Tao Hou
University of Oregon, OR·Computer Science
Complex data often have a shape, such as loops, clusters or holes, that standard statistical methods miss. Topological data analysis (TDA) uses topology, the branch of mathematics that studies properties unchanged by bending and stretching, to describe that shape.
- Fields
Computer Science
Mathematics & Statistics
- Topics
topological data analysis
persistent homology
zigzag persistence
- Grants
- 1 known grant, through Mar 2027
What they work on
- 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.
- Develop algorithms to compute vines and vineyards, records of how persistence summaries change as data are updated, for both standard persistence and zigzag persistence, which handles data that grow and shrink.
- Build efficient software implementing these computations, and clarify the link between the mathematical objects of persistence and their algorithmic interpretation.
More about the research
Several of the most useful TDA descriptors are hard to use in practice because nobody knows how efficiently they can be computed. This project aims to design fast algorithms and software for computing them.
Why it matters
Topological descriptors can reveal hidden structure in complex datasets, but slow or poorly understood computation limits their use. Efficient algorithms and software for persistence representatives and vineyards could make these tools practical for data analysts. This would allow them to locate meaningful features in data and follow how those features change as the data evolve.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Brittany Fasy
Montana State University, MT·Mathematics & Statistics·Early-career
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.
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.
Mohammed Qazi
Tuskegee University, AL·Mathematics & Statistics
Develop the mathematics of diffusion models for generative AI, which create new data by reversing a noising process, using stochastic modeling with applications such as wireless communications.
The school
University of Oregon: 14 labs on PI Pages, $175M a year on research, 219 research doctorates a year.
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