Separable Decomposition for Ragged Tensors

Tensor decompositions have proven highly effective in the analysis and processing of multidimensional data. However, many real-world datasets exhibit highly irregular index patterns that deviate from regular tensor structures, rendering classical tensor decomposition methods inapplicable. In this paper, we introduce a CANDECOMP/PARAFAC (CP)-based geometry-aware separable decomposition framework for directly factorizing multidimensionally irregular tensor data, which we term ragged tensors. We model the valid domain of a ragged tensor using a binary weighting tensor and exploit the linkage between CP factor rows and corresponding valid elements to decouple the global objective into independent, well-conditioned subproblems. This structural decoupling enables a domain-adapted proximal alternating minimization scheme with closed-form stabilized updates, yielding an efficient and scalable solver along with a rigorous convergence guarantee to a critical point. We validate the proposed method on a range of challenging datasets, including multispectral and hyperspectral images as well as spatial transcriptomics data. Experimental results demonstrate that our approach consistently achieves superior accuracy and efficiency compared to competing baselines, highlighting the effectiveness of our modeling and optimization strategy for ragged tensor data.