Fast Parallel Randomized Algorithm for Nonnegative Matrix Factorization with KL Divergence for Large Sparse Datasets

Nonnegative Matrix Factorization (NMF) with Kullback-Leibler Divergence (NMF-KL) is one of the most significant NMF problems and equivalent to Probabilistic Latent Semantic Indexing (PLSI), which has been successfully applied in many applications. For sparse count data, a Poisson distribution and KL divergence provide sparse models and sparse representation, which describe the random variation better than a normal distribution and Frobenius norm. Specially, sparse models provide more concise understanding of the appearance of attributes over latent components, while sparse representation provides concise interpretability of the contribution of latent components over instances. However, minimizing NMF with KL divergence is much more difficult than minimizing NMF with Frobenius norm; and sparse models, sparse representation and fast algorithms for large sparse datasets are still challenges for NMF with KL divergence. In this paper, we propose a fast parallel randomized coordinate descent algorithm having fast convergence for large sparse datasets to archive sparse models and sparse representation. The proposed algorithm's experimental results overperform the current studies' ones in this problem

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

AbstractGrain boundaries (GB) are characterized by disorientation of the neighboring grains and the direction of the boundary plane between them. A new approach presented here determines the projection of GB that can be used to determine the latter one. The novelty is that an additional parameter of GB is quantified in addition to the ones provided by the orientation maps, namely the width of the projection of the GB is measured from the same set of diffraction patterns that were recorded for the orientation map, without the need to take any additional images. The diffraction patterns are collected in nanobeam diffraction mode in a transmission electron microscope, pixel-by-pixel, from an area containing two neighboring grains and the boundary between them. In our case, the diffraction patterns were recorded using the beam scanning function of a commercially available system (ASTAR). Our method is based on non-negative matrix factorization applied to the mentioned set of diffraction patterns. The method is encoded in a MATLAB environment, making the results easy to interpret and visualize. The measured GB-projection width is used to determine the orientation of the GB-plane, as given in the study by Kiss et al.</jats:p

Investigating microstructural variation in the human hippocampus using non-negative matrix factorization

In this work we use non-negative matrix factorization to identify patterns of microstructural variance in the human hippocampus. We utilize high-resolution structural and diffusion magnetic resonance imaging data from the Human Connectome Project to query hippocampus microstructure on a multivariate, voxelwise basis. Application of non-negative matrix factorization identifies spatial components (clusters of voxels sharing similar covariance patterns), as well as subject weightings (individual variance across hippocampus microstructure). By assessing the stability of spatial components as well as the accuracy of factorization, we identified 4 distinct microstructural components. Furthermore, we quantified the benefit of using multiple microstructural metrics by demonstrating that using three microstructural metrics (T1-weighted/T2-weighted signal, mean diffusivity and fractional anisotropy) produced more stable spatial components than when assessing metrics individually. Finally, we related individual subject weightings to demographic and behavioural measures using a partial least squares analysis. Through this approach we identified interpretable relationships between hippocampus microstructure and demographic and behavioural measures. Taken together, our work suggests non-negative matrix factorization as a spatially specific analytical approach for neuroimaging studies and advocates for the use of multiple metrics for data-driven component analyses

Human Microbe-Disease Association Prediction With Graph Regularized Non-Negative Matrix Factorization

A microbe is a microscopic organism which may exists in its single-celled form or in a colony of cells. In recent years, accumulating researchers have been engaged in the field of uncovering microbe-disease associations since microbes are found to be closely related to the prevention, diagnosis, and treatment of many complex human diseases. As an effective supplement to the traditional experiment, more and more computational models based on various algorithms have been proposed for microbe-disease association prediction to improve efficiency and cost savings. In this work, we developed a novel predictive model of Graph Regularized Non-negative Matrix Factorization for Human Microbe-Disease Association prediction (GRNMFHMDA). Initially, microbe similarity and disease similarity were constructed on the basis of the symptom-based disease similarity and Gaussian interaction profile kernel similarity for microbes and diseases. Subsequently, it is worth noting that we utilized a preprocessing step in which unknown microbe-disease pairs were assigned associated likelihood scores to avoid the possible negative impact on the prediction performance. Finally, we implemented a graph regularized non-negative matrix factorization framework to identify potential associations for all diseases simultaneously. To assess the performance of our model, cross validations including global leave-one-out cross validation (LOOCV) and local LOOCV were implemented. The AUCs of 0.8715 (global LOOCV) and 0.7898 (local LOOCV) proved the reliable performance of our computational model. In addition, we carried out two types of case studies on three different human diseases to further analyze the prediction performance of GRNMFHMDA, in which most of the top 10 predicted disease-related microbes were verified by database HMDAD or experimental literatures

Inter- and intra-individual variation in brain structural-cognition relationships in aging

The sources of inter- and intra-individual variability in age-related cognitive decline remain poorly understood. We examined the association between 20-year trajectories of cognitive decline and multimodal brain structure and morphology in older age. We used the Whitehall II Study, an extensively characterised cohort with 3T brain magnetic resonance images acquired at older age (mean age = 69.52 ± 4.9) and 5 repeated cognitive performance assessments between mid-life (mean age = 53.2 ±4.9 years) and late-life (mean age = 67.7 ± 4.9). Using non-negative matrix factorization, we identified 10 brain components integrating cortical thickness, surface area, fractional anisotropy, and mean and radial diffusivities. We observed two latent variables describing distinct brain-cognition associations. The first describes variations in 5 structural components associated with low mid-life performance across multiple cognitive domains, decline in reasoning, but maintenance of fluency abilities. The second describes variations in 6 structural components associated with low mid-life performance in fluency and memory, but retention of multiple abilities. Expression of latent variables predicts future cognition 3.2 years later (mean age = 70.87 ± 4.9). This data-driven approach highlights brain-cognition relationships wherein individuals degrees of cognitive decline and maintenance across diverse cognitive functions are both positively and negatively associated with markers of cortical structure