  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: the significant increases in the time complexity derived
from the computation of eigenvectors and the memory space complexity 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. ASC with GNG 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. ASC with GNG
calculates the similarity matrix from both the reference vectors and the
topology of the network generated by GNG. Using the network generated from a
dataset by GNG, ASC with GNG achieves to reduce the computational and space
complexities and improve clustering quality. In this study, I demonstrate that
ASC with GNG effectively reduces the computational time. Moreover, this study
shows that ASC with GNG provides equal to or better clustering performance than
SC.
