Abstract
Recent development of high-throughput biotechnologies, such as Hi-C, have enabled genome-wide measurement of chromosomal conformation. The interaction signals among genomic loci are contaminated with noises. It remains largely unknown how well the underlying chromosomal conformation can be elucidated, based on massive and noisy measurements. We propose a new model-based distance embedding (MDE) framework, to reveal spatial organizations of chromosomes. The proposed framework is a general methodology, which allows us to link accurate probabilistic models, which characterize biological data properties, to efficiently recovering Euclidean distance matrices from noisy observations. The performance of MDE is shown through numerical experiments inspired by regular helix structure and random movement of chromosomes. The practical merits of MDE are also demonstrated by applications to real Hi-C data from both human and mouse cells which are further validated by gold standard benchmarks.
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