1 Pertemuan 10 PERFORMANCE SURFACES Matakuliah: H0434/Jaringan Syaraf Tiruan Tahun: 2005 Versi: 1
2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Menjelaskan pengertian tentang performance learning.
3 Outline Materi Permukaan kinerja. Titik Optimal
4 Taylor Series Expansion Fx Fx xd d Fx xx = xx – += x 2 2 d d Fx xx = xx – 2 ++ 1 n! x n n d d Fx xx = xx – n ++
5 Example Taylor series approximations: Taylor series of F(x) about x* = 0 :
6 Plot of Approximations
7 Vector Case
8 Matrix Form F x F x F x T xx = xx – += xx – T F x xx = xx – 2 ++ F x x 1 F x x 2 F x x n F x = GradientHessian
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
10 Example
11 Plots x1x1 x1x1 x2x2 x2x Directional Derivatives
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 Scalar Example Strong Minimum Strong Maximum Global Minimum
14 Vector Example