Parameter clustering in Bayesian functional principal component analysis of neuroscientific data

Anatomically compliant modes of variations: New tools for brain connectivity

Anatomical complexity and data dimensionality present major issues when analysing brain connectivity data. The functional and anatomical aspects of the connections taking place in the brain are in fact equally relevant and strongly intertwined. However, due to theoretical challenges and computational issues, their relationship is often overlooked in neuroscience and clinical research. In this work, we propose to tackle this problem through Smooth Functional Principal Component Analysis, which enables to perform dimensional reduction and exploration of the variability in functional connectivity maps, complying with the formidably complicated anatomy of the grey matter volume. In particular, we analyse a population that includes controls and subjects affected by schizophrenia, starting from fMRI data acquired at rest and during a task-switching paradigm. For both sessions, we first identify the common modes of variation in the entire population. We hence explore whether the subjects' expressions along these common modes of variation differ between controls and pathological subjects. In each session, we find principal components that are significantly differently expressed in the healthy vs pathological subjects (with p-values < 0.001), highlighting clearly interpretable differences in the connectivity in the two subpopulations. For instance, the second and third principal components for the rest session capture the imbalance between the Default Mode and Executive Networks characterizing schizophrenia patients.

Clustering Spatially Correlated Functional Data With Multiple Scalar Covariates

We propose a probabilistic model for clustering spatially correlated functional data with multiple scalar covariates. The motivating application is to partition the 29 provinces of the Chinese mainland into a few groups characterized by the epidemic severity of COVID-19, while the spatial dependence and effects of risk factors are considered. It can be regarded as an extension of mixture models, which allows different subsets of covariates to influence the component weights and the component densities by modeling the parameters of the mixture as functions of the covariates. In this way, provinces with similar spatial factors are a priori more likely to be clustered together. Posterior predictive inference in this model formalizes the desired prediction. Further, the identifiability of the proposed model is analyzed, and sufficient conditions to guarantee "generic" identifiability are provided. An L1 -penalized estimator is developed to assist variable selection and robust estimation when the number of explanatory covariates is large. An efficient expectation-minimization algorithm is presented for parameter estimation. Simulation studies and real-data examples are presented to investigate the empirical performance of the proposed method. Finally, it is worth noting that the proposed model has a wide range of practical applications, e.g., health management, environmental science, ecological studies, and so on.

clusterBMA: Bayesian model averaging for clustering

Various methods have been developed to combine inference across multiple sets of results for unsupervised clustering, within the ensemble clustering literature. The approach of reporting results from one 'best' model out of several candidate clustering models generally ignores the uncertainty that arises from model selection, and results in inferences that are sensitive to the particular model and parameters chosen. Bayesian model averaging (BMA) is a popular approach for combining results across multiple models that offers some attractive benefits in this setting, including probabilistic interpretation of the combined cluster structure and quantification of model-based uncertainty. In this work we introduce clusterBMA, a method that enables weighted model averaging across results from multiple unsupervised clustering algorithms. We use clustering internal validation criteria to develop an approximation of the posterior model probability, used for weighting the results from each model. From a combined posterior similarity matrix representing a weighted average of the clustering solutions across models, we apply symmetric simplex matrix factorisation to calculate final probabilistic cluster allocations. In addition to outperforming other ensemble clustering methods on simulated data, clusterBMA offers unique features including probabilistic allocation to averaged clusters, combining allocation probabilities from 'hard' and 'soft' clustering algorithms, and measuring model-based uncertainty in averaged cluster allocation. This method is implemented in an accompanying R package of the same name. We use simulated datasets to explore the ability of the proposed technique to identify robust integrated clusters with varying levels of separation between subgroups, and with varying numbers of clusters between models. Benchmarking accuracy against four other ensemble methods previously demonstrated to be highly effective in the literature, clusterBMA matches or exceeds the performance of competing approaches under various conditions of dimensionality and cluster separation. clusterBMA substantially outperformed other ensemble methods for high dimensional simulated data with low cluster separation, with 1.16 to 7.12 times better performance as measured by the Adjusted Rand Index. We also explore the performance of this approach through a case study that aims to identify probabilistic clusters of individuals based on electroencephalography (EEG) data. In applied settings for clustering individuals based on health data, the features of probabilistic allocation and measurement of model-based uncertainty in averaged clusters are useful for clinical relevance and statistical communication.