In various fields of science and engineering one seeks to solve perceptual grouping problems. Such problems can often be formulated as finding the optimal partition of a graph, where vertices represent points in feature space and edge-weights represent similarity of pairs of points. The usual objective in such partitioning is the minimization of a balanced cut, which represents low inter-cluster similarity while maintaining a reasonable size of each of the parts. Computing the optimal balanced partitioning is usually NP-hard, however, it can be approximated to the minimization of a ratio of two functionals. In this work we examine the problem of minimizing generalized Rayleigh quotients of two one-homogeneous functionals. We present an iterative algorithm which is fully analyzed and prove convergence of the iterative scheme. We use our method to estimate the optimal Cheeger cut and show experimentally that our algorithm obtains high quality classification.
Modeling of the Genome Compartments – secondary research
Chromosome conformation capture techniques are a set of molecular biology methods used to analyze the spatial organization of chromatin in a cell. Hi-C quantifies interactions between all possible pairs of fragments simultaneously, which has highlighted the critical role of spatial organization and compartmentalization on gene expression and structural variation. Deep sequencing of Hi- interaction produces a pattern known as “Checkerboard” matrix that is characterize by two different genomic compartments that overlap with several bio-track. Two regions of the same type tend to interact at higher frequency than regions of different type. We present a mechanistic probability model that overcomes many difficulties of current methods and works well on very high resolutions and low-quality data. Thus, we can now start searching for more rare biological events that could not be discover previously.
*M.Sc. Seminar under the supervision of Prof. Guy Gilboa and Prof. Noam Kaplan.
BIO:
Tal Feld received the B.Sc. degree Mathematics and Physics from the Technion – Israel Institute of Technology, Haifa, Israel, in 2016. Currently, he pursues his M.Sc. degree in Electrical Engineering from the Technion under the co-supervision of Guy Gilboa from the Electrical Engineering department and Noam Kaplan from the Medicine department.