The recently emerged spectral clustering surpasses conventional clustering methods by detecting clusters of any shape without the convexity assumption. Unfortunately, with a computational complexity of $O(n^3)$, it was infeasible for multiple real applications, where $n$ could be large. This stimulates researchers to propose the approximate spectral clustering (ASC). However, most of ASC methods assumed that the number of clusters $k$ was known. In practice, manual setting of $k$ could be subjective or time consuming. The proposed algorithm has two relevance metrics for estimating $k$ in two vital steps of ASC. One for selecting the eigenvectors spanning the embedding space, and the other to discover the number of clusters in that space. The algorithm used a growing neural gas (GNG) approximation, GNG is superior in preserving input data topology. The experimental setup demonstrates the efficiency of the proposed algorithm and its ability to compete with similar methods where $k$ was set manually.

翻译：最近出现的光谱聚集通过探测任何形状的集群,而不假定杂交,超过了常规集聚方法。不幸的是,由于计算复杂度为O(n)3美元,对于多种实际应用是行不通的,因为美元可能很大。这促使研究人员提出近似光谱聚集(ASC)建议。然而,大多数光谱聚集方法假定,聚集数是已知的。在实践中,人工设定美元可能是主观的或耗时的。提议的算法在ASC的两个关键步骤中有两个相关的指标用于估算美元。一个是选择嵌入空间的精子,另一个是发现该空间的组数。算法使用了不断增长的神经气体近似值,GNG在保存输入数据表学方面优势。实验设置显示了拟议算法的效率及其与以人工方式设定美元为单位的类似方法进行竞争的能力。