## 10-3 ?炵??ц看姝革?浣跨敤 fminsearch

癸τē獶絬┦癹耴Nonlinear Regression琌ゑ耕螟拜肈

• 礚猭Ωт程ㄎ秆
• 礚猭玂靡镑т程ㄎ秆
• 斗まノ贺獶絬┦程ㄎてよ猭
• 贺闽计厩┦借ぃ陪

计厩ㄓ磞瓃安砞┮ノ计厩家琌 $y=f(\mathbf{x}, \mathbf{\theta})$ㄤい $f(\mathbf{x}$ 琌块秖$\mathbf{\theta})$ 琌跑獶絬┦ㄧ计$y$ 琌块跑计玥羆キよ粇畉 $$E(\mathbf{\theta}) = \sum_{i=1}^n (y_i - f(\mathbf{x}_i, \mathbf{\theta}))^2$$

ㄤい $(\mathbf{x}_i, y_i)$ 琌材 $i$ 戈翴パ $\mathbf{\theta}$ 琌 $f$ 獶絬┦把计┮ $E(\mathbf{\theta})$ ぃ琌 $\mathbf{\theta}$ ΩΑи礚猭パ $\mathbf{\theta}$ 癸 $\mathbf{\theta}$ 旧Α箂ㄓ秆程ㄎ $\mathbf{\theta}$ 癶τ―ㄤΩиゲ斗ノ程ㄎてOptimizationよ猭ㄓт $E(\mathbf{\theta})$ 程ㄒ辫猭Gradient Descent┪琌 Simplex ℡Α穓碝Simplex Downhill search单

$$y= a_1 e^{\lambda_1 x} + a_2 e^{\lambda_2 x}$$

ㄤい$a_1$$a_2$ 絬┦把计 $\lambda_1$$\lambda_2$ 獶絬┦把计玥家獶絬┦羆キよ粇畉ボ $$E(a_1, a_2, \lambda_1, \lambda_2) = \sum_{i=1}^{m} (y_i - a_1 e^{\lambda_1 x_i} - a_2 e^{\lambda_2 x_i})^2$$

Example 1: 10-Ρ絬览籔癹耴だ猂/errorMeasure1.mfunction squaredError = errorMeasure1(theta, data) if nargin<1; return; end x = data(:,1); y = data(:,2); y2 = theta(1)*exp(theta(3)*x)+theta(2)*exp(theta(4)*x); squaredError = sum((y-y2).^2);

ㄤい theta 琌把计秖 $a_1$$a_2$$\lambda_1$ の $\lambda_2$data 玥琌芠诡戈翴肚玥琌羆キよ粇畉饼―ㄧΑ程иㄏノ fminsearch 叫ǎ絛ㄒ

Example 2: 10-Ρ絬览籔癹耴だ猂/nonlinearFit01.mload data.txt theta0 = [0 0 0 0]; tic theta = fminsearch(@(x)errorMeasure1(x, data), theta0); fprintf('璸衡丁 = %g\n', toc); x = data(:, 1); y = data(:, 2); y2 = theta(1)*exp(theta(3)*x)+theta(2)*exp(theta(4)*x); plot(x, y, 'ro', x, y2, 'b-'); legend('Sample data', 'Regression curve'); fprintf('粇畉キよ㎝ = %d\n', sum((y-y2).^2));璸衡丁 = 0.0762827 粇畉キよ㎝ = 5.337871e-01

瓜Ρ絬 fminsearch ┮玻ネ癹耴Ρ絬瓃祘Αいdata 痻皚跑计data(:,1)㎝跑计 data(:,2)よ獽盢ぇ肚ㄧΑ errorMeasure1.mTheta0 玥琌跑把计 theta 癬﹍fminsearch 玥琌ㄏノ Simplex ℡Α穓碝猭Downhill Simplex Search程ㄎてよ猭ノㄓт errorMeasure1 伐肚 theta 程ㄎ饼冈よ猭灿竊冈綷掸帝Neural-Fuzzy and Soft Computing  A Computational Approach to Learning and Machine IntelligencePrentice Hall 1997

MATLAB祘Α砞璸秈顶絞