Self organizing maps with the correntropy induced metric

The similarity measure popularly used in Kohonen´s self organizing maps and several of its other variants is the mean square error (MSE). It is shown that this leads to, in information theoretic sense, a suboptimal solution of distributing the centers of the map. Here we show that using a similarity measure called the correntropy induced metric (CIM) can lead to a solution with better magnification of the input density. It provides an insight into how the type of the kernel effects the mapping and also under what condition is using SOM with CIM (SOM-CIM) can perform better than SOM with MSE. We also show that the use of this in clustering and data visualization can provide better results.