Multiresolution orthonormal projective nonnegative matrix factorization for large surface data
Poster No:
1869
Submission Type:
Abstract Submission
Authors:
Sung Min Ha1, Abdalla Bani1, Braden Yang1, Deydeep Kothapalli1, Thomas Earnest1, Pan Xiao1, John Lee1, Theodore Satterthwaite2, Janine Bijsterbosch1, Matthew Glasser1, Adam Bauer1, Nico Dosenbach1, Deanna Barch1, Aristeidis Sotiras1
Institutions:
1Washington University in St. Louis, St. Louis, MO, 2University of Pennsylvania, Philadelphia, PA
First Author:
Co-Author(s):
Introduction:
Recent strides in in vivo neuroimaging technology and image analysis techniques, such as the Human Connectome Project (Glasser et al. 2016), have ushered in an era of high-resolution, large-scale neuroimaging surface data. The availability of such data necessitates the development of data-driven analysis approaches to gain deeper insights into human brain structure and disease from big data. Orthonormal projective nonnegative matrix factorization (opNMF) (Yang et al. 2010) has exhibited promising outcomes in the realm of neuroimaging analysis, yielding interpretable and reproducible patterns (Sotiras et al. 2015). Nevertheless, the application of opNMF on large-scale datasets has been impeded by its computationally intensive nature, characterized by large memory footprint and long runtime. In response, we present a new approach, multiresolution-opNMF (m-opNMF), which leverages graph reduction with spectral guarantees, thereby improving scalability without compromising the performance of opNMF.
Methods:
opNMF approximates a nonnegative matrix X as multiplication of two smaller nonnegative matrices, W and H, by minimizing the cost function, frobenius norm of X-WH. Employing a graph coarsening method with preserved spectral properties (Loukas 2019), m-opNMF sequentially reduces the surface in X to progressively lower resolutions. Subsequently, m-opNMF refines the matrices W and H across these resolutions, starting from the coarsest (Fig 1). This strategy enables the implementation of the iterative updates at lower resolutions, resulting in quicker runtime and a reduced memory footprint.
Results:
We included cortical thickness (CT) from baseline T1 MRI scans of 1,036 subjects (361 males, age 69.77 ± 9.53 years, Clinical Dementia Rating from 0 to 2) of Open Access Series of Imaging Studies 3. (Lamontagne et al. 2019) After undergoing the FreeSurfer pipeline, CT values were vectorized and concatenated to create X∈R^(149,955×1,036). We performed graph coarsening for m-opNMF with rank k=20 and reduction ratios (r_reduction) {0.5, 0.75, 0.875}, each with multiple resolutions and the lowest resolution containing approximately {1/2, 1/4, 1/8} vertices.
Frobenius norm of X-WH measured the reconstruction error, while the sparsity of component W evaluated the spatial specificity. Adjusted Rand Index (ARI), mean and median inner products of W were utilized to measure how well m-opNMF replicated the opNMF W. Total runtime gauged the computational loads.
Reconstruction errors were strikingly similar between the two methods (Fig 2a), and the sparsity values were also closely matched (Fig 2b). ARI value greater than 0.6 is typically considered good reproducibility in neuroimaging data. m-opNMF showed ARI≥0.6 for its reproduction of opNMF components for r_reduction=0.875 (Fig 2d). High mean and median inner product values echoed the high reproducibility of m-opNMF to opNMF (Fig 2e, 2f). These results underscored that m-opNMF not only performs on par with opNMF quantitatively, but also generates similar components. Consequently, the W derived from m-opNMF can readily serve as substitutes for opNMF components. Visualizations, where winner-takes-all approach was used to assign most prominent component rank to each vertex to create parcellations, confirmed the component similarity for r_reduction=0.875 (Fig 2j).
Most importantly, m-opNMF generated such components with comparable quality and similar composition at reduced runtime of less than a quarter of opNMF (Fig 2c).
Frobenius norm of X-WH measured the reconstruction error, while the sparsity of component W evaluated the spatial specificity. Adjusted Rand Index (ARI), mean and median inner products of W were utilized to measure how well m-opNMF replicated the opNMF W. Total runtime gauged the computational loads.
Reconstruction errors were strikingly similar between the two methods (Fig 2a), and the sparsity values were also closely matched (Fig 2b). ARI value greater than 0.6 is typically considered good reproducibility in neuroimaging data. m-opNMF showed ARI≥0.6 for its reproduction of opNMF components for r_reduction=0.875 (Fig 2d). High mean and median inner product values echoed the high reproducibility of m-opNMF to opNMF (Fig 2e, 2f). These results underscored that m-opNMF not only performs on par with opNMF quantitatively, but also generates similar components. Consequently, the W derived from m-opNMF can readily serve as substitutes for opNMF components. Visualizations, where winner-takes-all approach was used to assign most prominent component rank to each vertex to create parcellations, confirmed the component similarity for r_reduction=0.875 (Fig 2j).
Most importantly, m-opNMF generated such components with comparable quality and similar composition at reduced runtime of less than a quarter of opNMF (Fig 2c).
Conclusions:
m-opNMF reproduces the interpretable components of opNMF on high-resolution surface data, all the while avoiding the computational burdens associated with opNMF. Quantitative performance is virtually identical, while reproducibility metrics, both quantitative and qualitative, demonstrate sufficient similarity at higher r_reduction to function as drop-in replacement of opNMF. Furthermore, m-opNMF exhibits significantly reduced runtime, promising broader applications to large-scale data.
Lifespan Development:
Aging
Modeling and Analysis Methods:
Methods Development 1
Multivariate Approaches 2
Segmentation and Parcellation
Other Methods
Keywords:
Data analysis
Machine Learning
MRI
Multivariate
Segmentation
Other - Nonnegative Matrix Factorization; Dimensionality Reduction
1|2Indicates the priority used for review
Provide references using author date format
Lamontagne, P. J. (2019), OASIS-3: Longitudinal Neuroimaging, Clinical, and Cognitive Dataset for Normal Aging and Alzheimer Disease. medRxiv. doi:10.1101/2019.12.13.19014902.
Loukas, A. (2019). Graph Reduction with Spectral and Cut Guarantees. Journal of Machine Learning Research. vol. 20, no. 116, pp. 1-42.
Sotiras, A. (2015). Finding imaging patterns of structural covariance via Non-Negative Matrix Factorization. NeuroImage. vol. 108, pp. 1-16. doi:10.1016/j.neuroimage.2014.11.045.
Yang, Z. (2010). Linear and nonlinear projective nonnegative matrix factorization. IEEE Transactions on Neural Networks. vol. 21, no. 5, pp. 734-749. doi:10.1109/TNN.2010.2041361.