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Probability density estimation


Since the distribution of the weight vectors of the SOM approximates that of the training data, the SOM can be utilized in estimating the probability density function (PDF) of a data set. The estimation can be done using e.g. the reduced kernel density estimation (RKDE) [10]:


where M is the number of neurons in the map, K is a kernel function and the weights tex2html_wrap_inline3388 and the smoothing parameters tex2html_wrap_inline3390 are estimated from the data. The batch version of the algorithm proceeds as follows:

  1. Train the kernel centers tex2html_wrap_inline3162 using the SOM.
  2. Calculate the weights tex2html_wrap_inline3394 , where tex2html_wrap_inline3266 is the number of samples in the Voronoi region of the reference vector tex2html_wrap_inline3162 .
  3. Calculate a single smoothing parameter h, or perhaps different tex2html_wrap_inline3402 for each kernel. This can be done e.g. by computing the distance tex2html_wrap_inline3404 between tex2html_wrap_inline3162 and its nearest model vector, setting tex2html_wrap_inline3408 , and optimizing tex2html_wrap_inline3410 as the Breiman-Meisel-Purcell estimator.

Juha Vesanto
Tue May 27 12:40:37 EET DST 1997