Tracking and Visualization of Cluster Dynamics by Sequence-based SOM

Since events and physical phenomena change with time, it is important to capture the main transitions and elements of such events and phenomena. Such transitions can be seen to occur in the World Wide Web (Levene & Poulovassilis, 2004), news topics (Allan, 2002), a person’s health condition, and the state of an instrument or a plant. Transition, or change, refers to a sequential increase/decrease or generation/extinction of the feature of the object. Visualization of such transitions of dynamic clusters is helpful in understanding such phenomena instinctively and plays a useful role in many application domains, such as fault diagnosis and medial examinations. Although a number of clustering methods have been proposed (Jain et al., 1999), most conventional clustering methods deal with static data and cannot handle sequential changes of the cluster explicitly. Tracing the trajectory within clusters that have been collectively processed and a sliding window-based method to generate separate clusters can be considered as simple methods. Although the former method cannot trace changes of clusters, it can trace changes in the number of data that belong to each cluster. The latter method can handle changes of clusters to a certain degree. However, there are some problems, such as setting an appropriate window size, the inevitable decrease in the number of data within a window, and the correspondence relationships of clusters between windows. The present study considers a window-based approach using the temporal neighborhood to address the above-described problems. Kohonen's Self-Organizing Map (SOM) (Kohonen, 2000) is considered to be an appropriate technique for visualizing clusters and their similarity relationships. The SOM is an unsupervised neural network learning technique that produces clusters and subsequently projects them onto a low-dimensional (normally two-dimensional) topology map. The conventional SOM deals with static data. However, we have extended the SOM learning model by introducing the Sequencing Weight Function (SWF), so that the model can visualize the transition of dynamics clusters. This model is referred to herein as the Sequence-based SOM (SbSOM) (Fukui et al., 2008). A SOM-based method was selected because the SOM has a neuron topology in the feature space and that is associated with topology (visualization) space. The introduction of temporal order into the topology is natural. The proposed method mitigates the problems of appropriate 7