Fast Multi-scale Batch-Learning Growing Neural Gas

Recently, various types of unsupervised learning methods have been applied to data mining tasks. The main objectives of unsupervised learning are feature extraction, clustering, and the topological mapping of a dataset to find important information efficiently. In general, a topology is represented by the set of nodes and edges. For example, Growing Neural Gas (GNG) can obtain a topological structure by connecting an edge between the first and second nearest nodes with each sample data. Furthermore, Growing When Required (GWR), batch-learning GNG (BL-GNG), multi-scale BL-GNG (MS-BL-GNG), and others have been proposed to improve the learning speed and convergence property. In the above methods, we need many data sampling times sufficient to conduct the clustering and topological mapping simultaneously. However, it is difficult for standard GNG to enhance the learning speed drastically because a node is added to a current network after errors with sampling data are accumulated many times. Therefore, we have proposed new growing methods to enhance the learning speed of MS-BL-GNG drastically. In this method, a sample data is added as a new node directly to a current network according to the node addition probability calculated by the distance with the third nearest node in addition to the first and second nearest nodes at maximal. Based on this idea, we have proposed the overall methodology of multi-scale batch-leaning from the viewpoints of learning and growing procedures, that is called Fast GNG in short. In this paper, we discuss the effectiveness of Fast GNG through benchmark comparison. Furthermore, we discuss the future research direction of Fast GNG.