Separable Decomposition for Ragged Tensors

Area of Science:

• Multidimensional data analysis
• Applied mathematics
• Computational science

Background:

• Classical tensor decomposition methods are ineffective for irregular, real-world datasets.
• Irregular index patterns in multidimensional data pose significant analytical challenges.
• Existing methods fail to address the complexities of non-uniformly structured data.

Purpose of the Study:

• To introduce a novel framework for the direct factorization of multidimensionally irregular tensor data (ragged tensors).
• To develop an efficient and scalable solver for ragged tensor decomposition.
• To demonstrate the applicability and superiority of the proposed method on complex datasets.

Main Methods:

• A CANDECOMP/PARAFAC (CP)-based geometry-aware separable decomposition framework is proposed.
• A binary weighting tensor models the valid domain of ragged tensors.
• A domain-adapted proximal alternating minimization scheme with stabilized updates is employed.

Main Results:

• The proposed method achieves superior accuracy and efficiency compared to existing baselines.
• The framework successfully factorizes challenging multispectral, hyperspectral, and spatial transcriptomics data.
• The solver demonstrates scalability and provides a rigorous convergence guarantee.

Conclusions:

• The geometry-aware separable decomposition effectively handles ragged tensor data.
• The developed modeling and optimization strategy offers a robust solution for irregular multidimensional data analysis.
• This approach significantly advances the capabilities for processing complex scientific datasets.