TriSig: Assessing the statistical significance of triclusters

Tensor data analysis allows researchers to uncover novel patterns and relationships that cannot be obtained from matrix data alone. The information inferred from the patterns provides valuable insights into disease progression, bioproduction processes, weather fluctuations, and group dynamics. However, spurious and redundant patterns hamper this process. This work aims at proposing a statistical frame to assess the probability of patterns in tensor data to deviate from null expectations, extending well-established principles for assessing the statistical significance of patterns in matrix data. A comprehensive discussion on binomial testing for false positive discoveries is entailed at the light of: variable dependencies, temporal dependencies and misalignments, and \textit{p}-value corrections under the Benjamini-Hochberg procedure. Results gathered from the application of state-of-the-art triclustering algorithms over distinct real-world case studies in biochemical and biotechnological domains confer validity to the proposed statistical frame while revealing vulnerabilities of some triclustering searches. The proposed assessment can be incorporated into existing triclustering algorithms to mitigate false positive/spurious discoveries and further prune the search space, reducing their computational complexity. Availability: The code is freely available at https://github.com/JupitersMight/TriSig under the MIT license

Dynamic Tensor Clustering

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. Also there is often a gap between statistical guarantee and computational efficiency for existing tensor clustering solutions. In this article, we aim to bridge this gap by proposing a new dynamic tensor clustering method, which takes into account both sparsity and fusion structures, and enjoys strong statistical guarantees as well as high computational efficiency. Our proposal is based upon a new structured tensor factorization that encourages both sparsity and smoothness in parameters along the specified tensor modes. Computationally, we develop a highly efficient optimization algorithm that benefits from substantial dimension reduction. In theory, we first establish a non-asymptotic error bound for the estimator from the structured tensor factorization. Built upon this error bound, we then derive the rate of convergence of the estimated cluster centers, and show that the estimated clusters recover the true cluster structures with a high probability. Moreover, our proposed method can be naturally extended to co-clustering of multiple modes of the tensor data. The efficacy of our approach is illustrated via simulations and a brain dynamic functional connectivity analysis from an Autism spectrum disorder study.Comment: Accepted at Journal of the American Statistical Associatio