Brain functional network (BFN) has become an increasingly important tool to explore individual differences and identify neurological/mental diseases. For estimating a "good" BFN (with more discriminative information for example), researchers have developed various methods, in which the most popular and simplest is Pearson's correlation (PC). Despite its empirical effectiveness, PC only encodes the low-order (second-order) statistics between brain regions. To model high-order statistics, researchers recently proposed to estimate BFN by conducting two sequential PCs (denoted as PC 2 in this paper), and found that PC 2-based BFN can provide additional information for group difference analysis. This inspires us to think about (1) what will happen if continuing the correlation operation to construct much higher-order BFN by PC n (n>2), and (2) whether the higher-order correlation will result in stronger discriminative ability. To answer these questions, we use PC n -based BFNs to predict individual differences (Female vs. Male) as well as identify subjects with mild cognitive impairment (MCI) from healthy controls (HCs). Through experiments, we have the following findings: (1) with the increase of n, the discriminative ability of PC n -based BFNs tends to decrease; (2) fusing the PC n -based BFNs (n>1) with the PC 1-based BFN can generally improve the sensitivity for MCI identification, but fail to help the classification accuracy. In addition, we empirically find that the sequence of BFN adjacency matrices estimated by PC n (n = 1,2,3,⋯ ) will converge to a binary matrix with elements of ± 1.

中文翻译：

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脑功能网络：高阶与更多歧视。

脑功能网络（BFN）已成为探索个体差异和识别神经/精神疾病的越来越重要的工具。为了估计“好的”BFN（例如，具有更多判别信息），研究人员开发了各种方法，其中最流行和最简单的是 Pearson 相关性 (PC)。尽管其经验有效性，PC 仅编码大脑区域之间的低阶（二阶）统计数据。为了模拟高阶统计量，研究人员最近提出通过进行两个连续的 PC（本文中表示为 PC 2）来估计 BFN，并发现基于 PC 2 的 BFN 可以为组差异分析提供额外的信息。这激发了我们思考（1）如果继续相关操作以通过 PC n (n>2) 构造更高阶的 BFN 会发生什么，(2) 高阶相关性是否会导致更强的判别能力。为了回答这些问题，我们使用基于 PC n 的 BFN 来预测个体差异（女性与男性）以及从健康对照 (HC) 中识别出轻度认知障碍 (MCI) 的受试者。通过实验，我们有以下发现：（1）随着n的增加，基于PC n的BFNs的判别能力趋于下降；(2)将基于PC n的BFN(n>1)与基于PC 1的BFN融合，一般可以提高MCI识别的灵敏度，但不能提高分类精度。此外，我们凭经验发现由 PC n (n = 1,2,3,⋯) 估计的 BFN 邻接矩阵序列将收敛到元素为 ± 1 的二进制矩阵。