Spectral clustering (SC) is one of the most popular clustering methods and often outperforms traditional clustering methods. SC uses the eigenvectors of a Laplacian matrix calculated from a similarity matrix of a dataset. SC has serious drawbacks that are the significant increase in the computational complexity derived from the eigendecomposition and the memory space complexities to store the similarity matrix. To address the issues, I develop a new approximate spectral clustering using the network generated by growing neural gas (GNG), called ASC with GNG in this study. The proposed method uses not only reference vectors for vector quantization but also the topology of the network for extraction of the topological relationship between data points in a dataset. The similarity matrix used by ASC with GNG is made from both the reference vectors and the topology of the network generated by GNG. Using the network generated from a dataset by GNG, we achieve to reduce the computational and space complexities and to improve clustering quality. This paper demonstrates that the proposed method effectively reduces the computational time. Moreover, the results of this study show that the proposed method displays equal to or better performance of clustering than SC.

中文翻译：

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使用参考矢量和神经网络增长产生的网络拓扑进行近似光谱聚类

频谱聚类（SC）是最流行的聚类方法之一，通常优于传统聚类方法。SC使用从数据集的相似性矩阵计算出的拉普拉斯矩阵的特征向量。SC具有严重的缺点，即本征分解所产生的计算复杂性以及存储相似性矩阵的存储空间复杂性显着增加。为了解决这些问题，我使用由生长的神经气体（GNG）生成的网络（在本研究中称为ASC和GNG）开发了一种新的近似光谱聚类。所提出的方法不仅使用参考矢量进行矢量量化，还使用网络的拓扑结构来提取数据集中数据点之间的拓扑关系。ASC与GNG使用的相似性矩阵是由参考矢量和GNG生成的网络拓扑组成的。使用GNG从数据集生成的网络，我们实现了降低计算和空间复杂性并提高聚类质量的目的。本文证明了该方法有效地减少了计算时间。此外，这项研究的结果表明，所提出的方法显示出与SC相同或更好的聚类性能。