Multilayer Batch Learning Growing Neural Gas for Learning Multiscale Topologies

Hierarchical topological structure learning methods are expected to be developed in the field of data mining for extracting multiscale topological structures from an unknown dataset. However, most methods require user-defined parameters, and it is difficult for users to determine these parameters and effectively utilize the method. In this paper, we propose a new parameter-less hierarchical topological structure learning method based on growing neural gas (GNG). First, we propose batch learning GNG (BL-GNG) to improve the learning convergence and reduce the user-designed parameters in GNG. BL-GNG uses an objective function based on fuzzy C-means to improve the learning convergence. Next, we propose multilayer BL-GNG (MBL-GNG), which is a parameter-less unsupervised learning algorithm based on hierarchical topological structure learning. In MBL-GNG, the input data of each layer uses parent nodes to learn more abstract topological structures from the dataset. Furthermore, MBL-GNG can automatically determine the number of nodes and layers according to the data distribution. Finally, we conducted several experiments to evaluate our proposed method by comparing it with other hierarchical approaches and discuss the effectiveness of our proposed method.

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: 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.