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Results for “non-negative matrix factorization”

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75 records · Page 5

General-Purpose Unsupervised Cyber Anomaly Detection via Non-Negative Tensor Factorization

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, on the other hand, is a powerful unsupervised machine learning method that naturally models multi-dimensional data, capturing complex and multi-faceted details of behavior profiles. Herein, 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.

97 MATHEMATICS AND COMPUTING↗

Correlated mechanochemical maps of Arabidopsis thaliana primary cell walls using atomic force microscope infrared spectroscopy

Spatial heterogeneity in composition and organisation of the primary cell wall affects the mechanics of cellular morphogenesis. However, directly correlating cell wall composition, organisation and mechanics has been challenging. To overcome this barrier, we applied atomic force microscopy coupled with infrared (AFM-IR) spectroscopy to generate spatially correlated maps of chemical and mechanical properties for paraformaldehyde-fixed, intact Arabidopsis thaliana epidermal cell walls. AFM-IR spectra were deconvoluted by non-negative matrix factorisation (NMF) into a linear combination of IR spectral factors representing sets of chemical groups comprising different cell wall components. This approach enables quantification of chemical composition from IR spectral signatures and visualisation of chemical heterogeneity at nanometer resolution. Cross-correlation analysis of the spatial distribution of NMFs and mechanical properties suggests that the carbohydrate composition of cell wall junctions correlates with increased local stiffness. Together, our work establishes new methodology to use AFM-IR for the mechanochemical analysis of intact plant primary cell walls.

59 BASIC BIOLOGICAL SCIENCES↗

Enhanced relaxed physical factorization preconditioner for coupled poromechanics

The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled poromechanics. For its application, however, it is necessary to invert blocks with the algebraic form C^ = (C + βFF T ), where C is a symmetric positive definite matrix, FF T a rank-deficient term, and β a real non-negative coefficient. The inversion of C^, performed in an inexact way, can become unstable for large values of β, as it usually occurs at some stages of a full poromechanical simulation. In this work, we propose a family of algebraic techniques to stabilize the inexact solve with C^. This strategy can prove useful in other problems as well where such an issue might arise, such as augmented Lagrangian preconditioning techniques for Navier-Stokes or incompressible elasticity. First, we introduce an iterative scheme obtained by a natural splitting of matrix C^. Second, we develop a technique based on the use of a proper projection operator annihilating the near-kernel modes of C^. Both approaches give rise to a novel class of preconditioners denoted as Enhanced RPF (ERPF). Furthermore, effectiveness and robustness of the proposed algorithms are demonstrated in both theoretical benchmarks and real-world large-size applications, outperforming the native RPF preconditioner.

97 MATHEMATICS AND COMPUTING↗