Topological Methods for Data Fusion
Final rept. 1 Jul 2009-31 Dec 2013
STANFORD UNIV CA
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The project has studied a number of questions related to data fusion. One is the investigation of zig-zag persistent homology, which is a tool which permits one to study the behavior of qualitative shape invariants such as homology across different samples from a larger data set, as well as understand time varying data sets. We have also demonstrated the utility of the Mapper methodology in the study of various different data types, by demonstrating that it provides insight into complex data sets that allow one to obtain useful knowledge concerning the data. In addition, we have constructed a coordinatization of the space of persistence barcodes, which will be very useful in allowing the application of traditional machine learning to data sets where the entries themselves carry geometric structure, such as chemical compounds. We have also applied earlier topological findings to construct compression schemes as well as algorithms for discriminating between types of texture patches.
- Operations Research