Self-Organizing Maps and Their Applications in Image Processing, Information Organization, and Retrieval - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 417

0.7

sigma=1
sigma=2
sigma=3
sigma=4
sigma=5

0.65

0.6

0.55

0.5

0.45

0.2 0.3 0.4 0.5 0.6 0.7 0.8

epsilon
(a)

1.8

sigma=1
sigma=2
sigma=3
sigma=4
sigma=5

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1

0.9

0.2 0.3 0.4 0.5 0.6 0.7 0.8

e

(b)

FIGURE 11.7
Modified asymptotic relative efficiency of the MMSOM against the SOM vs. the contamination
percentage for several σ . (a) Gaussian mixture model; (b) Laplacian mixture model.

Let us first define when we declare that the learning procedure in the VQ
techniques included in our study has converged. During the learning phase,
each VQ algorithm is applied to the training set several times. Each presenta-
tion of the training set is called training session hereafter. At the end of each
training session k , the mean-squared error (MSE) between the quantized and