Directional clustering through matrix factorization

This paper deals with a clustering problem where feature vectors are clustered depending on the angle between feature vectors, that is, feature vectors are grouped together if they point roughly in the same direction. This directional distance measure arises in several applications, including document classification and human brain imaging. Using ideas from the field of constrained low-rank matrix factorization and sparse approximation, a novel approach is presented that differs from classical clustering methods, such as seminonnegative matrix factorization, K-EVD, or k-means clustering, yet combines some aspects of all these. As in nonnegative matrix factorization and K-EVD, the matrix decomposition is iteratively refined to optimize a data fidelity term; however, no positivity constraint is enforced directly nor do we need to explicitly compute eigenvectors. As in k-means and K-EVD, each optimization step is followed by a hard cluster assignment. This leads to an efficient algorithm that is shown here to outperform common competitors in terms of clustering performance and/or computation speed. In addition to a detailed theoretical analysis of some of the algorithm's main properties, the approach is empirically evaluated on a range of toy problems, several standard text clustering data sets, and a high-dimensional problem in brain imaging, where functional magnetic resonance imaging data are used to partition the human cerebral cortex into distinct functional regions

Multiscale, multimodal analysis of tumor heterogeneity in IDH1 mutant vs wild-type diffuse gliomas.

Glioma is recognized to be a highly heterogeneous CNS malignancy, whose diverse cellular composition and cellular interactions have not been well characterized. To gain new clinical- and biological-insights into the genetically-bifurcated IDH1 mutant (mt) vs wildtype (wt) forms of glioma, we integrated data from protein, genomic and MR imaging from 20 treatment-naïve glioma cases and 16 recurrent GBM cases. Multiplexed immunofluorescence (MxIF) was used to generate single cell data for 43 protein markers representing all cancer hallmarks, Genomic sequencing (exome and RNA (normal and tumor) and magnetic resonance imaging (MRI) quantitative features (protocols were T1-post, FLAIR and ADC) from whole tumor, peritumoral edema and enhancing core vs equivalent normal region were also collected from patients. Based on MxIF analysis, 85,767 cells (glioma cases) and 56,304 cells (GBM cases) were used to generate cell-level data for 24 biomarkers. K-means clustering was used to generate 7 distinct groups of cells with divergent biomarker profiles and deconvolution was used to assign RNA data into three classes. Spatial and molecular heterogeneity metrics were generated for the cell data. All features were compared between IDH mt and IDHwt patients and were finally combined to provide a holistic/integrated comparison. Protein expression by hallmark was generally lower in the IDHmt vs wt patients. Molecular and spatial heterogeneity scores for angiogenesis and cell invasion also differed between IDHmt and wt gliomas irrespective of prior treatment and tumor grade; these differences also persisted in the MR imaging features of peritumoral edema and contrast enhancement volumes. A coherent picture of enhanced angiogenesis in IDHwt tumors was derived from multiple platforms (genomic, proteomic and imaging) and scales from individual proteins to cell clusters and heterogeneity, as well as bulk tumor RNA and imaging features. Longer overall survival for IDH1mt glioma patients may reflect mutation-driven alterations in cellular, molecular, and spatial heterogeneity which manifest in discernable radiological manifestations

An Independent Component Analysis Based Tool for Exploring Functional Connections in the Brain

This thesis describes the use of independent component analysis (ICA) as a measure of voxel similarity, which allows the user to find and view statistically independent maps of correlated voxel activity. The tool developed in this work uses a specialized clustering technique, designed to find and characterize clusters of activated voxels, to compare the independent component spatial maps across patients. This same method is also used to compare SPM results across patients