TreeGNG - hierarchical topological clustering

This paper presents TreeGNG, a top-down unsupervised learning method that produces hierarchical classification schemes. TreeGNG extends the Growing Neural Gas algorithm by maintaining a time history of the learned topological mapping. TreeGNG is able to recover from poor decisions made during the construction of the tree, and provides the novel ability to influence the general shape of the hierarchy. 1 Background In this paper we present TreeGNG, a new hierarchical clustering algorithm based on a time audit trail of the graph connectivity of the Growing Neural Gas (GNG) [4] algorithm. GNG grows and prunes the network components in response to incremental learning. The dynamic nature of the network can produce disjoint graph structures, and these disconnected graphs “can be used to identify clusters in the input data” [5]. By maintaining a time audit trail of the graph connectivity, we can uncover hierarchical structure within the data. The use of unsupervised learning techniques to discover the hierarchy of concepts from unlabelled data, primarily focus on extensions to Kohonen’s Selforganising Feature Map (SOM) [8]. Recently, two hierarchical neural clusterers, HiGCS [1] and TreeGCS [6], have been proposed, both based on Bernd Fritzke’s Growing Cell Structures (GCS) [3]. However, there are some limitations of GCS, which are detailed in [7] and [1], and the results of our own evaluation of GCS concur with these findings. The models produced by the GCS and SOM algorithms are a topological mapping only if the topology of the graph matches the topological structure of the manifold from which the data are drawn. In [9], it was shown that an algorithm for the homogeneous distribution of the network nodes combined with the competitive Hebb rule produces the induced Delaunay triangulation of the manifold. GNG is an incremental implementation of this node distribution and competitive Hebbian learning concept, and the resultant graph structures are a topology preserving map of the manifold. It was reported in [2], that GNG converges rapidly and the quality of the clustering has little dependence on the network parameters. The results of our own evaluation of GNG agree with these findings. 2 TreeGNG Inspired by the claimed capabilities of TreeGCS, we investigated its performance. Whilst we believe the TreeGCS event auditing approach has potential, the resultant trees are binary, and we remain unconvinced as to the suitability of GCS as the underlying algorithm. In TreeGNG (Fig.1), we use GNG as the partitioning algorithm, and whilst the tree growth and pruning mechanisms follow the general outline of TreeGCS, we believe the inclusion of a growth window can improve the quality of the tree representation of data, as the resultant TreeGNG trees are not necessarily binary.