Greedy lowrank algorithm for spatial connectome regression
Abstract
Recovering brain connectivity from tract tracing data is an important computational problem in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as a structured matrix regression problem (Harris et al., 2016), but existing techniques do not scale to the wholebrain setting. The corresponding matrix equation is challenging to solve due to large scale, illconditioning, and a general form that lacks a convergent splitting. We propose a greedy lowrank algorithm for connectome reconstruction problem in very high dimensions. The algorithm approximates the solution by a sequence of rankone updates which exploit the sparse and positive definite problem structure. This algorithm was described previously (Kressner and Sirković, 2015) but never implemented for this connectome problem, leading to a number of challenges. We have had to design judicious stopping criteria and employ efficient solvers for the three main subproblems of the algorithm, including an efficient GPU implementation that alleviates the main bottleneck for large datasets. The performance of the method is evaluated on three examples: an artificial "toy" dataset and two wholecortex instances using data from the Allen Mouse Brain Connectivity Atlas. We find that the method is significantly faster than previous methods and that moderate ranks offer good approximation. This speedup allows for the estimation of increasingly largescale connectomes across taxa as these data become available from tracing experiments. The data and code are available online.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.05510
 Bibcode:
 2018arXiv180805510K
 Keywords:

 Mathematics  Numerical Analysis;
 15A24;
 15A83;
 65F10 92C20;
 94A08