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AbstractMixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are increasingly common in various fields. Despite their widespread use and successful applications, these models suffer from over-parameterization, making them not suitable for even moderately sized matrix-variate data. To address this issue, we introduce a sparse model-based clustering approach for three-way data. Our approach assumes that the matrix mixture parameters are sparse and have different degrees of sparsity across clusters, enabling the induction of parsimony in a flexible manner. Estimation relies on the maximization of a penalized likelihood, with specifically tailored group and graphical lasso penalties. These penalties facilitate the selection of the most informative features for clustering three-way data where variables are recorded over multiple occasions, as well as allowing the identification of cluster-specific association structures. We conduct extensive testing of the proposed methodology on synthetic data and validate its effectiveness through an application to time-dependent crime patterns across multiple U.S. cities. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

This paper presents a novel methodology for analyzing temporal directional data with scatter and heavy tails. A hidden Markov model with contaminated von Mises-Fisher emission distribution is developed. The model is implemented using forward and backward selection approach that provides additional flexibility for contaminated as well as non-contaminated data. The utility of the method for finding homogeneous time blocks (regimes) is demonstrated on several experimental settings and two real-life text data sets containing presidential addresses and corporate financial statements respectively. [ABSTRACT FROM AUTHOR]

Most studies have found that the Covid‐19 pandemic did not negatively impact the euro area banking industry's performance at an aggregate level. This study explores whether this finding still holds using the return on assets of 16 banking groups operating in the euro area and considering bank‐specific factors, idiosyncrasies related to different exposures of their portfolios to the business cycle and weaknesses stemming from underlying structural vulnerabilities. The banking groups are classified into clusters using unsupervised learning techniques. This research contributes to the empirical literature on the determinants of banks' performance by highlighting the importance of banks' heterogeneity, notably controlling for differential performance due to asset quality, solvency and business model. In addition, this paper shows that the magnitude of return on assets' exposure to the business cycle varies across banks and that inflation in the euro area matters only for a subset of them. Importantly, the study sheds some light on the possible reasons for the mixed results in the literature regarding the role of non‐interest income, the T1 capital ratio and inflation. Finally, no significant effects of the Covid‐19 variables on banks' return on assets are found during the first seven quarters of the pandemic. [ABSTRACT FROM AUTHOR]

AbstractThe traditional estimation of mixture regression models is based on the assumption of normal error components, making it susceptible to outliers or heavy-tailed errors. A new robust mixture regression model based on the symmetric α-stable (S α S) distribution, by extending the mixture of S α S distributions to the regression setting, is proposed. The S α S distribution is a heavy-tailed extension of the normal distribution, with the tails’ weight controlled by an additional parameter, α∈(0,2]. Generally, the variance of a S α S distribution diverges to infinity when α<2, and this allows the model to be more robust than competing heavy-tailed distributions such as the t-distribution when the degrees of freedom are larger than 2, which is advantageous because it allows robustness against the gross outliers in the data. The maximum likelihood estimates of the model parameters (except for α) are obtained using an expectation-maximization (EM) approach, and α is estimated via a stochastic EM based on a rejection sampling method. To demonstrate and contrast the proposal with other mixture regression models, real and simulated data are employed. [ABSTRACT FROM AUTHOR]

AbstractOne of the main objectives of cluster analysis is to determine the most effective clustering algorithm. With the wide variety of algorithms available, assessing which one performs better is important. The performance of different clustering methods is typically measured using the Adjusted Rand Index (ARI), which relies on knowledge of the original class labels. However, this study introduces flexible modified alternatives of density-based silhouette methods for evaluating cluster performance. These proposed Density-based silhouettes can be applied to any soft clustering algorithms and do not require the original class labels. Instead, they rely on posterior probabilities. In this study, eight different soft clustering algorithms were evaluated using real and simulated data sets. The goal is to compare their effectiveness and performance using existing and proposed measures based on silhouette and the ARI. [ABSTRACT FROM AUTHOR]

