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Methods and applications of topological data analysis

作者: Jennifer Novak Kloke; G Carlsson; Steve Kerckhoff; Rafe Mazzeo; Stanford University. Department of Mathematics.
出版商: 2010.
論文: Thesis (Ph. D.)--Stanford University, 2010.
版本/格式:   碩士/博士論文 : 文獻 : 碩士論文/博士論文 : 電子書   電腦資料 : 英語
資料庫:WorldCat
提要:
The focus of this dissertation is the development of methods for topological analysis as well as the application of topological tools to real world problems. The first half of the dissertation focuses on an algorithm for de-noising high-dimensional data for topological data analysis. This method significantly extends the applicability of many topological data analysis methods. In particular, this method extends the  再讀一些...
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資料類型: 文獻, 碩士論文/博士論文, 網際網路資源
文件類型: 網路資源, 電腦資料
所有的作者/貢獻者: Jennifer Novak Kloke; G Carlsson; Steve Kerckhoff; Rafe Mazzeo; Stanford University. Department of Mathematics.
OCLC系統控制編碼: 652792734
注意: Submitted to the Department of Mathematics.
描述: 1 online resource.
責任: Jennifer Novak Kloke.

摘要:

The focus of this dissertation is the development of methods for topological analysis as well as the application of topological tools to real world problems. The first half of the dissertation focuses on an algorithm for de-noising high-dimensional data for topological data analysis. This method significantly extends the applicability of many topological data analysis methods. In particular, this method extends the use of persistent homology, a generalized notion of homology for discrete data points, to data sets that were previously inaccessible because of noise. The second half of this dissertation focuses on a method for using topology to simplify complex chemical structures and to define a metric to quantify similarity for use in screening large databases of chemical compounds. This method has shown very promising initial results in locating new materials for efficiently separating carbon dioxide from the exhaust of coal-burning power plants.

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