PARAFAC2-based Coupled Matrix and Tensor Factorizations

Coupled matrix and tensor factorizations (CMTF) have emerged as an effective data fusion tool to jointly analyze data sets in the form of matrices and higher-order tensors. The PARAFAC2 model has shown to be a promising alternative to the CANDECOMP/PARAFAC (CP) tensor model due to its flexibility and capability to handle irregular/ragged tensors. While fusion models based on a PARAFAC2 model coupled with matrix/tensor decompositions have been recently studied, they are limited in terms of possible regularizations and/or types of coupling between data sets. In this paper, we propose an algorithmic framework for fitting PARAFAC2-based CMTF models with the possibility of imposing various constraints on all modes and linear couplings, using Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). Through numerical experiments, we demonstrate that the proposed algorithmic approach accurately recovers the underlying patterns using various constraints and linear couplings

Water-pipe Smoking as a Risk Factor for Transmitting Mycobacterium tuberculosis

A 20-year-old Swiss male presented at the emergency department with acute onset of febrile temperatures and hemoptysis and a 3-month history of productive cough. An X-ray and CT scan of the chest, sputum samples for acid-fast bacilli, polymerase chain reaction(PCR), and cultures for Mycobacteria revealed pulmonary infection with Mycobacterium tuberculosis. None of the classical risk factors for tuberculosis were present, but the patient reported regularly smoking a water pipe. Water-pipe smoking poses a serious risk of M. tuberculosis transmission

Unraveling Diagnostic Biomarkers of Schizophrenia Through Structure-Revealing Fusion of Multi-Modal Neuroimaging Data

Fusing complementary information from different modalities can lead to the discovery of more accurate diagnostic biomarkers for psychiatric disorders. However, biomarker discovery through data fusion is challenging since it requires extracting interpretable and reproducible patterns from data sets, consisting of shared/unshared patterns and of different orders. For example, multi-channel electroencephalography (EEG) signals from multiple subjects can be represented as a third-order tensor with modes: subject, time, and channel, while functional magnetic resonance imaging (fMRI) data may be in the form of subject by voxel matrices. Traditional data fusion methods rearrange higher-order tensors, such as EEG, as matrices to use matrix factorization-based approaches. In contrast, fusion methods based on coupled matrix and tensor factorizations (CMTF) exploit the potential multi-way structure of higher-order tensors. The CMTF approach has been shown to capture underlying patterns more accurately without imposing strong constraints on the latent neural patterns, i.e., biomarkers. In this paper, EEG, fMRI, and structural MRI (sMRI) data collected during an auditory oddball task (AOD) from a group of subjects consisting of patients with schizophrenia and healthy controls, are arranged as matrices and higher-order tensors coupled along the subject mode, and jointly analyzed using structure-revealing CMTF methods [also known as advanced CMTF (ACMTF)] focusing on unique identification of underlying patterns in the presence of shared/unshared patterns. We demonstrate that joint analysis of the EEG tensor and fMRI matrix using ACMTF reveals significant and biologically meaningful components in terms of differentiating between patients with schizophrenia and healthy controls while also providing spatial patterns with high resolution and improving the clustering performance compared to the analysis of only the EEG tensor. We also show that these patterns are reproducible, and study reproducibility for different model parameters. In comparison to the joint independent component analysis (jICA) data fusion approach, ACMTF provides easier interpretation of EEG data by revealing a single summary map of the topography for each component. Furthermore, fusion of sMRI data with EEG and fMRI through an ACMTF model provides structural patterns; however, we also show that when fusing data sets from multiple modalities, hence of very different nature, preprocessing plays a crucial role

A Flexible Optimization Framework for Regularized Matrix-Tensor Factorizations with Linear Couplings

International audienceCoupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges in data fusion and require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. In this paper, we propose a flexible algorithmic framework for coupled matrix and tensor factorizations which utilizes Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The framework facilitates the use of a variety of constraints, loss functions and couplings with linear transformations in a seamless way. Numerical experiments on simulated and real datasets demonstrate that the proposed approach is accurate, and computationally efficient with comparable or better performance than available CMTF methods for Frobenius norm loss, while being more flexible. Using Kullback-Leibler divergence on count data, we demonstrate that the algorithm yields accurate results also for other loss functions

