arXiv subjects

Sanjeena Subedi

Publications and source records attributed to Sanjeena Subedi.

At least 19 recordsLinked to original sources

arXiv2026

Mixtures of spatial factor analyzers for tensor-variate data

A mixture of spatial factor analyzers (MSFA) is introduced to address the challenges of clustering high-dimensional spatial data. By leveraging the underlying coordinate system, the proposed framework incorporates a flexible, spline-based spatial decay covariance structure that prevents parameter inflation as dimensionality increases. To model non-spatial dependence, matrix variate factor analyzers are employed for further dimensionality reduction. Parameter estimation is conducted via a variant of the expectation-maximization algorithm combined with a generalized least squares estimator. The proposed models are explored in the context of tensor-variate data analysis, where simulation studies and applications to Raman spectroscopy and hyperspectral texture databases demonstrate their capacity to accurately infer and differentiate distinct spatial patterns.

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arXiv2026

Spatial Covariance Constraints for Gaussian Mixture Models

Although extensive research exists in spatial modeling, few studies have addressed finite mixture model-based clustering methods for spatial data. Finite mixture models, especially Gaussian mixture models, particularly suffer from high dimensionality due to the number of free covariance parameters. This study introduces a spatial covariance constraint for Gaussian mixture models that requires only four free parameters for each component, independent of dimensionality. Using a coordinate system, the spatially constrained Gaussian mixture model enables clustering of multi-way spatial data and inference of spatial patterns. The parameter estimation is conducted by combining the expectation-maximization (EM) algorithm with the generalized least squares (GLS) estimator. Simulation studies and applications to Raman spectroscopy data are provided to demonstrate the proposed model.

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arXiv2025

Model-based bi-clustering using multivariate Poisson-lognormal with general block-diagonal covariance matrix and its applications

While several Gaussian mixture models-based biclustering approaches currently exist in the literature for continuous data, approaches to handle discrete data have not been well researched. A multivariate Poisson-lognormal (MPLN) model-based bi-clustering approach that utilizes a block-diagonal covariance structure is introduced to allow for a more flexible structure of the covariance matrix. Two variations of the algorithm are developed where the number of column clusters: 1) are assumed equal across groups or 2) can vary across groups. Variational Gaussian approximation is utilized for parameter estimation, and information criteria are used for model selection. The proposed models are investigated in the context of clustering multivariate count data. Using simulated data the models display strong accuracy and computational efficiency and is applied to breast cancer RNA-sequence data from The Cancer Genome Atlas.

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arXiv2024

Extending Cluster-Weighted Factor Analyzers for multivariate prediction and high-dimensional interpretability

Cluster-weighted factor analyzers (CWFA) are a versatile class of mixture models designed to estimate the joint distribution of a random vector that includes a response variable along with a set of explanatory variables. They are particularly valuable in situations involving high dimensionality. This paper enhances CWFA models in two notable ways. First, it enables the prediction of multiple response variables while considering their potential interactions. Second, it identifies factors associated with disjoint groups of explanatory variables, thereby improving interpretability. This development leads to the introduction of the multivariate cluster-weighted disjoint factor analyzers (MCWDFA) model. An alternating expectation-conditional maximization algorithm is employed for parameter estimation. The effectiveness of the proposed model is assessed through an extensive simulation study that examines various scenarios. The proposal is applied to crime data from the United States, sourced from the UCI Machine Learning Repository, with the aim of capturing potential latent heterogeneity within communities and identifying groups of socio-economic features that are similarly associated with factors predicting crime rates. Results provide valuable insights into the underlying structures influencing crime rates which may potentially be helpful for effective cluster-specific policymaking and social interventions.

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arXiv2023

Finite Mixtures of Multivariate Poisson-Log Normal Factor Analyzers for Clustering Count Data

A mixture of multivariate Poisson-log normal factor analyzers is introduced by imposing constraints on the covariance matrix, which resulted in flexible models for clustering purposes. In particular, a class of eight parsimonious mixture models based on the mixtures of factor analyzers model are introduced. Variational Gaussian approximation is used for parameter estimation, and information criteria are used for model selection. The proposed models are explored in the context of clustering discrete data arising from RNA sequencing studies. Using real and simulated data, the models are shown to give favourable clustering performance. The GitHub R package for this work is available at https://github.com/anjalisilva/mixMPLNFA and is released under the open-source MIT license.

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arXiv2023

Tackling the infinite likelihood problem when fitting mixtures of shifted asymmetric Laplace distributions

Mixtures of shifted asymmetric Laplace distributions were introduced as a tool for model-based clustering that allowed for the direct parameterization of skewness in addition to location and scale. Following common practices, an expectation-maximization algorithm was developed to fit these mixtures. However, adaptations to account for the `infinite likelihood problem' led to fits that gave good classification performance at the expense of parameter recovery. In this paper, we propose a more valuable solution to this problem by developing a novel Bayesian parameter estimation scheme for mixtures of shifted asymmetric Laplace distributions. Through simulation studies, we show that the proposed parameter estimation scheme gives better parameter estimates compared to the expectation-maximization based scheme. In addition, we also show that the classification performance is as good, and in some cases better, than the expectation-maximization based scheme. The performance of both schemes are also assessed using well-known real data sets.

