Greedy low-rank algorithm for spatial connectome regression

Patrick Kürschner, Sergey Dolgov, Kameron Decker Harris, Peter Benner

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)


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. in Neural Information Processing Systems, 2016), but existing techniques do not scale to the whole-brain setting. The corresponding matrix equation is challenging to solve due to large scale, ill-conditioning, and a general form that lacks a convergent splitting. We propose a greedy low-rank algorithm for the connectome reconstruction problem in very high dimensions. The algorithm approximates the solution by a sequence of rank-one updates which exploit the sparse and positive definite problem structure. This algorithm was described previously (Kressner and Sirković in Numer Lin Alg Appl 22(3):564–583, 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 sub-problems 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 whole-cortex 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 a good approximation. This speedup allows for the estimation of increasingly large-scale connectomes across taxa as these data become available from tracing experiments. The data and code are available online.

Original languageEnglish
Article number9
JournalThe Journal of Mathematical Neuroscience
Issue number1
Early online date14 Nov 2019
Publication statusPublished - 1 Dec 2019


  • Computational neuroscience
  • Low-rank approximation
  • Matrix equations
  • Networks

ASJC Scopus subject areas

  • Neuroscience (miscellaneous)


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