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

Kazuhisa Fujita

doi:10.7717/peerj-cs.679

Abstract

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.

Highlights

A clustering method is a workhorse and becomes more important for data analysis, data mining, image segmentation, and pattern recognition
I develop a new approximate spectral clustering (ASC) using a similarity matrix calculated from both the reference vectors and the topology of the network generated by growing neural gas (GNG), called ASC with GNG
ASC with GNG partitions a dataset using a similarity matrix calculated from both reference vectors and the topology of the network generated by GNG

Summary

INTRODUCTION

A clustering method is a workhorse and becomes more important for data analysis, data mining, image segmentation, and pattern recognition. The last approach is to reduce a data size using a vector quantization method such as k-means (Yan et al, 2009), self-organizing map (SOM) (Duan et al, 2012) and neural gas (NG) (Moazzen and Tasdemir, 2016). This method is called approximate spectral clustering or two-level approach. The reference vectors are regarded as local averages of data points, less sensitive to noise than the original data (Vesanto and Alhoniemi, 2000) This may improve the clustering performance of SC. I compare ASC with GNG with ASC using a similarity matrix calculated from quantization results generated by neural gas, Kohonen’s SOM, and k-means instead of GNG

RELATED WORKS

APPROXIMATE SPECTRAL CLUSTERING WITH GROWING NEURAL GAS

Algorithm

RESULTS

CONCLUSION

A SELF-ORGANIZING MAP AND ITS ALTERNATIVES