Spectral clustering views the similarity matrix as a weighted graph, and partitions the data by minimizing a graph-cut loss. Since it minimizes the across-cluster similarity, there is no need to model the distribution within each cluster. As a result, one reduces the chance of model misspecification, which is often a risk in mixture model-based clustering. Nevertheless, compared to the latter, spectral clustering has no direct ways of quantifying the clustering uncertainty (such as the assignment probability), or allowing easy model extensions for complicated data applications. To fill this gap, we propose the Bayesian forest model as a generative graphical model for spectral clustering. This is motivated by our discovery that the posterior connecting matrix in a forest model has almost the same leading eigenvectors, as the ones used by normalized spectral clustering. To induce a distribution for the forest, we develop a "forest process" as a graph extension to the urn process, while we carefully characterize the differences in the partition probability. We derive a simple Markov chain Monte Carlo algorithm for posterior estimation, and demonstrate superior performance compared to existing algorithms. We illustrate several model-based extensions useful for data applications, including high-dimensional and multi-view clustering for images. for this article are available online. [ABSTRACT FROM AUTHOR]

Summary Clustering of longitudinal data is becoming increasingly popular in many fields such as social sciences, business, environmental science, medicine and healthcare. However, it is often challenging due to the complex nature of the data, such as dependencies between observations collected over time, missingness, sparsity and non‐linearity, making it difficult to identify meaningful patterns and relationships among the data. Despite the increasingly common application of cluster analysis for longitudinal data, many existing methods are still less known to researchers, and limited guidance is provided in choosing between methods and software packages. In this paper, we review several commonly used methods for clustering longitudinal data. These methods are broadly classified into three categories, namely, model‐based approaches, algorithm‐based approaches and functional clustering approaches. We perform a comparison among these methods and their corresponding R software packages using real‐life datasets and simulated datasets under various conditions. Findings from the analyses and recommendations for using these approaches in practice are discussed. [ABSTRACT FROM AUTHOR]

Researchers classify political parties into families by their shared cleavage origins. However, as parties have drifted from the original ideological commitments, it is unclear to what extent party families today can function as effective heuristics for shared positions. We propose an alternative way of classifying parties based solely on their ideological positions as one solution to this challenge. We use model‐based clustering to recast common subjective decisions involved in the process of creating party groups as problems of model selection, thus, providing non‐subjective criteria to define ideological clusters. By comparing canonical families to our ideological clusters, we show that while party families on the right are often too similar to justify categorizing them into different clusters, left‐wing families are weakly internally cohesive. Moreover, we identify two clusters predominantly composed of parties in Eastern Europe, questioning the degree to which categories originally designed to describe Western Europe can generalize to other regions. [ABSTRACT FROM AUTHOR]

We derive a multivariate latent Markov model with number of latent states that can possibly change at each time point. We model both the manifest and latent distributions conditionally on explanatory variables. Bayesian inference is based on a transdimensional Markov Chain Monte Carlo approach, where Reversible Jump is separately performed for each time occasion. In a simulation study, we show how our approach can recover the true underlying sequence of latent states with high probability, and that it has lower bias than competitors. We conclude with an analysis of the well-being of 100 nations, as expressed by the dimensions of the Human Development Index, for six-time points spanning a period of 22 years. R code with an implementation is available as supplementary material, together with files for reproducing the data analysis. [ABSTRACT FROM AUTHOR]

Model-based unsupervised learning, as any learning task, stalls as soon as missing data occurs. This is even more true when the missing data are informative, or said missing not at random (MNAR). In this paper, we propose model-based clustering algorithms designed to handle very general types of missing data, including MNAR data. To do so, we introduce a mixture model for different types of data (continuous, count, categorical and mixed) to jointly model the data distribution and the MNAR mechanism, remaining vigilant to the relative degrees of freedom of each. Several MNAR models are discussed, for which the cause of the missingness can depend on both the values of the missing variable themselves and on the class membership. However, we focus on a specific MNAR model, called MNARz, for which the missingness only depends on the class membership. We first underline its ease of estimation, by showing that the statistical inference can be carried out on the data matrix concatenated with the missing mask considering finally a standard MAR mechanism. Consequently, we propose to perform clustering using the Expectation Maximization algorithm, specially developed for this simplified reinterpretation. Finally, we assess the numerical performances of the proposed methods on synthetic data and on the real medical registry TraumaBase as well. [ABSTRACT FROM AUTHOR]

