The Self-Organizing Hierarchical Variance Map

This chapter introduces and develops a new model for clustering data, offering a number of enhancements and features over the self-organizing tree map (SOTM). The model is known as the Self-Organizing Hierarchical Variance Map (SOHVM). The chapter highlights some of its limitations. In so doing, a motivation is provided for a more advanced clustering algorithm, one that retains some of the desirable properties of the SOTM. The component responsible for mapping local variance information is known as a Hebbian Maximal Eigenfilter (HME). It outlines and justifies the key components and principles of operation for the new model. In addition, the implementation details are discussed. Finally, a series of visual simulations on synthetic two-dimensional (2D) data are presented, with the goal of providing a simple and clear demonstration of the new model in operation, highlighting some of its key features and strengths over popular existing architectures from the literature.