Geometry and topology of data

Credit: D. Merck and K. N. Keshavamurthy

In new directions, we seek to apply methods from coarse geometry and infinite metric spaces to thinking about large complex data sets. How does the geometric structure of a large point set determine its information theoretic aspects? How can we make inferences about metric geometry from sparse samples? How do we metrize and measure distance between data sets? Tools from geometry and topology developed in the infinite setting are ripe for applications, leading to the field of applied geometry and topology.

Related Papers

Machine learning algorithm for automatic detection of CT-identifiable hyperdense lesions associated with traumatic brain injury

Krishna N. Keshavamurthy; Owen P. Leary; Lisa H. Merck; Benjamin Kimia; Scott Collins; David W. Wright; Jason W. Allen; Jeffrey F. Brock; Derek Merck. Proc. SPIE 10134, Medical Imaging 2017: Computer-Aided Diagnosis, 101342G (March 23, 2017); DOI: 10.1117/12.2254227.

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