Using Topological Data Analysis on your BigDataAnalyticsWeek
Synopsis:
Topological Data Analysis (TDA) is a framework for data analysis and machine learning and represents a breakthrough in how to effectively use geometric and topological information to solve 'Big Data' problems. TDA provides meaningful summaries (in a technical sense to be described) and insights into complex data problems. In this talk, Anthony will begin with an overview of TDA and describe the core algorithm that is utilized. This talk will include both the theory and real world problems that have been solved using TDA. After this talk, attendees will understand how the underlying TDA algorithm works and how it improves on existing “classical” data analysis techniques as well as how it provides a framework for many machine learning algorithms and tasks.
Speaker:
Anthony Bak, Senior Data Scientist, Ayasdi
Prior to coming to Ayasdi, Anthony was at Stanford University where he did a postdoc with Ayasdi co-founder Gunnar Carlsson, working on new methods and applications of Topological Data Analysis. He completed his Ph.D. work in algebraic geometry with applications to string theory at the University of Pennsylvania and ,along the way, he worked at the Max Planck Institute in Germany, Mount Holyoke College in Germany, and the American Institute of Mathematics in California.
Topological Data Analysis: visual presentation of multidimensional data setsDataRefiner
Topology data analysis (TDA) is an unsupervised approach which may revolutionise the way data can be mined and eventually drive the new generation of analytical tools. The idea behind TDA is an attempt to "measure" shape of data and find compressed combinatorial representation of the shape. In ordinary topology, the combinatorial representations serve the purpose of providing the compressed representation of high dimensional data sets which retains information about the geometric relationships between data points. TDA can also be used as a very powerful clustering technique. Edward will present the comparison between TDA and other dimension reduction algorithms like PCA, LLE, Isomap, MDS, and Spectral Embedding.
Using Topological Data Analysis on your BigDataAnalyticsWeek
Synopsis:
Topological Data Analysis (TDA) is a framework for data analysis and machine learning and represents a breakthrough in how to effectively use geometric and topological information to solve 'Big Data' problems. TDA provides meaningful summaries (in a technical sense to be described) and insights into complex data problems. In this talk, Anthony will begin with an overview of TDA and describe the core algorithm that is utilized. This talk will include both the theory and real world problems that have been solved using TDA. After this talk, attendees will understand how the underlying TDA algorithm works and how it improves on existing “classical” data analysis techniques as well as how it provides a framework for many machine learning algorithms and tasks.
Speaker:
Anthony Bak, Senior Data Scientist, Ayasdi
Prior to coming to Ayasdi, Anthony was at Stanford University where he did a postdoc with Ayasdi co-founder Gunnar Carlsson, working on new methods and applications of Topological Data Analysis. He completed his Ph.D. work in algebraic geometry with applications to string theory at the University of Pennsylvania and ,along the way, he worked at the Max Planck Institute in Germany, Mount Holyoke College in Germany, and the American Institute of Mathematics in California.
Topological Data Analysis: visual presentation of multidimensional data setsDataRefiner
Topology data analysis (TDA) is an unsupervised approach which may revolutionise the way data can be mined and eventually drive the new generation of analytical tools. The idea behind TDA is an attempt to "measure" shape of data and find compressed combinatorial representation of the shape. In ordinary topology, the combinatorial representations serve the purpose of providing the compressed representation of high dimensional data sets which retains information about the geometric relationships between data points. TDA can also be used as a very powerful clustering technique. Edward will present the comparison between TDA and other dimension reduction algorithms like PCA, LLE, Isomap, MDS, and Spectral Embedding.
23. 穴の生死とパーシステントホモロジー
円の半径を 0 から大きくしていくことを考える.
a hole is born
at radius
接する
a hole is dead at radius
すると,ある r1 で穴が生じ,連続的に変化していって r2
で消える.この穴の種類と数に加えて,各穴の生死の情
報を保持しているのがパーシステンスホモロジーで
ある.
大林一平 (京大マイコンクラブ (KMC)/京都大学数学教室/JST-CREST)Topological data analysis 2015 年 3 月 KMC 春合宿 23 / 30
24. a hole is born
at radius
接する
a hole is dead at radius
穴の死の時刻 (半径) はおよそ穴の大きさを表して
いる
穴の生の時刻はループを構成する点の密度を表し
ている
生死の時刻差はそれが穴としてどれくらい意味が
あるか,を示している.
(ループを構成する点の密度)≈(穴の大きさ) ならばその
穴はあまり穴の体をなしていない
生死の時刻差が小さいならば,その穴はノイズ的なもの
と見なしてよい
大林一平 (京大マイコンクラブ (KMC)/京都大学数学教室/JST-CREST)Topological data analysis 2015 年 3 月 KMC 春合宿 24 / 30