Approximate spectral clustering using both reference vectors and topology of the network generated by growing neural gas

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.