Finding imaging patterns of structural covariance via Non-Negative Matrix Factorization

Abstract

In this paper, we investigate the use of Non-Negative Matrix Factorization (NNMF) for the analysis of structural neuroimaging data. The goal is to identify the brain regions that co-vary across individuals in a consistent way, hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies. NNMF offers a directly data-driven way of extracting relatively localized co-varying structural regions, thereby transcending limitations of Principal Component Analysis (PCA), Independent Component Analysis (ICA) and other related methods that tend to produce dispersed components of positive and negative loadings. In particular, leveraging upon the well known ability of NNMF to produce parts-based representations of image data, we derive decompositions that partition the brain into regions that vary in consistent ways across individuals. Importantly, these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split-sample experiments. We empirically validate NNMF in two data sets: i) a Diffusion Tensor (DT) mouse brain development study, and ii) a structural Magnetic Resonance (sMR) study of human brain aging. We demonstrate the ability of NNMF to produce sparse parts-based representations of the data at various resolutions. These representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes. Moreover, we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like PCA and ICA.

Abnormality Detection via Iterative Deformable Registration and Basis-Pursuit Decomposition

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Determining Projections of Grain Boundaries from Diffraction Data in Transmission Electron Microscope

“…in ranging from biology (Sotiras et al, 2015, Brunet et al, 2004, nuclear sciences or in to computer sciences (e. g. signal processing and pattern recognition; Smaragdis et al, 2003, Buciu et al, 2004). Devarajan's work focuses on the field of computational biology, however it also gives a remarkable outlook to the capabilities of NMF-analysis (Devarajan, 2008).…”

Computational neuroanatomy using brain deformations: From brain parcellation to multivariate pattern analysis and machine learning

“…NNMF has gained a great deal of attention in the computer vision field, where it has shown to effectively achieve parts-based decompositions of images into meaningful components, not otherwise obtained via commonly used PCA- and ICA-types of methods. Sotiras et al (2015) applied this method to brain MRI images, and discovered structural brain networks that display coordinated change across individuals. Such components might reflect the influence of underlying neurodevelopmental and neurodegenerative biological processes that affect brain structure and function in coordinated ways that are manifested by statistical covariance.…”