PARAFAC2 AO-ADMM: Constraints in all modes

5 pages, 4 figuresInternational audienceThe PARAFAC2 model provides a flexible alternative to the popular CANDECOMP/PARAFAC (CP) model for tensor decompositions. Unlike CP, PARAFAC2 allows factor matrices in one mode (i.e., evolving mode) to change across tensor slices, which has proven useful for applications in different domains such as chemometrics, and neuroscience. However, the evolving mode of the PARAFAC2 model is traditionally modelled implicitly, which makes it challenging to regularise it. Currently, the only way to apply regularisation on that mode is with a flexible coupling approach, which finds the solution through regularised least-squares subproblems. In this work, we instead propose an alternating direction method of multipliers (ADMM)-based algorithm for fitting PARAFAC2 and widen the possible regularisation penalties to any proximable function. Our numerical experiments demonstrate that the proposed ADMM-based approach for PARAFAC2 can accurately recover the underlying components from simulated data while being both computationally efficient and flexible in terms of imposing constraints

PARAFAC2 AO-ADMM: Constraints in all modes

5 pages, 4 figuresInternational audienceThe PARAFAC2 model provides a flexible alternative to the popular CANDECOMP/PARAFAC (CP) model for tensor decompositions. Unlike CP, PARAFAC2 allows factor matrices in one mode (i.e., evolving mode) to change across tensor slices, which has proven useful for applications in different domains such as chemometrics, and neuroscience. However, the evolving mode of the PARAFAC2 model is traditionally modelled implicitly, which makes it challenging to regularise it. Currently, the only way to apply regularisation on that mode is with a flexible coupling approach, which finds the solution through regularised least-squares subproblems. In this work, we instead propose an alternating direction method of multipliers (ADMM)-based algorithm for fitting PARAFAC2 and widen the possible regularisation penalties to any proximable function. Our numerical experiments demonstrate that the proposed ADMM-based approach for PARAFAC2 can accurately recover the underlying components from simulated data while being both computationally efficient and flexible in terms of imposing constraints

Adapted Contour Integration for Nonlinear Eigenvalue Problems in Waveguide Coupled Resonators

Contour integration methods are claimed to be the methods of choice for computing many (several hundred) eigenvalues of a nonlinear eigenvalue problem inside a closed region of the complex plane. Typically, contour integration methods are designed for circular (or more generally elliptic) shaped contours and rely on the exponential convergence of the trapezoidal rule applied to periodic functions. In this paper, the curl-curl eigenvalue problem in a resonator coupled with a waveguide boundary in a way that allows outgoing waves along longitudinally homogeneous waveguide structures is considered. This problem has a square root dependence on the frequency and thus adapted integration contours are required to reliably find eigenvalues in the vicinity of branch cuts. The filter function based analysis of the quadrature rules has been used and improved to reduce the problem to considering the behavior of filter functions on eigenvalues and singular points only. First, conformally mapped circular contours are considered for problems with one branch cut. For problems where there are several branch cuts necessary, the Gau\ss-Legendre quadrature rules on closed polygonal contours had been analyzed. In both cases, exponential convergence rates were obtained. The estimates are validated numerically using the example of the TESLA cavity

Evaluation of Tumor Budding in Primary Colorectal Cancer and Corresponding Liver Metastases Based on H&E and Pancytokeratin Staining.

