Testing whether two graphs come from the same distribution is of interest in many real-world scenarios, including brain network analysis. Under the random dot product graph model, the nonparametric hypothesis testing framework consists of embedding the graphs using the adjacency spectral embedding (ASE), followed by aligning the embeddings using the median flip heuristic and finally applying the nonparametric maximum mean discrepancy (MMD) test to obtain a p value. Using synthetic data generated from Drosophila brain networks, we show that the median flip heuristic results in an invalid test and demonstrate that optimal transport Procrustes (OTP) for alignment resolves the invalidity. We further demonstrate that substituting the MMD test with the multiscale graph correlation (MGC) test leads to a more powerful test both in synthetic and in simulated data. Lastly, we apply this powerful test to the right and left hemispheres of the larval Drosophila mushroom body brain networks and conclude that there is not sufficient evidence to reject the null hypothesis that the two hemispheres are equally distributed.

中文翻译：

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通过优化传输 Procrustes 和多尺度图相关性与连接组学中的应用进行有效的两样本图测试

测试两个图是否来自同一分布在许多现实世界场景中都很有趣，包括大脑网络分析。在随机点积图模型下，非参数假设检验框架包括使用邻接谱嵌入 (ASE) 嵌入图，然后使用中值翻转启发式对齐嵌入，最后应用非参数最大均值差异 (MMD) 检验获得一个p值。使用从果蝇生成的合成数据在大脑网络中，我们展示了中值翻转启发式导致无效测试，并证明用于对齐的最佳传输 Procrustes (OTP) 解决了无效性。我们进一步证明，用多尺度图相关 (MGC) 测试代替 MMD 测试会导致在合成数据和模拟数据中进行更强大的测试。最后，我们将这一强有力的测试应用于幼虫果蝇蘑菇体脑网络的左右半球，并得出结论，没有足够的证据来拒绝两个半球均匀分布的零假设。