≡

( )[ ]=

⋅⋅==

[ ]=

[ ]=

2333

978-1-4244-1821-3/08/$25.00 c©2008 IEEE

∏=

≡ φ

( )−−=

σφ

σ

( ) ( )( )−=−=

( )( ) ( )⋅⋅−=

−=Δ

α

∂

∂α

α

= ∏= φ

≤∏φ

≤∏φ

∏φ

≤∏φ

-2-1

01

2

-2

-1

0

1

20

0.1

0.20.3

0.4

0.50.6

0.7

0.80.9

1

2334 2008 International Joint Conference on Neural Networks (IJCNN 2008)

ππ=

−=

( )=

−=

=

=∏φ

∏φ

=

=∏φ

∏φ

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-1-0.5

00.5

1

-1

-0.5

0

0.5

10

0.2

0.4

0.6

0.8

1

-1.5 -1 -0.5 0 0.5 1 1.5-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

2008 International Joint Conference on Neural Networks (IJCNN 2008) 2335

-1-0.500.51

-1

0

1

0

0.2

0.4

0.6

0.8

1

−−+

−−+

−−=

ππ

ππ

ππ

−−+

−−+

−−=

π

π

π

-1-0.5

00.5

1

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0

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0.5

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0.5

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x1x3

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-1

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1.5

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x3x4

-1-0.5

00.5

1

-1

-0.5

0

0.5

10.5

1

1.5

2

x3x4

2336 2008 International Joint Conference on Neural Networks (IJCNN 2008)

-1-0.5

00.5

1

-1

-0.5

0

0.5

1-0.5

0

0.5

1

1.5

x1x3

-1-0.5

00.5

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∏= φ

Δ

( )( )

( )( )

( )

( )( ) ( )

( ) ( )( )−−−−−

−−−−−

−

−

−

−−−−

−−

−+=

−+=

−+=

Δ+=

α

α

α

( ) ( ) ( )[ ]≡

≡

2008 International Joint Conference on Neural Networks (IJCNN 2008) 2337

( ) ( )

( ) ( )

( ) ( )

( ) ( ) −−−

−+

−−−−

−−−−

+−−−−−

−−+

−+

−

+

−=

−−=

−−

−+=

Δ+−Δ+=

−=

α

α

α

α

( ) ( ) ( )α−≡≡

( ) ( ) ( )α−≡

( )

( ) ( ) ≠−

=−

=α

α ( )=

⋅

⋅=

( )

( )

( ) ( )

( )

( )−+=

+−=

++++

+++−=

−++

−+−=

⋅++++⋅+++

⋅+++==

===

=====

===

====

=

==

=

αα

αα

α

α

α

αα

=

( ) <−=

αα

=

( ) αα−

=

( )( )

<

−

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=

αααα

( )=

<< α

( )

( ) ( )( )

≡

=

=

−−

−−−

−−≡

( ) ( )

( ) ( )

( ) ( )−+⋅⋅⋅

+−

+−

=

−−−−

++++

α

( ) =

2338 2008 International Joint Conference on Neural Networks (IJCNN 2008)

2008 International Joint Conference on Neural Networks (IJCNN 2008) 2339