Spectral clustering is a well-known method for clustering the vertices of an undirected network. Although its use in network psychometrics has been limited, spectral clustering has a close relationship to the commonly used walktrap algorithm. In this article, we report results from simulation experiments designed to evaluate the ability of spectral clustering and the walktrap algorithm to recover underlying cluster (or community) structure in networks. The salient findings include: (a) the recovery performance of the walktrap algorithm can be improved by using K-means clustering instead of hierarchical clustering; (b) K-means and K-median clustering led to comparable recovery performance when used to cluster vertices based on the eigenvectors of Laplacian matrices in spectral clustering; (c) spectral clustering using the unnormalized Laplacian matrix generally yielded inferior cluster recovery in comparison to the other methods; (d) when the correct number of clusters was provided for the methods, spectral clustering using the normalized Laplacian matrix led to better recovery than the walktrap algorithm; and (e) when the correct number of clusters was not provided, the walktrap algorithm using the Q^w modularity index was better than spectral clustering using the eigengap heuristic at determining the appropriate number of clusters. Overall, both the walktrap algorithm and spectral clustering of the normalized Laplacian matrix are effective for partitioning the vertices of undirected networks, with the latter performing better in most instances.

中文翻译：

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网络心理测量中社区检测的谱聚类和walktrap算法的比较。

谱聚类是一种众所周知的用于对无向网络的顶点进行聚类的方法。尽管它在网络心理测量学中的使用受到了限制，但谱聚类与常用的 walktrap 算法有着密切的关系。在本文中，我们报告了旨在评估谱聚类和 walktrap 算法恢复网络中底层集群（或社区）结构的能力的模拟实验的结果。主要发现包括：（a）walktrap 算法的恢复性能可以通过使用 K-means 聚类而不是层次聚类来提高；(b) K均值和K- 在谱聚类中基于拉普拉斯矩阵的特征向量对顶点进行聚类时，中值聚类导致可比的恢复性能；(c) 与其他方法相比，使用非归一化拉普拉斯矩阵的谱聚类通常产生较差的聚类恢复；(d) 当为这些方法提供正确的聚类数量时，使用归一化拉普拉斯矩阵的谱聚类比 walktrap 算法有更好的恢复；(e) 当没有提供正确的簇数时，使用Q ^{w的 walktrap 算法}在确定适当的聚类数量时，模块化指数优于使用 eigengap 启发式的谱聚类。总的来说，walktrap 算法和归一化拉普拉斯矩阵的谱聚类对于划分无向网络的顶点都是有效的，后者在大多数情况下表现更好。