Statistics Seminars: Introduction to Topological Data Analysis
23 November 2015 14:00 in CM221
Topological Data Analysis has emerged about 10 years ago as a revolutionary application of algebraic topology to multi-scale analysis of unstructured data such as point clouds. The key idea is to summarise topological changes when the data is progressively analysed across all scales. The resulting topological summary is provably stable under perturbations of original data. These topological tools helped identify a new type of breast cancer that has 100% survival rate and requires no surgery. Another application is a discovery that small patches in natural grayscale images are concentrated around a Klein bottle in a high-dimensional space. More applications to Computer Vision will be presented at the pure colloquium on Monday 23 November at 4pm in CM 107. We hope to initiate collaboration with statisticians to combine Topological Data Analysis with traditional methods of statistics and machine learning.
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