Networks consist of interconnected units, known as nodes, and allow to formally describe interactions within a system. Specifically, bipartite networks depict relationships between two distinct sets of nodes, designated as sending and receiving nodes. An integral aspect of bipartite network analysis often involves identifying clusters of nodes with similar behaviors. The computational complexity of models for large bipartite networks poses a challenge. To mitigate this challenge, we employ a Mixture of Latent Trait Analyzers (MLTA) for node clustering. Our approach extends the MLTA to include covariates and introduces a double EM algorithm for estimation. Applying our method to COVID-19 data, with sending nodes representing patients and receiving nodes representing preventive measures, enables dimensionality reduction and the identification of meaningful groups. We present simulation results demonstrating the accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging data play an important role in the advancement of science. Imaging data that measure brain function are usually multivariate high-density longitudinal data and are heterogeneous across both imaging sources and subjects, which lead to various statistical and computational challenges. In this article, we propose a group-based method to cluster a collection of multivariate high-density longitudinal data via a Bayesian mixture of smoothing splines. Our method assumes each multivariate high-density longitudinal trajectory is a mixture of multiple components with different mixing weights. Time-independent covariates are assumed to be associated with the mixture components and are incorporated via logistic weights of a mixture-of-experts model. We formulate this approach under a fully Bayesian framework using Gibbs sampling where the number of components is selected based on a deviance information criterion. The proposed method is compared to existing methods via simulation studies and is applied to a study on functional near-infrared spectroscopy, which aims to understand infant emotional reactivity and recovery from stress. The results reveal distinct patterns of brain activity, as well as associations between these patterns and selected covariates. [ABSTRACT FROM AUTHOR]

Clustering is one of the most widely used unsupervised learning techniques. However, it is well‐known that outliers can have a significantly adverse impact on commonly applied clustering methods. On the other hand, clustered outliers can be particularly detrimental to (even robust) statistical procedures. Therefore, it makes sense to combine concepts from Robust Statistics and Cluster Analysis to deal with both clusters and outliers simultaneously through robust clustering approaches. Among the existing robust clustering techniques, we focus on those that rely on (impartial) trimming. Trimming offers the user an easy interpretation, as standard well‐known clustering methods are applied after a fraction of the potentially most outlying observations is removed. This trimming approach, when combined with appropriate constraints on the clusters' dispersion parameters, has shown a good performance and can be implemented efficiently thorough available algorithms. This article is categorized under:Statistical Learning and Exploratory Methods of the Data Sciences > Clustering and ClassificationStatistical and Graphical Methods of Data Analysis > Robust Methods [ABSTRACT FROM AUTHOR]

Estimates of population abundance are required to study the impacts of human activities on populations and assess their conservation status. Despite considerable effort to improve data collection, uncertainty around estimates of cetacean densities can remain large. A fundamental concept underlying distance sampling is the detection function. Here we focus on reducing the uncertainty in the estimation of detection function parameters in analyses combining data sets from multiple surveys, with known effects on the precision of density estimates. We developed detection functions using infinite mixture models that can be applied on data collating multiple species and/or surveys. These models enable automatic clustering by fusing the species and surveys with similar detection functions. We present a simulation analysis of a multisurvey data set in a Bayesian framework where we demonstrated that distance sampling models including fusion effects showed lower uncertainty than classical distance sampling models. We illustrated the benefits of this new model using data of line transect surveys from the Bay of Biscay and Iberian Coast. Future estimates of abundance using conventional distance sampling models on large multispecies surveys or on data sets combining multiple surveys could benefit from this new model to provide more precise density estimates. [ABSTRACT FROM AUTHOR]

This thesis aims to apply model-based clustering in grouping regencies/cities in North Sumatra based on Community Welfare Indicators to determine the number of groups (clusters) formed based on community welfare indicators in regencies/cities in North Sumatra and to understand the level of community welfare from this grouping in planning and managing community welfare in regencies/cities in North Sumatra, with the hope of achieving equal welfare in every region. The research method used is Model-Based Clustering, which uses 5 research data variables: HDI, Poor Population, Unemployment Rate, GDP, and Health. In this millennial era, the assessment of community welfare requires more attention. Rapid social, technological, and environmental changes have created new dynamics that can affect community welfare. The evaluation of community welfare is not only limited to economic parameters but also considers health, unemployment, and other factors. By using Model-Based Clustering, it is possible to determine the optimal number of groups (clusters) from various and possibly correlated variables, and the results are easier to understand, making the analysis and understanding of the results easier. Readers can learn about the level of community welfare, and the community and government can evaluate their welfare for future improvements. The research results show that among the groups of regencies/cities formed, five cities consistently show lower Gross Regional Domestic Product (GDP) and Human Development Index (HDI) than other cities. Therefore, a sustainable approach is needed to improve these cities' economic conditions and social welfare.

