Persistent Homology in Sparse Regression and Its Application to Brain Morphometry

Moo K. Chung, Jamie L. Hanson, Jieping Ye, Richard J. Davidson, Seth D. Pollak

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in drastically speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.

Original languageEnglish (US)
Article number7066892
Pages (from-to)1928-1939
Number of pages12
JournalIEEE Transactions on Medical Imaging
Volume34
Issue number9
DOIs
StatePublished - Sep 1 2015
Externally publishedYes

Keywords

  • GLASSO
  • maltreated children
  • persistent homology
  • sparse brain networks
  • sparse correlations
  • tensor-based morphometry

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering

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    Chung, M. K., Hanson, J. L., Ye, J., Davidson, R. J., & Pollak, S. D. (2015). Persistent Homology in Sparse Regression and Its Application to Brain Morphometry. IEEE Transactions on Medical Imaging, 34(9), 1928-1939. [7066892]. https://doi.org/10.1109/TMI.2015.2416271