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1. Evaluating methods for addressing skewness in clustering: a focus on generalized hyperbolic mixture models

   https://doi.org/10.1080/00949655.2025.2502535  

   Tortora, Cristina (May 2025, Journal of Statistical Computation and Simulation)

   In model-based clustering, the population is assumed to be a combination of sub-populations. Typically, each sub-population is modeled by a mixture model component, distributed according to a known probability distribution. Each component is considered a cluster. Two primary approaches have been used in the literature when clusters are skewed: (1) transforming the data within each cluster and applying a mixture of symmetric distributions to the transformed data, and (2) directly modeling each cluster using a skewed distribution. Among skewed distributions, the generalized hyperbolic distribution is notably flexible and includes many other known distributions as special or limiting cases. This paper achieves two goals. First, it extends the flexibility of transformation-based methods as outlined in approach (1) by employing a flexible symmetric generalized hyperbolic distribution to model each transformed cluster. This innovation results in the introduction of two new models, each derived from distinct within-cluster data transformations. Second, the paper benchmarks the approaches listed in (1) and (2) for handling skewness using both simulated and real data. The findings highlight the necessity of both approaches in varying contexts. 

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2. A Bayesian semiparametric mixture model for clustering zero-inflated microbiome data

   https://doi.org/10.1093/biomtc/ujaf125  

   Korsurat, Suppapat; Koslovsky, Matthew D (July 2025, Biometrics)

   Microbiome research has immense potential for unlocking insights into human health and disease. A common goal in human microbiome research is identifying subgroups of individuals with similar microbial composition that may be linked to specific health states or environmental exposures. However, existing clustering methods are often not equipped to accommodate the complex structure of microbiome data and typically make limiting assumptions regarding the number of clusters in the data which can bias inference. Designed for zero-inflated multivariate compositional count data collected in microbiome research, we propose a novel Bayesian semiparametric mixture modeling framework that simultaneously learns the number of clusters in the data while performing cluster allocation. In simulation, we demonstrate the clustering performance of our method compared to distance- and model-based alternatives and the importance of accommodating zero-inflation when present in the data. We then apply the model to identify clusters in microbiome data collected in a study designed to investigate the relation between gut microbial composition and enteric diarrheal disease. 

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3. Nonparametric clustering of RNA-sequencing data

   https://doi.org/10.1002/sam.11638  

   Lozano, Gabriel; Atallah, Nadia; Levine, Michael (December 2023, Statistical Analysis and Data Mining: The ASA Data Science Journal)

   Abstract 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 

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4. A Dirichlet Mixture Model of Hawkes Processes for Event Sequence Clustering

   Xu, Hongteng; Zha, Hongyuan (January 2017, Advances in neural information processing systems)

   How to cluster event sequences generated via different point processes is an interesting and important problem in statistical machine learning. To solve this problem, we propose and discuss an effective model-based clustering method based on a novel Dirichlet mixture model of a special but significant type of point processes — Hawkes process. The proposed model generates the event sequences with different clusters from the Hawkes processes with different parameters, and uses a Dirichlet distribution as the prior distribution of the clusters. We prove the identifiability of our mixture model and propose an effective variational Bayesian inference algorithm to learn our model. An adaptive inner iteration allocation strategy is designed to accelerate the convergence of our algorithm. Moreover, we investigate the sample complexity and the computational complexity of our learning algorithm in depth. Experiments on both synthetic and real-world data show that the clustering method based on our model can learn structural triggering patterns hidden in asynchronous event sequences robustly and achieve superior performance on clustering purity and consistency compared to existing methods. 

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5. Constructing Cell‐Type Taxonomy by Optimal Transport With Relaxed Marginal Constraints

   https://doi.org/10.1002/sam.70049  

   Pena, Sebastian; Lin, Lin; Li, Jia (October 2025, Statistical Analysis and Data Mining: An ASA Data Science Journal)

   ABSTRACT The rapid emergence of single‐cell data has facilitated the study of many different biological conditions at the cellular level. Cluster analysis has been widely applied to identify cell types, capturing the essential patterns of the original data in a much more concise form. One challenge in the cluster analysis of cells is matching clusters extracted from datasets of different origins or conditions. Many existing algorithms cannot recognize new cell types present in only one of the two samples when establishing a correspondence between clusters obtained from two samples. Additionally, when there are more than two samples, it is advantageous to align clusters across all samples simultaneously rather than performing pairwise alignment. Our approach aims to construct a taxonomy for cell clusters across all samples to better annotate these clusters and effectively extract features for downstream analysis. A new system for constructing cell‐type taxonomy has been developed by combining the technique of optimal transport with relaxed marginal constraints (OT‐RMC) and the simultaneous alignment of clusters across multiple samples. OT‐RMC allows us to address challenges that arise when the proportions of clusters vary substantially between samples or when some clusters do not appear in all the samples. Experiments on more than 20 datasets demonstrate that the taxonomy constructed by this new system can yield highly accurate annotation of cell types. Additionally, sample‐level features extracted based on the taxonomy result in accurate classification of samples. 

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