The Fellegi-Sunter model is a latent class model widely used in probabilistic linkage to identify records that belong to the same entity. Record linkage practitioners typically employ all available matching fields in the model with the premise that more fields convey greater information about the true match status and hence result in improved match performance. In the context of model-based clustering, it is well known that such a premise is incorrect and the inclusion of noisy variables could compromise the clustering. Variable selection procedures have therefore been developed to remove noisy variables. Although these procedures have the potential to improve record matching, they cannot be applied directly due to the ubiquity of the missing data in record linkage applications. In this paper, we modify the stepwise variable selection procedure proposed by Fop, Smart, and Murphy and extend it to account for missing data common in record linkage. Through simulation studies, our proposed method is shown to select the correct set of matching fields across various settings, leading to better-performing algorithms. The improved match performance is also seen in a real-world application. We therefore recommend the use of our proposed selection procedure to identify informative matching fields for probabilistic record linkage algorithms. [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. [ABSTRACT FROM AUTHOR]

Tensor eigenvectors naturally generalize matrix eigenvectors to multi-way arrays: eigenvectors of symmetric tensors of order k and dimension p are stationary points of polynomials of degree k in p variables on the unit sphere. Dominant eigenvectors of symmetric tensors maximize polynomials in several variables on the unit sphere, while base eigenvectors are roots of polynomials in several variables. In this paper, we focus on skewness-based projection pursuit and on third-order tensor eigenvectors, which provide the simplest, yet relevant connections between tensor eigenvectors and projection pursuit. Skewness-based projection pursuit finds interesting data projections using the dominant eigenvector of the sample third standardized cumulant to maximize skewness. Skewness-based projection pursuit also uses base eigenvectors of the sample third cumulant to remove skewness and facilitate the search for interesting data features other than skewness. Our contribution to the literature on tensor eigenvectors and on projection pursuit is twofold. Firstly, we show how skewness-based projection pursuit might be helpful in sequential cluster detection. Secondly, we show some asymptotic results regarding both dominant and base tensor eigenvectors of sample third cumulants. The practical relevance of the theoretical results is assessed with six well-known data sets. [ABSTRACT FROM AUTHOR]

Gaussian mixture models represent a conceptually and mathematically elegant class of models for casting the density of a heterogeneous population where the observed data is collected from a population composed of a finite set of G homogeneous subpopulations with a Gaussian distribution. A limitation of these models is that they suffer from the curse of dimensionality, and the number of parameters becomes easily extremely large in the presence of high-dimensional data. In this paper, we propose a class of parsimonious Gaussian mixture models with constrained extended ultrametric covariance structures that are capable of exploring hierarchical relations among variables. The proposal shows to require a reduced number of parameters to be fit and includes constrained covariance structures across and within components that further reduce the number of parameters of the model. [ABSTRACT FROM AUTHOR]

AbstractThis paper presents a Bayesian nonparametric model for clustering datasets with continuous, ordinal, and nominal variables. The ordinal and nominal variables are treated using the latent variables framework based on the multivariate probit and the multinomial probit models. Combining the continuous variables with the latent continuous variables allows us to jointly model a set of mixed-type variables via the Dirichlet process Gaussian mixture model. The use of hierarchical shrinkage prior on the component means leads to improved clustering performances and provides an intuitive way to identify relevant clustering variables. The numerical results on simulated and real data illustrate the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

The chemical characterization of materials recovered from archaeological sites has been used to relate artifacts to their respective sources of raw material. For this, conventional methods of classical statistics are commonly used, such as bivariate graphs, cluster analysis and linear data transformations. Those who have applied these methods claim to have a high degree of confidence in the correct assignment of materials to their respective sources. However, if empirical data deviate from theoretical assumptions, classical statistical techniques can produce incorrect assignments. In this paper, we propose a semi-supervised learning procedure using clustering and classification based on models of mixtures of multivariate asymmetric exponential power distributions. The objective is to trace the origin and provenance of obsidian archaeological materials from the archaeological zone of Izapa, Chiapas, significantly optimizing the result of the correct allocation of unlabeled data by employing only limited supervision in the form of labeled instances. The effectiveness of the proposed method was evaluated by a controlled experiment using data from a set of geological samples from obsidian deposits. Subsequently, the method was applied to analyze a set of obsidian artifacts collected in excavations within Izapa dated for the Classic period. In both cases, well-defined classifications were obtained that, in the case of Izapa, allowed to determine the consumption of materials from Guatemalan sources, as well as some relationship with sources from western and central Mexico. [ABSTRACT FROM AUTHOR]

