PRSOM: A New Visualization Method by Hybridizing Multi-Dimensional Scaling and Self-Organizing Map

Sitao Wu, Tommy W. S. Chow

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 inter-neuron 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[1], 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 Multi-Dimensional Scaling (MDS) and SOM are incorporated in PRSOM. Like MDS, The inter-neuron 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.

Method( batch mode):

Step 1: Compute the assignment probability of x(t) for all input data and neurons according to

.

Step 2: Perform the batch weight-updating rule for all neurons:

,

where k is current epoch, k+1 is the next epoch.

Step 3:  Terminate the algorithm until certain criterion is satisfied. Otherwise, go to step 1.

Source Code:prsom.zip

Reference:

[1] S. Wu, T. W. S. Chow, “PRSOM - a probabilistic regularized self-organizing map for data projection and visualization,” IEEE trans. Neural Networks, vol. 16, no. 6, 1362-1380, 2005.