Welcome to the Topology, Geometry and  Statistics  lab led by professors Lizhen Lin and Dong Quan Nguyen!

The goal of our lab is to study broad statistical and machine learning problems arising in data science with main applications in biomedical fields.  One of our key insights are to employ geometric and topological tools such as persistent homology from algebraic topology for mining complex data arising in medical imaging, neuroscience, network analysis,  DNA sequence analysis and so on.  Some of our recent work have been focusing on using persistent homology for DNA sequence  analysis by viewing  DNA sequences as topological and geometric objects such as persistence diagrams, persistence landscapes and persistence images,  which we call Persistence DNA Analysis (Per DNA analysis). 

Our research can be summarized in the following four general categories.

We gratefully acknowledge the funding support from NSF DMS program, NSF IIS program, Army's Research Office and DARPA. 

Geometry and Statistics

Geometry and Statistics

Geometry (e.g., differential geometry, Riemannian geometry, information geometry and Algebraic geometry) is inherent in many areas of statistics with geometry is either unknown or to be learnt, which should be incorporated or utilized for inference.
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Persistence DNA, RNA and Protein Analysis

Persistence DNA, RNA and Protein Analysis

Algebraic topological and geometric tools are employed to represent DNA sequences as topological objects using the idea of persistent homology. The space of these topological objects such as persistence landscape will be equipped with a Hibertian structure allowing the use of machine learning tools such as kernel-based methods for further downstream analysis.
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Network Analysis

Network Analysis

Algebraic and geometric tools are utilized for network analysis leveraging insights from algebraic topology and geometry. Bayesian modeling strategies are also considered for network models. Multiplex and dynamic networks are primary objects of study.
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Big Data Analysis

Big Data Analysis

The focus is on (1) learning lower-dimensional structure of big data; (2) estimation and hypothesis testing of covariance matrices of high-dimensional data; (3) developing dividing and conquering strategy of big data analysis.
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News and Announcements

New papers on persistent DNA analysis!!

Nguyen et al. (2021). A topological characterization of DNA sequences based on chaos geometry and persistent homology.

Nguyen et al. (2021). A topological approach to DNA similarity analysis from 5-dimensional representation.pdf.