In the literature on modeling heterogeneous data via mixture models, it is generally assumed that the samples are drawn from the underlying population using the simple random sampling (SRS) technique. This study exploits the bivariate ranked set sampling (BVRSS) technique to learn finite mixture models. We generalize the expectation-maximization (EM) algorithm under univariate RSS to the bivariate case. Computationally, through a simulation study under a noisy setting, we compare the performance of the proposed rank-based estimators with that of the SRS-based competitors in estimating unknown parameters and cluster assignments. The proposed methodology is applied to a breast cancer data set to diagnose malignant or benign tumors in patients. The results showed that the extra rank information in BVRSS samples leads to a better inference about the unknown features of mixture models. [ABSTRACT FROM AUTHOR]

A new model-based procedure is developed for sparse clustering of functional data that aims to classify a sample of curves into homogeneous groups while jointly detecting the most informative portions of the domain. The proposed method is referred to as sparse and smooth functional clustering (SaS-Funclust) and relies on a general functional Gaussian mixture model whose parameters are estimated by maximizing a log-likelihood function penalized with a functional adaptive pairwise fusion penalty and a roughness penalty. The former allows identifying the noninformative portion of the domain by shrinking the means of separated clusters to some common values, whereas the latter improves the interpretability by imposing some degree of smoothing to the estimated cluster means. The model is estimated via an expectation-conditional maximization algorithm paired with a cross-validation procedure. Through a Monte Carlo simulation study, the SaS-Funclust method is shown to outperform other methods that already appeared in the literature, both in terms of clustering performance and interpretability. Finally, three real-data examples are presented to demonstrate the favourable performance of the proposed method. The SaS-Funclust method is implemented in the R package sasfunclust, available on CRAN. [ABSTRACT FROM AUTHOR]

Cluster analysis is a method that identifies similar groups of data without any prior knowledge of the relevant groups. One of the most widely used clustering methods is model-based clustering, in which data clustering is performed by fitting a probabilistic model to the data. Mixture of Gaussian distributions is a commonly used model in model-based clustering. Unfortunately, the number of covariance matrices parameters rapidly increases by increasing the number of variables or components in these models. So far, various classes of the parsimonious Gaussian mixture models, by applying various constraints on the covariance matrices, have been introduced to solve this problem. Unfortunately, the number of models in each of these classes is so small such that in practice it does not allow the study and selection of models with any number of parameters, which can vary between the minimum number (one parameter) and the maximum number (no constraints model) of parameters. In this paper, to deal with this problem a family of the parsimonious Gaussian mixture models is introduced. This is done by identifying and determining the appropriate partitions of the variances and correlation coefficients between variables among clusters. We call these models "the parsimonious Gaussian mixture models with partitioned parameters". The generalized Expectation-Conditional Maximization algorithm, by employing the Fisher scoring method within the algorithm, is used to compute the maximum likelihood estimates of parameters. Bayesian information criterion is used for comparing and selecting the best model. Also, the steepest ascent method is adapted to search the best model. Finally, performances of these models are examined on two real datasets and a brief simulation study. [ABSTRACT FROM AUTHOR]

In social sciences, studies are often based on questionnaires asking participants to express ordered responses several times over a study period. We present a model-based clustering algorithm for such longitudinal ordinal data. Assuming that an ordinal variable is the discretization of an underlying latent continuous variable, the model relies on a mixture of matrix-variate normal distributions, accounting simultaneously for within- and between-time dependence structures. The model is thus able to concurrently model the heterogeneity, the association among the responses and the temporal dependence structure. An EM algorithm is developed and presented for parameters estimation, and approaches to deal with some arising computational challenges are outlined. An evaluation of the model through synthetic data shows its estimation abilities and its advantages when compared to competitors. A real-world application concerning changes in eating behaviors during the Covid-19 pandemic period in France will be presented. [ABSTRACT FROM AUTHOR]

Abstract RNA sequencing of time-course experiments results in three-way count data where the dimensions are the genes, the time points and the biological units. Clustering RNA-seq data allows to extract groups of co-expressed genes over time. After standardisation, the normalised counts of individual genes across time points and biological units have similar properties as compositional data. We propose the following procedure to suitably cluster three-way RNA-seq data: (1) pre-process the RNA-seq data by calculating the normalised expression profiles, (2) transform the data using the additive log ratio transform to map the composition in the D-part Aitchison simplex to a $$D-1$$ D - 1 -dimensional Euclidean vector, (3) cluster the transformed RNA-seq data using matrix-variate Gaussian mixture models and (4) assess the quality of the overall cluster solution and of individual clusters based on cluster separation in the transformed space using density-based silhouette information and on compactness of the cluster in the original space using cluster maps as a suitable visualisation. The proposed procedure is illustrated on RNA-seq data from fission yeast and results are also compared to an analogous two-way approach after flattening out the biological units.

