Brittany Fasy
Montana State University, MT·Mathematics & Statistics·Early-career
Data often have a "shape": loops in a network, holes in an image or clusters in a cloud of points. Topological data analysis (TDA) captures that shape with summaries called topological descriptors.
- Fields
Mathematics & Statistics
Computer Science
- Topics
topological data analysis
topological descriptors
topological transforms
- Grants
- 1 known grant, through Jun 2027
What they work on
- Quantify how well topological transforms, families of descriptors such as persistence diagrams or Euler characteristic curves computed over many directions or subspaces, represent a topological space.
- Reframe existing topological and data-analysis concepts as topological transforms and propose new transforms suited to large, complex data.
- Define distances between topological transforms and study them as distributions over spaces of descriptors, to enable statistical comparison of networks, images and point clouds.
More about the research
Examples include persistence diagrams, which record features that appear and disappear across scales, and Reeb graphs, skeleton-like sketches of a shape. These tools are powerful, but one descriptor often cannot capture large, complex, noisy real-world data, and comparing shapes remains hard.
Why it matters
The project adds mathematical understanding of how families of shape summaries can fully represent and compare complex spaces. The resulting tools could help scientists and data analysts summarize and compare large, noisy data sets such as networks, images and point clouds, and use shape information in statistical analyses.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Tao Hou
University of Oregon, OR·Computer Science
Devise efficient algorithms and new data structures for computing representatives, the concrete cycles in a dataset that realize each feature found by persistent homology, a tool tracking holes and loops across scales.
Arjun Krishnan
University of Colorado Denver/Anschutz Medical Campus, CO·Plant Science & Agriculture
Measure the total information in Arabidopsis leaf shape from X-ray CT scans using the Euler Characteristic Transform, and compare it with traditional shape measures to reveal hidden trait information.
Chul Moon
Southern Methodist University, TX·Mathematics & Statistics
Develop methods that pair a tumor's location with its topological shape features in three-dimensional MRI scans of gliomas, and test how these features relate to the tumors' genomic characteristics.
The school
Montana State University: 15 labs on PI Pages, $258M a year on research, 85 research doctorates a year.
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