Integration of Imaging Genomics Data for the Study of Alzheimer's Disease Using Joint-Connectivity-Based Sparse Nonnegative Matrix Factorization

Image genetics reveal the connection between microscopic genetics and macroscopic imaging and then detect diseases’ biomarkers. In this research, we make full use of the prior knowledge that has significant reference value for exploring the correlation of brain and genetics to explore more biologically substantial biomarkers. In this paper, we propose Joint-Connectivity-Based Sparse Nonnegative Matrix Factorization (JCB-SNMF). The algorithm simultaneously projects structural Magnetic Resonance Imaging (sMRI), Single Nucleotide Polymorphism sites (SNPs), and gene expression data onto a common feature space, where heterogeneous variables with large coefficients in the same projection direction form a common module. In addition, the connectivity information of each region of the brain and genetic data are added as prior knowledge to identify regions of interest (ROI), SNP, and gene-related risks related to Alzheimer's disease (AD) patients. GraphNet regularization increases the anti-noise performance of the algorithm and the biological interpretability of the results. The simulation results show that compared with other NMF-based algorithms (JNMF, JSNMNMF), JCB-SNMF has better anti-noise performance and can identify and predict biomarkers closely related to AD from significant modules. By constructing a protein-protein interaction network (PPI), we identified SF3B1, RPS20, and RBM14 as potential biomarkers of AD. We also find some significant SNP-ROI and Gene-ROI pairs. Among them, two SNPs of rs4472239 and rs11918049 and three genes of KLHL8, ZC3H11A, and OSGEPL1 may have effects on the gray matter volume of multiple brain regions. This model provides a new way to further integrate multimodal impact genetic data to identify complex disease association patterns.

Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing Based on Endmember Independence and Spatial Weighted Abundance

Hyperspectral image unmixing is an important task for remote sensing image processing. It aims at decomposing the mixed pixel of the image to identify a set of constituent materials called endmembers and to obtain their proportions named abundances. Recently, number of algorithms based on sparse nonnegative matrix factorization (NMF) have been widely used in hyperspectral unmixing with good performance. However, these sparse NMF algorithms only consider the correlation characteristics of abundance and usually just take the Euclidean structure of data into account, which can make the extracted endmembers become inaccurate. Therefore, with the aim of addressing this problem, we present a sparse NMF algorithm based on endmember independence and spatial weighted abundance in this paper. Firstly, it is assumed that the extracted endmembers should be independent from each other. Thus, by utilizing the autocorrelation matrix of endmembers, the constraint based on endmember independence is to be constructed in the model. In addition, two spatial weights for abundance by neighborhood pixels and correlation coefficient are proposed to make the estimated abundance smoother so as to further explore the underlying structure of hyperspectral data. The proposed algorithm not only considers the relevant characteristics of endmembers and abundances simultaneously, but also makes full use of the spatial-spectral information in the image, achieving a more desired unmixing performance. The experiment results on several data sets further verify the effectiveness of the proposed algorithm.

Hierarchical Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing with Spectral Variability

Accounting for endmember variability is a challenging issue when unmixing hyperspectral data. This paper models the variability that is associated with each endmember as a conical hull defined by extremal pixels from the data set. These extremal pixels are considered as so-called prototypal endmember spectra that have meaningful physical interpretation. Capitalizing on this data-driven modeling, the pixels of the hyperspectral image are then described as combinations of these prototypal endmember spectra weighted by bundling coefficients and spatial abundances. The proposed unmixing model not only extracts and clusters the prototypal endmember spectra, but also estimates the abundances of each endmember. The performance of the approach is illustrated thanks to experiments conducted on simulated and real hyperspectral data and it outperforms state-of-the-art methods.