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Distinguishing malicious anomalous activities from unusual but benign activities is a fundamental challenge for cyber defenders. Prior studies have shown that statistical user behavior analysis yields accurate detections by learning behavior profiles from observed user activity. These unsupervised models are able to generalize to unseen types of attacks by detecting deviations from normal behavior without knowledge of specific attack signatures. However, approaches proposed to date based on probabilistic matrix factorization are limited by the information conveyed in a two-dimensional space. Non-negative tensor factorization, however, is a powerful unsupervised machine learning method that naturally models multi-dimensional data, capturing complex and multi-faceted details of behavior profiles. Our new unsupervised statistical anomaly detection methodology matches or surpasses state-of-the-art supervised learning baselines across several challenging and diverse cyber application areas, including detection of compromised user credentials, botnets, spam e-mails, and fraudulent credit card transactions.

Mutational signature analysis is commonly performed in cancer genomic studies. Here, we present SigProfilerExtractor, an automated tool for de novo extraction of mutational signatures, and benchmark it against another 13 bioinformatics tools by using 34 scenarios encompassing 2,500 simulated signatures found in 60,000 synthetic genomes and 20,000 synthetic exomes. For simulations with 5% noise, reflecting high-quality datasets, SigProfilerExtractor outperforms other approaches by elucidating between 20% and 50% more true-positive signatures while yielding 5-fold less false-positive signatures. Applying SigProfilerExtractor to 4,643 whole-genome- and 19,184 whole-exome-sequenced cancers reveals four novel signatures. Two of the signatures are confirmed in independent cohorts, and one of these signatures is associated with tobacco smoking. In summary, this report provides a reference tool for analysis of mutational signatures, a comprehensive benchmarking of bioinformatics tools for extracting signatures, and several novel mutational signatures, including one putatively attributed to direct tobacco smoking mutagenesis in bladder tissues. published

A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with an additional constraint over an auxiliary matrix whose Boolean structure is identical to the initial Boolean data. This additional auxiliary matrix constraint forces the support of the NMF solution to adhere to that of a BMF solution. The solution of the nonnegative auxiliary optimization problem is thresholded to provide a solution for the BMF problem. We provide the proofs for the equivalencies of the two solution spaces under the existence of an exact solution. Moreover, the nonincreasing property of the algorithm is also proven. Experiments on synthetic and real datasets are conducted to show the effectiveness and complexity of the algorithm compared to other current methods.

Nonnegative Matrix Factorization (NMF) is a well-known method for Blind Source Separation (BSS). Recently, BSS for polarized signals in spectropolarimetric data, containing both polarization and spectral information, was introduced. This information was encoded in 4-dimensional Stokes vectors represented by quaternion numbers. In the proposed Quaternion NMF (QNMF), the common challenge of determining the (usually) unknown number of quaternion signals remained unaddressed. Estimating the number of signals (aka model determination) is important, since an underestimation of this number results in poor source separation and omission of signals, while overestimation leads to extraction of noisy signals without physical meaning. Here, we introduce a method for determining the number of polarized signals in spectropolarimetric data, named QNMF $k$ . QNMF $k$ integrates: (a) Quaternion Alternating Direction Method of Multipliers (QADMM) implemented for QNMF, (b) random resampling of the initial quaternion data, and (c) custom clustering of sets of QADMM solutions with same number of sources, $k$ , needed to estimate the stability of the solutions. The appropriate latent dimension is determined based on the stability of the solutions. We demonstrate that, without any prior information, QNMF $k$ accurately extracts the correct number of signals used to generate synthetic quaternion datasets and a benchmark spectropolarimetric data.

The holistic analysis and understanding of the latent (that is, not directly observable) variables and patterns buried in large datasets is crucial for data-driven science, decision making and emergency response. Such exploratory analyses require devising unsupervised learning methods for data mining and extraction of the latent features, and non-negative matrix factorization (NMF) is one of the prominent such methods. NMF is based on compute-intense non-convex constrained minimization, which, for large datasets requires fast and distributed algorithms. However, current parallel implementations of NMF fail to estimate the number of latent features. In practice, identifying these features is both difficult and significant for pattern recognition and latent feature analysis, especially for large dense matrices. In this paper, we introduce a distributed NMF algorithm coupled with distributed custom clustering followed by a stability analysis on dense data, which we call DnMFk, to determine the number of latent variables. The results on synthetic data and the classical Swimmer data set demonstrate the accuracy of model determination while scaling nearly linearly across multiple processors for large data. Further, we employ DnMFk to determine the number of hidden features from a terabyte matrix.

Singular value decomposition (SVD) is a matrix factorization method widely used for dimension reduction, data analytics, information retrieval, and unsupervised learning. In general, only singular values of SVD are needed for most big-data applications. Methods such as tensor networks require an accurate computation of a substantial number of singular vectors, which can be accomplished through truncated SVD (tSVD). Additionally, many real-world datasets are too big to fit into the available memory, which mandates the development of out of memory algorithms that assume that most of the data resides on an external disk during the entire computation. These algorithms reduce communication to disk and hide part of the communication by overlapping it with communication on blocks of work. Here, building upon previous works on SVD for dense matrices, we present a method for computation of a predetermined number, $K$ , of SVD singular vectors, and the corresponding $K$ singular values, of a matrix that cannot fit in the memory. Our out of memory tSVD can be used for tensor networks algorithms. We describe ways for reducing the communication during the computation of the left and right reflectors, needed to compute the singular vectors, and introduce a method for estimating the block-sizes needed to hide the communication on parallel file systems.

Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., {0, 1}) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called \textit{parallel quantum annealing}, we demonstrate that tensor with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer., Updated with new figures and fixed typos. 18 pages

Mutational signature analysis is commonly performed in cancer genomic studies. Here, we present SigProfilerExtractor, an automated tool for

Analysis of reactive-diffusion simulations requires a large number of independent model runs. For each high-fidelity simulation, inputs are varied and the predicted mixing behavior is represented by changes in species concentration. It is then required to discern how the model inputs impact the mixing process. This task is challenging and typically involves interpretation of large model outputs. However, the task can be automated and substantially simplified by applying Machine Learning (ML) methods. In this paper, we present an application of an unsupervised ML method (called NTFk) using Non-negative Tensor Factorization (NTF) coupled with a custom clustering procedure based on k-means to reveal hidden features in product concentration. An attractive aspect of the proposed ML method is that it ensures the extracted features are non-negative, which are important to obtain a meaningful deconstruction of the mixing processes. The ML method is applied to a large set of high-resolution FEM simulations representing reaction-diffusion processes in perturbed vortex-based velocity fields. The applied FEM ensures that species concentration are always non-negative. The simulated reaction is a fast irreversible bimolecular reaction. The reactive-diffusion model input parameters that control mixing include properties of velocity field, anisotropic dispersion, and molecular diffusion. We demonstrate the applicability of the ML method to produce a meaningful deconstruction of model outputs to discriminate between different physical processes impacting the reactants, their mixing, and the spatial distribution of the product. The presented ML analysis allowed us to identify additive features that characterize mixing behavior., 34 pages

Phase separation in mixed lipid systems has been extensively studied both experimentally and theoretically because of its biological importance. A detailed description of such complex systems undoubtedly requires novel mathematical frameworks that are capable of decomposing and categorizing the evolution of thousands if not millions of lipids involved in the phenomenon. The interpretation and analysis of molecular dynamics (MD) simulations representing temporal and spatial changes in such systems are still a challenging task. Here, we present an unsupervised machine learning approach based on nonnegative matrix factorization called NMFk that successfully extracts latent (i.e., not directly observable) features from the second layer neighborhood profiles derived from coarse-grained MD simulations of a ternary lipid mixture. Our results demonstrate that NMFk extracts physically meaningful features that uniquely describe the phase separation such as locations and roles of different lipid types, formation of nanodomains, and timescales of lipid segregation.

Unsupervised Machine Learning (ML) is becoming increasingly popular for solving various types of data analytics problems including feature extraction, blind source separation, exploratory analyses, model diagnostics, etc. Here, we have developed a new unsupervised ML method based on Nonnegative Tensor Factorization (NTF) for identification of the original groundwater types (including contaminant sources) present in geochemical mixtures observed in an aquifer . Frequently, groundwater types with different geochemical signatures are related to different background and/or contamination sources. The characterization of groundwater mixing processes is a challenging but very important task critical for any environmental management project aiming to characterize the fate and transport of contaminants in the subsurface and perform contaminant remediation. This task typically requires solving complex inverse models representing groundwater flow and geochemical transport in the aquifer, where the inverse analysis accounts for available site data. Usually, the model is calibrated against the available data characterizing the spatial and temporal distribution of the observed geochemical types. Numerous different geochemical constituents and processes may need to be simulated in these models which further complicates the analyses. Additionally, the application of inverse methods may introduce biases in the analyses through the assumptions made in the model development process. Here, we substitute the model inversion with unsupervised ML analysis. The ML analysis does not make any assumptions about underlying physical and geochemical processes occurring in the aquifer. Our ML methodology, called NTF k, is capable of identifying (1) the unknown number of groundwater types (contaminant sources) present in the aquifer, (2) the original geochemical concentrations (signatures) of these groundwater types and (3) spatial and temporal dynamics in the mixing of these groundwater types. These results are obtained only from the measured geochemical data without any additional site information. In general, the NTFk methodology allows for interpretation of large high-dimensional datasets representing diverse spatial and temporal components such as state variables and velocities. NTFk has been tested on synthetic and real-world site three-dimensional datasets. The NTFk algorithm is designed to work with geochemical data represented in the form of concentrations, ratios (of two constituents; for example, isotope ratios), and delta notations (standard normalized stable isotope ratios).

Although metabolic syndrome (MetS) is linked to an elevated risk of cardiovascular disease (CVD), the cardiac-specific risk mechanism is unknown. Obesity, hypertension, and diabetes (all MetS components) are the most common form of CVD and represent risk factors for worse COVID-19 outcomes compared to their non MetS peers. Here, we use obese Yorkshire pigs as a highly relevant animal model of human MetS, where pigs develop the hallmarks of human MetS and reproducibly mimics the myocardial pathophysiology in patients. Myocardium-specific mass spectroscopy-derived metabolomics, proteomics, and transcriptomics enabled the identity and quality of proteins and metabolites to be investigated in the myocardium to greater depth. Myocardium-specific deregulation of pro-inflammatory markers, propensity for arterial thrombosis, and platelet aggregation was revealed by computational analysis of differentially enriched pathways between MetS and control animals. While key components of the complement pathway and the immune response to viruses are under expressed, key N6-methyladenosin RNA methylation enzymes are largely overexpressed in MetS. Blood tests do not capture the entirety of metabolic changes that the myocardium undergoes, making this analysis of greater value than blood component analysis alone. Our findings create data associations to further characterize the MetS myocardium and disease vulnerability, emphasize the need for a multimodal therapeutic approach, and suggests a mechanism for observed worse outcomes in MetS patients with COVID-19 comorbidity.