PRSOM: a new visualization method by hybridizing multidimensional scaling and self-organizing map.

Abstract

Self-organizing map (SOM) is an approach of nonlinear dimension reduction and can be used for visualization. It only preserves topological structures of input data on the projected output space. The interneuron distances of SOM are not preserved from input space into output space such that the visualization of SOM can be degraded. Visualization-induced SOM (ViSOM) has been proposed to overcome this problem. However, ViSOM is derived from heuristic and no cost function is assigned to it. In this paper, a probabilistic regularized SOM (PRSOM) is proposed to give a better visualization effect. It is associated with a cost function and gives a principled rule for weight-updating. The advantages of both multidimensional scaling (MDS) and SOM are incorporated in PRSOM. Like MDS, The interneuron distances of PRSOM in input space resemble those in output space, which are predefined before training. Instead of the hard assignment by ViSOM, the soft assignment by PRSOM can be further utilized to enhance the visualization effect. Experimental results demonstrate the effectiveness of the proposed PRSOM method compared with other dimension reduction methods.