1 Pertemuan 10 PERFORMANCE SURFACES Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1.

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1 1 Pertemuan 10 PERFORMANCE SURFACES Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1

2 2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Menjelaskan pengertian tentang performance learning.

3 3 Outline Materi Permukaan kinerja. Titik Optimal

4 4 Taylor Series Expansion Fx  Fx   xd d Fx  xx  = xx  –  += 1 2 --- x 2 2 d d Fx  xx  = xx  –  2  ++ 1 n! ----- x n n d d Fx  xx  = xx  –  n  ++

5 5 Example Taylor series approximations: Taylor series of F(x) about x* = 0 :

6 6 Plot of Approximations

7 7 Vector Case

8 8 Matrix Form F x  F x   F x  T xx  = xx  –  += 1 2 --- xx  –  T F x  xx  = xx  –  2  ++ F x  x 1   F x  x 2   F x   x n   F x  = GradientHessian

9 9 Directional Derivatives First derivative (slope) of F(x) along x i axis: Second derivative (curvature) of F(x) along x i axis: (ith element of gradient) (i,i element of Hessian) p T F x  p ----------------------- First derivative (slope) of F(x) along vector p: Second derivative (curvature) of F(x) along vector p: p T F x  2 p p 2 ------------------------------

10 10 Example

11 11 Plots x1x1 x1x1 x2x2 x2x2 1.4 1.3 0.5 0.0 1.0 Directional Derivatives

12 12 Minima The point x* is a strong minimum of F(x) if a scalar   >  0 exists, such that F(x*) ||  x|| > 0. Strong Minimum The point x* is a unique global minimum of F(x) if F(x*) < F(x* +  x) for all  x ° 0. Global Minimum The point x* is a weak minimum of F(x) if it is not a strong minimum, and a scalar   >  0 exists, such that F(x*) Š F(x* +  x) for all  x such that  > ||  x|| > 0. Weak Minimum

13 13 Scalar Example Strong Minimum Strong Maximum Global Minimum

14 14 Vector Example