Graph-based clustering methods like spectral clustering and SpectralNet are very efficient in detecting clusters of non-convex shapes. Unlike the popular $k$-means, graph-based clustering methods do not assume that each cluster has a single mean. However, these methods need a graph where vertices in the same cluster are connected by edges of large weights. To achieve this goal, many studies have proposed graph reduction methods with parameters. Unfortunately, these parameters have to be tuned for every dataset. We introduce a graph reduction method that does not require any parameters. First, the distances from every point $p$ to its neighbors are filtered using an adaptive threshold to only keep neighbors with similar surrounding density. Second, the similarities with close neighbors are computed and only high similarities are kept. The edges that survive these two filtering steps form the constructed graph that was passed to spectral clustering and SpectralNet. The experiments showed that our method provides a stable alternative, where other methods performance fluctuated according to the setting of their parameters.

翻译：基于图的聚类方法（如谱聚类和SpectralNet）在检测非凸形状的聚类时非常有效。与流行的$k$-means算法不同，基于图的聚类方法不假设每个聚类具有单一均值。然而，这类方法需要构建一个图，其中同一聚类内的顶点由大权重的边连接。为实现这一目标，许多研究提出了带参数的图简化方法。遗憾的是，这些参数需要针对每个数据集进行调优。我们提出一种无需任何参数的图简化方法。首先，通过自适应阈值过滤每个点$p$到其邻居的距离，仅保留周围密度相似的邻居；其次，计算与近邻的相似度并仅保留高相似度边。经这两步过滤后存续的边构成最终图，并将其输入谱聚类与SpectralNet。实验表明，我们的方法提供了稳定的替代方案，而其他方法的性能则随参数设置波动。