MEE with Continuous Errors - Minimum Error Entropy Classification - page 83

Tabl e 3 . 6 Error rates for the empirical and theoretical MEE algorithms, together
with min P e values, for three datasets.

Dataset No. classes No. instances Empirical MEE Theoretical MEE min P e

Error Rate Error Rate

Wine 2 3 5000 0.0415 0.0512 0.0402

Thyroid 2 3 2509 0.0494 0.2152 0.0359

Ionosphere 2 2 5778 0.1888 - 0.1865

theoretical and empirical SEE. We present the results reported in [219] for
the datasets Wine 2 , Thyroid 2 ,andIonosphere 2 , i.e., the versions of the orig-
inal Wine, Thyroid, and Ionosphere datasets made of their first two principal
components (the original Ionosphere dataset is from [13]). The aim in these
experiments is simply to discriminate one class from the other ones.

3 2

x 2

x 2

1

2

0

1

−1

−2

0

−3

−1

−4

−2 −5

x 1

x 1

−6

−3

−4 −3 −2 −1 0 1 2 3 4 −6 −4 −2 0 2 4 6

(a) (b)

x 2

1.5

1

0.5

0

−0.5

−1

−1.5

x 1

−2

−3 −2 −1 0 1 2

(c)

Fig. 3.26 Decision borders obtained with empirical MEE (dashed), theoretical MEE
(dotted), and min P e (solid) for Wine 2 (a), Thyroid 2 (b), and Ionosphere 2 (c) datasets.

Table 3.6 shows the training set error rates obtained with both, theoretical
and empirical, algorithms. They are in general close to the min P e values
(obtained with the Nelder-Mead algorithm), the only exceptions being the