Kernel based statistic: identifying topological differences in brain networks

Abstract

Background

Brain network describing interconnections between brain regions contains abundant topological information. It is a challenge for the existing statistical methods (e.g., t test) to investigate the topological differences of brain networks.

Methods

We proposed a kernel based statistic framework for identifying topological differences in brain networks. In our framework, the topological similarities between paired brain networks were measured by graph kernels. Then, graph kernels are embedded into maximum mean discrepancy for calculating kernel based test statistic. Based on this test statistic, we adopted conditional Monte Carlo simulation to compute the statistical significance (i.e., P value) and statistical power. We recruited 33 patients with Alzheimer's disease (AD), 33 patients with early mild cognitive impairment (EMCI), 33 patients with late mild cognitive impairment (LMCI) and 33 normal controls (NC) in our experiment. There are no statistical differences in demographic information between patients and NC. The compared state-of-the-art statistical methods include t test, t squared test, two-sample permutation test and non-normal test.

Results

We applied the proposed shortest path matched kernel to our framework for investigating the statistical differences of shortest path topological structures in brain networks of AD and NC. We compared our method with the existing state-of-the-art statistical methods in brain network characteristic including clustering coefficient and functional connection among EMCI, LMCI, AD, and NC. The results indicate that our framework can capture the statistically discriminative shortest path topological structures, such as shortest path from right rolandic operculum to right supplementary motor area (P = 0.00314, statistical power = 0.803). In clustering coefficient and functional connection, our framework outperforms the state-of-the-art statistical methods, such as P = 0.0013 and statistical power = 0.83 in the analysis of AD and NC.

Conclusion

Our proposed kernel based statistic framework not only can be used to investigate the topological differences of brain network, but also can be used to investigate the static characteristics (e.g., clustering coefficient and functional connection) of brain network.