AF:Small: Novel Geometric Techniques for Several Biomedical Problems

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Recent progress in biomedicine has relied heavily on computer science technology. As the territory of biomedicine is rapidly enlarging, more powerful computational techniques are needed to foster its continuous growth. This project develops efficient computer algorithms for three fundamental geometric problems arising in several biomedical applications: (1) Truth Discovery, (2) Abnormal Clusters Detection, and (3) Resource Allocation Voronoi Diagram. Problem (1) develops quality-guaranteed polynomial time solutions to a key problem in data crowdsourcing, finding trustworthy information from multiple data sources, which is also motivated by the biomedical problem of learning critical information for improving treatment planning of endovascular intervention. Problem (2) detects extremely small-sized abnormal clusters from large datasets, which is motivated by detecting genomic structure variants from large populations. Problem (3) investigates new generalizations of the classical Voronoi diagram, which are motivated by a segmentation problem of biological images. This project will provide educational and research opportunities to undergraduate and graduate students (including those from under-represented groups), and develop a teaching evaluation tool for improving the quality of education. This project uses computational geometry techniques to develop novel algorithms for the proposed problems. It will introduce several general algorithmic techniques to the area of computational geometry, enriching and prodding its further development. These algorithmic techniques are also likely to be used in other areas, such as machine learning, computer vision, data mining, and pattern recognition, and bring new ideas to these areas. This project could lead to several long term impacts. It could potentially improve the quality of endovascular intervention, help identifying potential genomic structural variants in some genetic disorders, and provide more accurate quantitative information for medical image analysis.