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arXiv2023

Estimation of Gaussian Bi-Clusters with General Block-Diagonal Covariance Matrix and Applications

Bi-clustering is a technique that allows for the simultaneous clustering of observations and features in a dataset. This technique is often used in bioinformatics, text mining, and time series analysis. An important advantage of biclustering algorithm is the ability to uncover multiple ``views'' (i.e., through rows and column groupings) in the data. Several Gaussian mixture model based biclustering approach currently exist in the literature. However, they impose severe restrictions on the structure of the covariance matrix. Here, we propose a Gaussian mixture model-based bi-clustering approach that provides a more flexible block-diagonal covariance structure. We show that the clustering accuracy of the proposed model is comparable to other known techniques but our approach provides a more flexible covariance structure and has substantially lower computational time. We demonstrate the application of the proposed model in bioinformatics and topic modelling.

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arXiv2022

Finite mixtures of matrix-variate Poisson-log normal distributions for three-way count data

Three-way data structures, characterized by three entities, the units, the variables and the occasions, are frequent in biological studies. In RNA sequencing, three-way data structures are obtained when high-throughput transcriptome sequencing data are collected for $n$ genes across $p$ conditions at $r$ occasions. Matrix variate distributions offer a natural way to model three-way data and mixtures of matrix variate distributions can be used to cluster three-way data. Clustering of gene expression data is carried out as means of discovering gene co-expression networks. In this work, a mixture of matrix variate Poisson-log normal distributions is proposed for clustering read counts from RNA sequencing. By considering the matrix variate structure, full information on the conditions and occasions of the RNA sequencing dataset is simultaneously considered, and the number of covariance parameters to be estimated is reduced. We propose three different frameworks for parameter estimation: a Markov chain Monte Carlo based approach, a variational Gaussian approximation based approach, and a hybrid approach. Various information criteria are used for model selection. The models are applied to both real and simulated data, and we demonstrate that the proposed approaches can recover the underlying cluster structure in both cases. In simulation studies where the true model parameters are known, our proposed approach shows good parameter recovery.

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arXiv2022

Clustering microbiome data using mixtures of logistic normal multinomial models

Discrete data such as counts of microbiome taxa resulting from next-generation sequencing are routinely encountered in bioinformatics. Taxa count data in microbiome studies are typically high-dimensional, over-dispersed, and can only reveal relative abundance therefore being treated as compositional. Analyzing compositional data presents many challenges because they are restricted on a simplex. In a logistic normal multinomial model, the relative abundance is mapped from a simplex to a latent variable that exists on the real Euclidean space using the additive log-ratio transformation. While a logistic normal multinomial approach brings in flexibility for modeling the data, it comes with a heavy computational cost as the parameter estimation typically relies on Bayesian techniques. In this paper, we develop a novel mixture of logistic normal multinomial models for clustering microbiome data. Additionally, we utilize an efficient framework for parameter estimation using variational Gaussian approximations (VGA). Adopting a variational Gaussian approximation for the posterior of the latent variable reduces the computational overhead substantially. The proposed method is illustrated on simulated and real datasets.

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arXiv2021

Logistic Normal Multinomial Factor Analyzers for Clustering Microbiome Data

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 (2020) 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 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.

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arXiv2020

A Family of Mixture Models for Biclustering

Biclustering is used for simultaneous clustering of the observations and variables when there is no group structure known \textit{a priori}. It is being increasingly used in bioinformatics, text analytics, etc. Previously, biclustering has been introduced in a model-based clustering framework by utilizing a structure similar to a mixture of factor analyzers. In such models, observed variables $\mathbf{X}$ are modelled using a latent variable $\mathbf{U}$ that is assumed to be from $N(\mathbf{0}, \mathbf{I})$. Clustering of variables is introduced by imposing constraints on the entries of the factor loading matrix to be 0 and 1 that results in a block diagonal covariance matrices. However, this approach is overly restrictive as off-diagonal elements in the blocks of the covariance matrices can only be 1 which can lead to unsatisfactory model fit on complex data. Here, the latent variable $\mathbf{U}$ is assumed to be from a $N(\mathbf{0}, \mathbf{T})$ where $\mathbf{T}$ is a diagonal matrix. This ensures that the off-diagonal terms in the block matrices within the covariance matrices are non-zero and not restricted to be 1. This leads to a superior model fit on complex data. A family of models are developed by imposing constraints on the components of the covariance matrix. For parameter estimation, an alternating expectation conditional maximization (AECM) algorithm is used. Finally, the proposed method is illustrated using simulated and real datasets.

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arXiv2020

Infinite mixtures of multivariate normal-inverse Gaussian distributions for clustering of skewed data

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework, either the number of components 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 number 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 $\infty$ (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 provide real data applications with benchmark datasets as well as a small simulation experiment to compare with other existing models. The proposed method provides competitive clustering results to other clustering approaches for both simulation and real data and parameter recovery are illustrated using simulation studies.