Time series clustering is a usual task in many different areas. Algorithms such as K-means and model-based clustering procedures are used relating to multivariate assumptions on the datasets, as the consideration of Euclidean distances, or a probabilistic distribution of the observed variables. However, in many cases the observed time series are of unequal length and/or there is missing data or, simply, the time periods observed for the series are not comparable between them, which does not allow the direct application of these methods. In this framework, dynamic time warping is an advisable and well-known elastic dissimilarity procedure, in particular when the analysis is accomplished in terms of the shape of the time series. In relation to a dissimilarity matrix, K-means clustering can be performed using a particular procedure based on classical multidimensional scaling in full dimension, which can result in a clustering problem in high dimensionality for large sample sizes. In this paper, we propose a procedure robust to dimensionality reduction, based on an auxiliary configuration estimated from the squared dynamic time warping dissimilarities, using an alternating least squares procedure. The performance of the model is compared to that obtained using classical multidimensional scaling, as well as to that of model-based clustering using this related auxiliary linear projection. An extensive Monte Carlo procedure is employed to analyze the performance of the proposed method in which real and simulated datasets are considered. The results obtained indicate that the proposed K-means procedure, in general, slightly improves the one based on the classical configuration, both being robust in reduced dimensionality, making it advisable for large datasets. In contrast, model-based clustering in the classical projection is greatly affected by high dimensionality, offering worse results than K-means, even in reduced dimension.

Precision medicine is an approach for disease treatment that defines treatment strategies based on the individual characteristics of the patients. Motivated by an open problem in cancer genomics, we develop a novel model that flexibly clusters patients with similar predictive characteristics and similar treatment responses; this approach identifies, via predictive inference, which one among a set of treatments is better suited for a new patient. The proposed method is fully model based, avoiding uncertainty underestimation attained when treatment assignment is performed by adopting heuristic clustering procedures, and belongs to the class of product partition models with covariates, here extended to include the cohesion induced by the normalized generalized gamma process. The method performs particularly well in scenarios characterized by considerable heterogeneity of the predictive covariates in simulation studies. A cancer genomics case study illustrates the potential benefits in terms of treatment response yielded by the proposed approach. Finally, being model based, the approach allows estimating clusters' specific response probabilities and then identifying patients more likely to benefit from personalized treatment. [ABSTRACT FROM AUTHOR]

A dataset may exhibit multiple class labels for each observation; sometimes, these class labels manifest in a hierarchical structure. A textbook analogy would be that a book can be labelled as statistics as well as the encompassing label of non-fiction. To capture this behaviour in a model-based clustering context, we describe a model formulation and estimation procedure for performing clustering with nested Gaussian clusters in orthogonal intrinsic variable subspaces. We elucidate a two-stage clustering model, whereby the observed manifest variables are assumed to be a rotation of intrinsic primary and secondary clustering subspaces with additional noise subspaces. In a hierarchical sense, secondary clusters are presumed to be subclusters of primary clusters and so share Gaussian cluster parameters in the primary cluster subspace. An estimation procedure using the expectation-maximization algorithm is provided, with model selection via Bayesian information criterion. Real-world datasets are evaluated under the proposed model. [ABSTRACT FROM AUTHOR]

Since data may be distributed on an irregular manifold, where the underlying clusters often exhibit non-convex shapes and structures, the clustering problems for such data are collectively referred to as non-convex clustering. However, existing mainstream non-convex clustering methods, including clustering based on original space and clustering based on Space Transformation, ignore the explicit description of non-convex data patterns and fail to understand and describe the underlying mechanisms that produce such structures. Therefore, a descriptive clustering model is proposed to act on non-convex clustering. Firstly, a feature-weighted kernel density model with a hybrid form is defined based on the kernel density method that does not need to assume any probability distribution model in advance and does not restrict the shape of clusters, which cannot be achieved by traditional model-based clustering methods. Secondly, the clustering objective function is derived based on the proposed model, and an optimization algorithm for solving the local density maximum of the density function is proposed based on the expectation maximization algorithm. The clusters are divided into those samples that rise to the same density maximum of the density function. Finally, a model-based non-convex clustering algorithm is defined. The algorithm does not need to manually define the number of clusters, and can assign an explicit probability density function to each cluster, which helps to characterize clusters more robustly and accurately. In addition, the algorithm not only performs adaptive bandwidth selection, but also gives the feature weight of the sample space, enabling the automatic embedded feature selection during the clustering process. [ABSTRACT FROM AUTHOR]

