Existing tensor factorization methods assume that the input tensor follows some specific distribution (i.e. Poisson, Bernoulli, and Gaussian), and solve the factorization by minimizing some empirical loss functions defined based on the corresponding distribution. However, it suffers from several drawbacks: 1) In reality, the underlying distributions are complicated and unknown, making it infeasible to be approximated by a simple distribution. 2) The correlation across dimensions of the input tensor is not well utilized, leading to sub-optimal performance. Although heuristics were proposed to incorporate such correlation as side information under Gaussian distribution, they can not easily be generalized to other distributions. Thus, a more principled way of utilizing the correlation in tensor factorization models is still an open challenge. Without assuming any explicit distribution, we formulate the tensor factorization as an optimal transport problem with Wasserstein distance, which can handle non-negative inputs. We introduce SWIFT, which minimizes the Wasserstein distance that measures the distance between the input tensor and that of the reconstruction. In particular, we define the N-th order tensor Wasserstein loss for the widely used tensor CP factorization and derive the optimization algorithm that minimizes it. By leveraging sparsity structure and different equivalent formulations for optimizing computational efficiency, SWIFT is as scalable as other well-known CP algorithms. Using the factor matrices as features, SWIFT achieves up to 9.65% and 11.31% relative improvement over baselines for downstream prediction tasks. Under the noisy conditions, SWIFT achieves up to 15% and 17% relative improvements over the best competitors for the prediction tasks.

Binary data with one-class missing values are ubiquitous in real-world applications. They can be represented by irregular tensors with varying sizes in one dimension, where value one means presence of a feature while zero means unknown (i.e., either presence or absence of a feature). Learning accurate low-rank approximations from such binary irregular tensors is a challenging task. However, none of the existing models developed for factorizing irregular tensors take the missing values into account, and they assume Gaussian distributions, resulting in a distribution mismatch when applied to binary data. In this paper, we propose Logistic PARAFAC2 (LogPar) by modeling the binary irregular tensor with Bernoulli distribution parameterized by an underlying real-valued tensor. Then we approximate the underlying tensor with a positive-unlabeled learning loss function to account for the missing values. We also incorporate uniqueness and temporal smoothness regularization to enhance the interpretability. Extensive experiments using large-scale real-world datasets show that LogPar outperforms all baselines in both irregular tensor completion and downstream predictive tasks. For the irregular tensor completion, LogPar achieves up to 26% relative improvement compared to the best baseline. Besides, LogPar obtains relative improvement of 13.2% for heart failure prediction and 14% for mortality prediction on average compared to the state-of-the-art PARAFAC2 models.

PARAFAC2 has demonstrated success in modeling irregular tensors, where the tensor dimensions vary across one of the modes. An example scenario is modeling treatments across a set of patients with the varying number of medical encounters over time. Despite recent improvements on unconstrained PARAFAC2, its model factors are usually dense and sensitive to noise which limits their interpretability. As a result, the following open challenges remain: a) various modeling constraints, such as temporal smoothness, sparsity and non-negativity, are needed to be imposed for interpretable temporal modeling and b) a scalable approach is required to support those constraints efficiently for large datasets. To tackle these challenges, we propose a COnstrained PARAFAC2 (COPA) method, which carefully incorporates optimization constraints such as temporal smoothness, sparsity, and non-negativity in the resulting factors. To efficiently support all those constraints, COPA adopts a hybrid optimization framework using alternating optimization and alternating direction method of multiplier (AO-ADMM). As evaluated on large electronic health record (EHR) datasets with hundreds of thousands of patients, COPA achieves significant speedups (up to 36 times faster) over prior PARAFAC2 approaches that only attempt to handle a subset of the constraints that COPA enables. Overall, our method outperforms all the baselines attempting to handle a subset of the constraints in terms of speed, while achieving the same level of accuracy. Through a case study on temporal phenotyping of medically complex children, we demonstrate how the constraints imposed by COPA reveal concise phenotypes and meaningful temporal profiles of patients. The clinical interpretation of both the phenotypes and the temporal profiles was confirmed by a medical expert.

Extracting patterns and deriving insights from spatio-temporal data finds many target applications in various domains, such as in urban planning and computational sustainability. Due to their inherent capability of simultaneously modeling the spatial and temporal aspects of multiple instances, tensors have been successfully used to analyze such spatio-temporal data. However, standard tensor factorization approaches often result in components that are highly overlapping, which hinders the practitioner's ability to interpret them without advanced domain knowledge. In this work, we tackle this challenge by proposing a tensor factorization framework, called CP-ORTHO, to discover distinct and easily-interpretable patterns from multi-modal, spatio-temporal data. We evaluate our approach on real data reflecting taxi drop-off activity. CP-ORTHO provides more distinct and interpretable patterns than prior art, as measured via relevant quantitative metrics, without compromising the solution's accuracy. We observe that CP-ORTHO is fast, in that it achieves this result in 5x less time than the most accurate competing approach.

Community detection approaches are useful tools for revealing the structure and properties of networks. There are many approaches for identifying communities, some require inaccessible information, others need initializing parameters to perform well. Many existing algorithms require centralized decision maker to reveal communities. This paper proposes a non-centralized parameter-free method that only uses attainable information. The proposed method is examined using real as well as synthetic social networks. Experimental results suggest that this approach can perform as well as centralized approaches that require global information for detecting communities.