Triclustering Model for Three-Dimensional Time-Series Gene Expression Data

With the rapid advancement and cost reduction in high-throughput sequencing technologies, the accumulation of large-scale, three-dimensional gene expression data has surged. Consequently, effectively reducing the dimensionality of these complex datasets to extract critical biological information remains a significant challenge. Although various methods for identifying gene expression modules have been developed, most do not explicitly account for the multifactorial interactions among the temporal, spatial, and environmental dimensions. To address this limitation, we propose a novel three-dimensional triclustering technique based on a multivariate Gaussian mixture model (MVGMM) within a maximum likelihood framework. Specifically, our approach incorporates Legendre polynomials to model the temporal dynamics of gene expression and utilizes the Bayesian Information Criterion (BIC) to determine the optimal number of clusters. To further evaluate the model's robustness against the high background noise typically present in empirical datasets (such as Arabidopsis thaliana), we conducted a rigorous sensitivity analysis by artificially injecting high-intensity Gaussian white noise into the simulated dataset. Despite severe noise interference, the global minimum of the BIC consistently remained at K = 6. Furthermore, the penalty term in the BIC successfully suppressed artificial cluster proliferation, preventing the model from fitting the noise as new functional modules. The MVGMM framework successfully recovered the predefined cluster structure in simulation studies and identified distinct expression modules in empirical Arabidopsis thaliana data. By jointly modeling temporal, spatial, and environmental variation, this study provides a statistical framework for exploring multidimensional gene expression patterns and may facilitate the identification of coordinated regulatory programs in complex biological systems.