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arXiv2020

A Bayesian approach for clustering skewed data using mixtures of multivariate normal-inverse Gaussian distributions

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented, based on the multivariate normal inverse Gaussian (MNIG) distribution. For parameter estimation of the mixture, a Bayesian approach via Gibbs sampler is used; for this, a novel approach to simulate univariate generalized inverse Gaussian random variables and matrix generalized inverse Gaussian random matrices is provided. The proposed algorithm will be applied to both simulated and real data. Through simulation studies and real data analysis, we show parameter recovery and that our approach provides competitive clustering results compared to other clustering approaches.

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arXiv2020

A parsimonious family of multivariate Poisson-lognormal distributions for clustering multivariate count data

Multivariate count data are commonly encountered through high-throughput sequencing technologies in bioinformatics, text mining, or in sports analytics. Although the Poisson distribution seems a natural fit to these count data, its multivariate extension is computationally expensive.In most cases mutual independence among the variables is assumed, however this fails to take into account the correlation among the variables usually observed in the data. Recently, mixtures of multivariate Poisson-lognormal (MPLN) models have been used to analyze such multivariate count measurements with a dependence structure. In the MPLN model, each count is modeled using an independent Poisson distribution conditional on a latent multivariate Gaussian variable. Due to this hierarchical structure, the MPLN model can account for over-dispersion as opposed to the traditional Poisson distribution and allows for correlation between the variables. Rather than relying on a Monte Carlo-based estimation framework which is computationally inefficient, a fast variational-EM based framework is used here for parameter estimation. Further, a parsimonious family of mixtures of Poisson-lognormal distributions are proposed by decomposing the covariance matrix and imposing constraints on these decompositions. Utility of such models is shown using simulated and benchmark datasets.

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arXiv2019

A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting

Mixture model-based clustering has become an increasingly popular data analysis technique since its introduction over fifty years ago, and is now commonly utilized within a family setting. Families of mixture models arise when the component parameters, usually the component covariance (or scale) matrices, are decomposed and a number of constraints are imposed. Within the family setting, model selection involves choosing the member of the family, i.e., the appropriate covariance structure, in addition to the number of mixture components. To date, the Bayesian information criterion (BIC) has proved most effective for model selection, and the expectation-maximization (EM) algorithm is usually used for parameter estimation. In fact, this EM-BIC rubric has virtually monopolized the literature on families of mixture models. Deviating from this rubric, variational Bayes approximations are developed for parameter estimation and the deviance information criterion for model selection. The variational Bayes approach provides an alternate framework for parameter estimation by constructing a tight lower bound on the complex marginal likelihood and maximizing this lower bound by minimizing the associated Kullback-Leibler divergence. This approach is taken on the most commonly used family of Gaussian mixture models, and real and simulated data are used to compare the new approach to the EM-BIC rubric.

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arXiv2017

A Multivariate Poisson-Log Normal Mixture Model for Clustering Transcriptome Sequencing Data

High-dimensional data of discrete and skewed nature is commonly encountered in high-throughput sequencing studies. Analyzing the network itself or the interplay between genes in this type of data continues to present many challenges. As data visualization techniques become cumbersome for higher dimensions and unconvincing when there is no clear separation between homogeneous subgroups within the data, cluster analysis provides an intuitive alternative. The aim of applying mixture model-based clustering in this context is to discover groups of co-expressed genes, which can shed light on biological functions and pathways of gene products. A mixture of multivariate Poisson-Log Normal (MPLN) model is proposed for clustering of high-throughput transcriptome sequencing data. The MPLN model is able to fit a wide range of correlation and overdispersion situations, and is ideal for modeling multivariate count data from RNA sequencing studies. Parameter estimation is carried out via a Markov chain Monte Carlo expectation-maximization algorithm (MCMC-EM), and information criteria are used for model selection.

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arXiv2013

Variational Bayes Approximations for Clustering via Mixtures of Normal Inverse Gaussian Distributions

Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are considered. The use of variational Bayes approximations here is a substantial departure from the traditional EM approach and alleviates some of the associated computational complexities and uncertainties. Our variational algorithm is applied to simulated and real data. The paper concludes with discussion and suggestions for future work.

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arXiv2013

Constrained Optimization for a Subset of the Gaussian Parsimonious Clustering Models

The expectation-maximization (EM) algorithm is an iterative method for finding maximum likelihood estimates when data are incomplete or are treated as being incomplete. The EM algorithm and its variants are commonly used for parameter estimation in applications of mixture models for clustering and classification. This despite the fact that even the Gaussian mixture model likelihood surface contains many local maxima and is singularity riddled. Previous work has focused on circumventing this problem by constraining the smallest eigenvalue of the component covariance matrices. In this paper, we consider constraining the smallest eigenvalue, the largest eigenvalue, and both the smallest and largest within the family setting. Specifically, a subset of the GPCM family is considered for model-based clustering, where we use a re-parameterized version of the famous eigenvalue decomposition of the component covariance matrices. Our approach is illustrated using various experiments with simulated and real data.

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