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September 17-18, 2017: Training
September 18-20, 2017: Tutorials & Conference
San Francisco, CA

Topological data analysis as a framework for machine intelligence

Gunnar Carlsson (Ayasdi)
1:30pm–5:00pm Monday, September 18, 2017
Implementing AI
Location: Yosemite A Level: Advanced
Secondary topics:  Data science and AI, Tools and frameworks
Average rating: *****
(5.00, 1 rating)

Prerequisite Knowledge

  • A basic understanding of the underlying concepts behind and algorithms for both supervised and unsupervised learning

What you'll learn

  • Explore topological data analysis, a framework for machine learning that synthesizes and combines machine learning algorithms to identify the shape of data

Description

Topological data analysis (TDA) is a framework for machine learning that synthesizes and combines machine learning algorithms to identify the shape of data. The technique is responsible for several major breakthroughs in our understanding of science and business. Gunnar Carlsson offers an overview of TDA’s mathematical underpinnings and its practical application through software.

TDA is based on a branch of pure mathematics called topology, which studies the notion of shape. Topology takes on two main tasks: the measurement of shape and the representation of shape. Both tasks are meaningful in the context of large, complex, and high-dimensional datasets. They permit you to measure shape-related properties within the data, such as the presence of loops, and they provide methods for creating compressed representations of datasets that retain features and reflect the relationships among points in the dataset in the form of a topological network or combinatorial graph—a very simple and intuitive object to work with using graph layout algorithms, which makes machine learning algorithms dramatically more effective.

Topics include:

  • How TDA uses maps or functions as input to produce a superior output
  • How TDA uses clustering in unsupervised applications to build a network representation of data
  • TDA support for the automatic execution and synthesis of dimensionality reduction algorithms
  • How TDA augments supervised learning algorithms by eliminating systematic errors and optimizing for local datasets
  • TDA’s collection or ensemble of models approach
Photo of Gunnar Carlsson

Gunnar Carlsson

Ayasdi

Gunnar Carlsson is a professor of mathematics (emeritus) at Stanford University and is cofounder and president at Ayasdi, which is commercializing products based on machine intelligence and topological data analysis. Gunnar has spent his career devoted to the study of topology, the mathematical study of shape. Originally, his work focused on the pure aspects of the field, but in 2000 he began work on the applications of topology to the analysis of large and complex datasets, which led to a number of projects, notably a multi-university initiative funded by the Defense Advanced Research Projects Agency. He has taught at the University of Chicago, the University of California, San Diego, Princeton University, and, since 1991, Stanford University, where he has served as the chair of the Mathematics Department. He is also a founder of the ATMCS series of conferences focusing on the applications of topology, and is a founding editor of the Journal for Applied and Computational Topology. Gunnar is the author of over 100 academic papers and has given numerous addresses to scholarly meetings. He holds a BA in mathematics from Harvard and a PhD in mathematics from Stanford. He is married with three grown children.