Generalized Co-Clustering Analysis via Regularized Alternating Least Squares.

Area of Science:

• Data Mining
• Machine Learning
• Statistical Analysis

Background:

• Biclustering is a valuable exploratory analysis technique for identifying row-column associations in data matrices.
• Existing biclustering methods often assume Gaussian distributions and are limited to matrix data, restricting their applicability.
• Real-world data frequently exhibit non-Gaussian properties or multi-way tensor structures, necessitating more advanced methods.

Purpose of the Study:

• To propose a novel CO-clustering method (CORALS) that generalizes biclustering to handle non-Gaussian data and multi-way tensor arrays.
• To model non-Gaussian data using single-parameter exponential family distributions.
• To identify co-clusters within the natural parameter space using sparse CANDECOMP/PARAFAC tensor decomposition.

Main Methods:

• A regularized alternating least squares (CORALS) algorithm is developed for fitting the proposed model.
• Iteratively reweighted least squares are employed within the CORALS algorithm.
• A deflation procedure is utilized to automatically determine the optimal number of co-clusters.

Main Results:

• The proposed CORALS method effectively generalizes biclustering to non-Gaussian and multi-way tensor data.
• Simulation studies demonstrated the method's efficacy in identifying co-clusters.
• Application to three real-world datasets confirmed the practical utility of CORALS.

Conclusions:

• CORALS provides a robust and flexible framework for biclustering diverse data types, including non-Gaussian and tensor data.
• The method successfully identifies checkerboard-like co-clusters, revealing intrinsic associations.
• Publicly available data and code facilitate the adoption and further development of CORALS.