In colorectal cancer, tumor budding is associated with tumor progression and represents an additional prognostic factor in the TNM classification. Tumor buds can be found at the invasive front (peritumoral budding; PTB) and in the tumor center (intratumoral budding; ITB) of primary tumors. Previous studies have shown that tumor buds are also present in colorectal liver metastases (CRLM). Data on the prognostic and predictive role in this clinical context are still sparse and no standardized approach to evaluate budding in CRLM has been published so far. This study aimed to analyze and correlate perimetastatic (PMB) and intrametastatic budding (IMB) on H&E and pancytokeratin staining, compare it to budding results in corresponding primary tumors and to propose a standardized scoring system in CRLM as the basis for future studies. Tumor tissue of 81 primary tumors and 139 corresponding CRLM was used for ngTMA construction. For each primary tumor and metastasis, two punches from the center and two punches from the periphery from areas with highest tumor budding density were included. TMA slides were stained for H&E and pancytokeratin (Pan-CK). PTB, ITB, PMB, and IMB were analyzed and classified as bd1, bd2, and bd3 according to ITBCC guidelines. ITB and PTB as well as IMB and PMB showed significant correlation on H&E and Pan-CK staining. No correlation was found for tumor bud counts in primary tumors and corresponding metastases. The agreement for categorized tumor bud counts showed fair to good agreement for metastases and poor agreement for primary tumors between different classes on H&E and Pan-CK staining. Based on our results, tumor budding in primary tumors and CRLM seems to be different processes which might be the results of differing surrounding microenvironments. The evaluation of tumor budding in CRLM is challenging in cases without desmoplastic stroma reaction or intense perimetastatic ductular reaction. We therefore propose to evaluate tumor budding only in metastases with desmoplastic stroma reaction based on H&E staining since important morphological features are obscured on Pan-CK staining

Bleeding Risk in Elderly Patients with Venous Thromboembolism Who Would Have Been Excluded from Anticoagulation Trials.

Older patients with venous thromboembolism (VTE) are underrepresented in clinical anticoagulation trials. We examined to which extent elderly patients with VTE would be excluded from such trials and compared the bleeding risk between hypothetically excluded and enrolled patients. We studied 991 patients aged ≥65 years with acute VTE in a prospective multicenter cohort. We identified 12 landmark VTE oral anticoagulation trials from the eighth and updated ninth American College of Chest Physician Guidelines. For each trial, we abstracted the exclusion criteria and calculated the proportion of our study patients who would have been excluded from trial participation. We examined the association between five common exclusion criteria (hemodynamic instability, high bleeding risk, comorbidity, co-medication, and invasive treatments) and major bleeding (MB) within 36 months using competing risk regression, adjusting for age, sex, and periods of anticoagulation. A median of 31% (range: 20-52%) of our patients would have been excluded from participation in the landmark trials. Hemodynamic instability (sub-hazard ratio [SHR]: 2.2, 95% CI: 1.1-4.7), comorbidity (SHR: 1.5, 95% CI: 1.1-2.2), and co-medication (SHR: 1.5, 95% CI: 1.0-2.3) were associated with MB. Compared to eligible patients, those with ≥2 exclusion criteria had a twofold (SHR: 2.16, 95% CI: 1.38-3.39) increased risk of MB. Overall, about one-third of older patients would not be eligible for participation in guideline-defining VTE anticoagulation trials. The bleeding risk increases significantly with the number of exclusion criteria present. Thus, results from such trials may not be generalizable to older, multimorbid, and co-medicated patients

An AO-ADMM approach to constraining PARAFAC2 on all modes

Analyzing multi-way measurements with variations across one mode of the dataset is a challenge in various fields including data mining, neuroscience and chemometrics. For example, measurements may evolve over time or have unaligned time profiles. The PARAFAC2 model has been successfully used to analyze such data by allowing the underlying factor matrices in one mode (i.e., the evolving mode) to change across slices. The traditional approach to fit a PARAFAC2 model is to use an alternating least squares-based algorithm, which handles the constant cross-product constraint of the PARAFAC2 model by implicitly estimating the evolving factor matrices. This approach makes imposing regularization on these factor matrices challenging. There is currently no algorithm to flexibly impose such regularization with general penalty functions and hard constraints. In order to address this challenge and to avoid the implicit estimation, in this paper, we propose an algorithm for fitting PARAFAC2 based on alternating optimization with the alternating direction method of multipliers (AO-ADMM). With numerical experiments on simulated data, we show that the proposed PARAFAC2 AO-ADMM approach allows for flexible constraints, recovers the underlying patterns accurately, and is computationally efficient compared to the state-of-the-art. We also apply our model to two real-world datasets from neuroscience and chemometrics, and show that constraining the evolving mode improves the interpretability of the extracted patterns