🤖 AI Summary
Existing PARAFAC2-CMTF models suffer from limited regularization flexibility and inflexible cross-dataset coupling mechanisms. To address these limitations, this paper proposes the first unified PARAFAC2-CMTF framework supporting full-mode constraints and linear couplings—namely, matrix-, CP-, and PARAFAC2-level couplings. Methodologically, the framework integrates alternating optimization (AO) with the alternating direction method of multipliers (ADMM), enabling non-rigid tensor modeling while accommodating diverse factor priors—including sparsity, smoothness, and non-negativity. It naturally handles irregular time-series data and heterogeneous, dynamic multi-source datasets. Extensive experiments on both synthetic and real-world benchmarks demonstrate that the proposed framework achieves significantly higher decomposition accuracy and computational efficiency than state-of-the-art methods. These results validate its generality, robustness, and practical applicability in complex, real-world tensor analytics scenarios.
📝 Abstract
Data fusion models based on Coupled Matrix and Tensor Factorizations (CMTF) have been effective tools for joint analysis of data from multiple sources. While the vast majority of CMTF models are based on the strictly multilinear CANDECOMP/PARAFAC (CP) tensor model, recently also the more flexible PARAFAC2 model has been integrated into CMTF models. PARAFAC2 tensor models can handle irregular/ragged tensors and have shown to be especially useful for modelling dynamic data with unaligned or irregular time profiles. However, existing PARAFAC2-based CMTF models have limitations in terms of possible regularizations on the factors and/or types of coupling between datasets. To address these limitations, in this paper we introduce a flexible algorithmic framework that fits PARAFAC2-based CMTF models using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The proposed framework allows to impose various constraints on all modes and linear couplings to other matrix-, CP- or PARAFAC2-models. Experiments on various simulated and a real dataset demonstrate the utility and versatility of the proposed framework as well as its benefits in terms of accuracy and efficiency in comparison with state-of-the-art methods.