penalized model-based clustering in the presence of large precision matrices. Notwithstanding, current methodologies implicitly assume similar levels of sparsity across the classes, not accounting for different degrees of association between the variables across groups. We overcome this limitation by deriving group-wise penalty factors, which automatically enforce under or over-connectivity in the estimated graphs. The approach is entirely data-driven and does not require additional hyper-parameter specification. Analyses on synthetic and real data showcase the validity of our proposal. [ABSTRACT FROM AUTHOR]

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. For cluster analysis, using a traditional finite mixture model framework, the number of components either needs to be known a priori or needs to be estimated a posteriori using some model selection criterion after deriving results for a range of possible number of components. However, different model selection criteria can sometimes result in different numbers of components yielding uncertainty. Here, an infinite mixture model framework, also known as Dirichlet process mixture model, is proposed for the mixtures of MNIG distributions. This Dirichlet process mixture model approach allows the number of components to grow or decay freely from 1 to ∞ (in practice from 1 to N) and the number of components is inferred along with the parameter estimates in a Bayesian framework, thus alleviating the need for model selection criteria. We run our algorithm on simulated as well as real benchmark datasets and compare with other clustering approaches. The proposed method provides competitive results for both simulations and real data. [ABSTRACT FROM AUTHOR]

Clustering has received much attention in statistics and machine learning with the aim of developing statistical models and autonomous algorithms which are capable of acquiring information from raw data in order to perform exploratory analysis. Several techniques have been developed to cluster sampled univariate vectors only considering the average value over the whole period and as such they have not been able to explore fully the underlying distribution as well as other features of the data, especially in presence of structured time series. We propose a model‐based clustering technique that is based on quantile regression permitting us to cluster bivariate time series at different quantile levels. We model the within cluster density using asymmetric Laplace distribution allowing us to take into account asymmetry in the distribution of the data. We evaluate the performance of the proposed technique through a simulation study. The method is then applied to cluster time series observed from Glob‐color satellite data related to trophic status indices with aim of evaluating their temporal dynamics in order to identify homogeneous areas, in terms of trophic status, in the Gulf of Gabes. [ABSTRACT FROM AUTHOR]

Finite mixture model-based clustering is a popular method to perform unsupervised learning, however the classic approach for parameter estimation, the expectation-maximization algorithm, is quite susceptible to converging to, at times extremely poor, local maxima. Recently, swarm-based algorithms have gained popularity in a number of optimization scenarios. One such swarm-based optimization procedure, the artificial bee colony, incorporates both local searching and multiple solution generating to explore the parameter space. Herein, we propose hybridizing these algorithms for the task of fitting a multivariate Gaussian mixture model. This algorithm's performance is contrasted with both the traditional approach and another hybrid algorithm on simulated and real data. [ABSTRACT FROM AUTHOR]

Data-driven stochastic parameterization methods use observational data to support and improve existing prediction systems. Specifically in atmospheric sciences, uncertainty in observations is a challenge for modeling because several aspects of the physical processes are yet to be understood in some contexts. A key goal in constructing atmospheric models is to express unresolved processes using the resolved variables of a prediction system. Estimating parameterisations for highly nonlinear systems with non stationary data requires application-specific tools. Previous work on methods for analyzing nonstationary data presents a exible model-based nonparametric clustering methodology that can be exploited for parameterization development. This paper adapts the existing framework for stochastic parameterization by combining the continuous-time formulation of stochastic differential equations (SDE) with the clustering method. We use a closed-form likelihood function approach based on a suitable Hermite expansion to approximate the parameter values of the SDE with arbitrary nonlinear drift and nonlinear diffusion. The novel parameterization framework provides a smooth classification function that allows us to recover the underlying temporal parameter modulation of a nonstationary one-dimensional SDE. The numerical examples show that the clustering approach recovers a hidden functional relationship between the parameters of the SDE model and an additional auxiliary process. The study builds upon this functional relationship to develop closed-form, nonstationary, data-driven stochastic models for multiscale dynamical systems in real-world applications. [ABSTRACT FROM AUTHOR]

We introduce a model-based approach for clustering multivariate functional data observations. We utilize theoretical results regarding a surrogate density on the truncated Karhunen–Loeve expansions along with a direct sum specification of the functional space to define a matrix normal distribution on functional principal components. This formulation allows for individual parsimonious modelling of the function space and coefficient space of the univariate components of the multivariate functional observations in the form a subspace projection and latent factor analyzers, respectively. The approach facilitates interpretation at both the full multivariate level and the component level, which is of specific interest when the component functions have clear meaning. We derive an AECM algorithm for fitting the model, and discuss appropriate initialization strategies, convergence and model selection criteria. We demonstrate the model’s applicability through simulation and two data analyses on observations that have many functional components. [ABSTRACT FROM AUTHOR]