Mapping Heritability of LargeScale Brain Networks with a Billion Connections {\em via} Persistent Homology
Abstract
In many human brain network studies, we do not have sufficient number (n) of images relative to the number (p) of voxels due to the prohibitively expensive cost of scanning enough subjects. Thus, brain network models usually suffer the smalln largep problem. Such a problem is often remedied by sparse network models, which are usually solved numerically by optimizing L1penalties. Unfortunately, due to the computational bottleneck associated with optimizing L1penalties, it is not practical to apply such methods to construct largescale brain networks at the voxellevel. In this paper, we propose a new scalable sparse network model using crosscorrelations that bypass the computational bottleneck. Our model can build sparse brain networks at the voxel level with p > 25000. Instead of using a single sparse parameter that may not be optimal in other studies and datasets, the computational speed gain enables us to analyze the collection of networks at every possible sparse parameter in a coherent mathematical framework via persistent homology. The method is subsequently applied in determining the extent of heritability on a functional brain network at the voxellevel for the first time using twin fMRI.
 Publication:

arXiv eprints
 Pub Date:
 September 2015
 DOI:
 10.48550/arXiv.1509.04771
 arXiv:
 arXiv:1509.04771
 Bibcode:
 2015arXiv150904771C
 Keywords:

 Computer Science  Artificial Intelligence;
 Quantitative Biology  Neurons and Cognition;
 Statistics  Machine Learning