In archaeometry, the correct assignment of archaeological artefacts with their original geological sources continues to be an indispensable tool for determining exploitation patterns, trade routes, tool production and the movement of goods in ancient times. Statistically, Mahalanobis distance has been an integral part of the artefact provenance methodology. However, this method presents disadvantages when some of the theoretical assumptions are not fulfilled. In this way and with a focus on the veracity of the correct assignment of archaeological samples to their geological sources, we present a technique that employs a semi‐supervised classification based on finite mixture models. This procedure uses labelled and unlabelled data to assign samples to groups with the advantage that it does not depend on the sample size of the groups as required by Mahalanobis distance. This procedure was first applied in a controlled experiment where the exact origin of the samples is known in order to verify the accuracy of the method; afterwards, it was applied to artefacts recovered from the archaeological site of Xalasco, Tlaxcala (Mexico), from both surface and excavation collections and analysed with a portable X‐ray fluorescence spectrometer. The resulting groups defined that the ancient dwellers of Xalasco exploited six supply sources located in Central Mexico. [ABSTRACT FROM AUTHOR]

Multivariate panel data of mixed type are routinely collected in many different areas of application, often jointly with additional covariates which complicate the statistical analysis. Moreover, it is often of interest to identify unknown groups of subjects in a study population using such data structure, i.e., to perform clustering. In the Bayesian framework, we propose a finite mixture of multivariate generalised linear mixed effects regression models to cluster numeric, binary, ordinal and categorical panel outcomes jointly. The specification of suitable priors on the model parameters allows for convenient posterior inference based on Markov chain Monte Carlo (MCMC) sampling with data augmentation. This approach allows to classify subjects in the data and new subjects as well as to characterise the cluster-specific models. Model estimation and selection of the number of data clusters are simultaneously performed when approximating the posterior for a single model using MCMC sampling without resorting to multiple model estimations. The performance of the proposed methodology is evaluated in a simulation study. Its application is illustrated on two data sets, one from a longitudinal patient study to infer prognosis groups, and a second one from the Czech part of the EU-SILC survey where households are annually interviewed to obtain insights into changes in their financial capability. [ABSTRACT FROM AUTHOR]

A model-based biclustering method for multivariate discrete longitudinal data is proposed. We consider a finite mixture of generalized linear models to cluster units and, within each mixture component, we adopt a flexible and parsimonious parameterization of the component-specific canonical parameter to define subsets of variables (segments) sharing common dynamics over time. We develop an Expectation-Maximization-type algorithm for maximum likelihood estimation of model parameters. The performance of the proposed model is evaluated on a large scale simulation study, where we consider different choices for the sample the size, the number of measurement occasions, the number of components and segments. The proposal is applied to Italian crime data (font ISTAT) with the aim to detect areas sharing common longitudinal trajectories for specific subsets of crime types. The identification of such biclusters may potentially be helpful for policymakers to make decisions on safety. [ABSTRACT FROM AUTHOR]

Abstract 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.

Clustering techniques are used to group observations and discover interesting patterns within data. Model-based clustering is one such method that is often an attractive choice due to the specification of a generative model for the given data and the ability to calculate model-selection criteria, which is in turn used to select the number of clusters. However, when only distances between observations are available, model-based clustering can no longer be used, and heuristic algorithms without the aforementioned advantages are usually used instead. As a solution, Oh and Raftery (2007) suggest a Bayesian model-based clustering method (named BMCD) that only requires a dissimilarity matrix as input, while also accounting for the measurement error that may be present within the observed data. In this paper, we extend the BMCD framework by proposing several additional models, alternative model selection criteria, and strategies for reducing computing time of the algorithm. These extensions ensure that the algorithm is effective even in high-dimensional spaces and provides a wide range of choices to the practitioner that can be used with a variety of data. Additionally, a publicly available software implementation of the algorithm is provided as a package in the R programming language.

