SCOREH+：一种用于社区检测的基于特征向量比值的高阶节点邻近度谱聚类算法
SCOREH+: A High-Order Node Proximity Spectral Clustering on Ratios-of-Eigenvectors Algorithm for Community Detection
AI总结：
本研究针对复杂网络社区检测问题，提出SCOREH+算法，通过优化高阶邻近度矩阵、弱信号图增设特征向量等改进，在多类网络中性能优于现有基线方法，可生成高质量社区结构。
摘要：
复杂网络研究在揭示网络介观特征方面已取得显著进展，社区检测是理解现实世界复杂系统的重要方向。本文提出一种用于复杂网络社区定位的高阶节点邻近度特征向量比值谱聚类（SCOREH+）算法。该算法对SCORE和SCORE+进行了改进，保留了网络亲和矩阵的高阶传递性信息。我们利用径向基函数（RBFs）和Katz指数，从初始亲和矩阵出发优化高阶邻近度矩阵。除了对拉普拉斯矩阵进行优化外，我们还实现了一个流程：若网络被判定为“弱信号”图，则将额外的一个特征向量（第k+1个主特征向量）加入谱域以进行聚类。该算法已成功应用于真实数据集与合成数据集。我们将所提算法与ASE、Louvain、Fast-Greedy、谱聚类（SC）、SCORE、SCORE+等现有先进算法进行了对比。为验证所提方法的高效性，我们在11个真实网络和多个含噪声的合成网络上开展了对比实验。在多数网络中的实验结果表明，SCOREH+的性能优于基线方法。此外，通过调整RBFs及其形状参数，我们可以在所有真实网络甚至含噪声的合成网络上生成达到当前最优水平的社区结构。
英文摘要：
The research on complex networks has achieved significant progress in revealing the mesoscopic features of networks. Community detection is an important aspect of understanding real-world complex systems. We present in this paper a High-order node proximity Spectral Clustering on Ratios-of-Eigenvectors (SCOREH+) algorithm for locating communities in complex networks. The algorithm improves SCORE and SCORE+ and preserves high-order transitivity information of the network affinity matrix. We optimize the high-order proximity matrix from the initial affinity matrix using the Radial Basis Functions (RBFs) and Katz index. In addition to the optimization of the Laplacian matrix, we implement a procedure that joins an additional eigenvector (the $(k+1)^{th}$ leading eigenvector) to the spectrum domain for clustering if the network is considered to be a "weak signal" graph. The algorithm has been successfully applied to both real-world and synthetic data sets. The proposed algorithm is compared with state-of-art algorithms, such as ASE, Louvain, Fast-Greedy, Spectral Clustering (SC), SCORE, and SCORE+. To demonstrate the high efficacy of the proposed method, we conducted comparison experiments on eleven real-world networks and a number of synthetic networks with noise. The experimental results in most of these networks demonstrate that SCOREH+ outperforms the baseline methods. Moreover, by tuning the RBFs and their shaping parameters, we may generate state-of-the-art community structures on all real-world networks and even on noisy synthetic networks.
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