Summary: Background: Predicting adverse disease outcomes and high‐volume users of healthcare amongst patients with inflammatory bowel disease (IBD) is difficult. Aims: The aim of this study is to use latent class analysis to create novel clusters of patients and to assess whether these predict outcomes during 6.5 years of longitudinal follow‐up. Methods: Baseline demographic features, disease activity indices, anxiety, depression, and somatoform symptom‐reporting scores were recorded for 692 adults. Faecal calprotectin (FC) was analysed at baseline in 348 (50.3%) patients (<250 mcg/g defined biochemical remission). Using baseline gastrointestinal and psychological symptoms, latent class analysis identified specific patient clusters. Rates of glucocorticosteroid prescription or flare, escalation, hospitalisation, or intestinal resection were compared between clusters using multivariate Cox regression. Results: A three‐cluster model was the optimum solution; 132 (19.1%) patients had below‐average gastrointestinal and psychological symptoms (cluster 1), 352 (50.9%) had average levels of gastrointestinal and psychological symptoms (cluster 2), and 208 (30.1%) had the highest levels of both gastrointestinal and psychological symptoms (cluster 3). Compared with cluster 1, cluster 3 had significantly increased risk of flare or glucocorticosteroid prescription (hazard ratio (HR): 2.13; 95% confidence interval (CI): 1.46–3.10), escalation (HR: 1.92; 95% CI: 1.34–2.76), a composite of escalation, hospitalisation, or intestinal resection (HR: 2.05; 95% CI: 1.45–2.88), or any of the endpoints of interest (HR: 2.06; 95% CI: 1.45–2.93). Healthcare utilisation was highest in cluster 3. Conclusions: Novel model‐based clusters identify patients with IBD at higher risk of adverse disease outcomes who are high‐volume users of healthcare. [ABSTRACT FROM AUTHOR]

Identification of clusters of co‐expressed genes in transcriptomic data is a difficult task. Most algorithms used for this purpose can be classified into two broad categories: distance‐based or model‐based approaches. Distance‐based approaches typically utilize a distance function between pairs of data objects and group similar objects together into clusters. Model‐based approaches are based on using the mixture‐modeling framework. Compared to distance‐based approaches, model‐based approaches offer better interpretability because each cluster can be explicitly characterized in terms of the proposed model. However, these models present a particular difficulty in identifying a correct multivariate distribution that a mixture can be based upon. In this manuscript, we review some of the approaches used to select a distribution for the needed mixture model first. Then, we propose avoiding this problem altogether by using a nonparametric MSL (maximum smoothed likelihood) algorithm. This algorithm was proposed earlier in statistical literature but has not been, to the best of our knowledge, applied to transcriptomics data. The salient feature of this approach is that it avoids explicit specification of distributions of individual biological samples altogether, thus making the task of a practitioner easier. We performed both a simulation study and an application of the proposed algorithm to two different real datasets. When used on a real dataset, the algorithm produces a large number of biologically meaningful clusters and performs at least as well as several other mixture‐based algorithms commonly used for RNA‐seq data clustering. Our results also show that this algorithm is capable of uncovering clustering solutions that may go unnoticed by several other model‐based clustering algorithms. Our code is publicly available on Github at https://github.com/Matematikoi/non_parametric_clustering [ABSTRACT FROM AUTHOR]

Real data is taking on more and more complex structures, raising the necessity for more flexible and parsimonious statistical methodologies. Tensor-variate (or multi-way) structures are a typical example of such kind of data. Unfortunately, real data often present atypical observations that make the traditional normality assumption inadequate. Thus, in this paper, we first introduce two new tensor-variate distributions, both heavy-tailed generalizations of the tensor-variate normal distribution. Then, we use these distributions for model-based clustering via finite mixture models. To introduce parsimony in the models, we use the eigen-decomposition of the components’ scale matrices, obtaining two families of parsimonious tensor-variate mixture models. As a by-product, we also introduce the parsimonious version of tensor-variate normal mixtures. As for parameter estimation, we illustrate variants of the well-known EM algorithm. Since the number of parsimonious models depends on the order of the tensors, we implement strategies intending to shorten the initialization and fitting processes. These procedures are investigated via simulated analyses. Finally, we fitted our parsimonious models to two real datasets having a 4-way and a 5-way structure, respectively. [ABSTRACT FROM AUTHOR]