%?Exercise?3?--?Multivariate?Linear?Regression

clear?all;?close?all;?clc

x?=?load（‘ex3x.dat‘）;?
y?=?load（‘ex3y.dat‘）;

m?=?length（y）;

%?Add?intercept?term?to?x
x?=?[ones（m?1）?x];

%?Save?a?copy?of?the?unscaled?features?for?later
x_unscaled?=?x;

%?Scale?features?and?set?them?to?zero?mean
mu?=?mean（x）;

sigma?=?std（x）;

x（:2）?=?（x（:2）?-?mu（2））./?sigma（2）;
x（:3）?=?（x（:3）?-?mu（3））./?sigma（3）;

%?Prepare?for?plotting
figure;
%?plot?each?alpha‘s?data?points?in?a?different?style
%?braces?indicate?a?cell?not?just?a?regular?array.
plotstyle?=?{‘b‘?‘r‘?‘g‘?‘k‘?‘b--‘?‘r--‘};


%?Gradient?Descent?
alpha?=?[0.01?0.03?0.1?0.3?1?1.3];
MAX_ITR?=?100;
%?this?will?contain?my?final?values?of?theta
%?after?I‘ve?found?the?best?learning?rate
theta_grad_descent?=?zeros（size（x（1:）））;?
for?i?=?1:length（alpha）
????theta?=?zeros（size（x（1:）））‘;?%?initialize?fitting?parameters
????J?=?zeros（MAX_ITR?1）;
????for?num_iterations?=?1:MAX_ITR
????????%?Calculate?the?J?term
????????J（num_iterations）?=?（0.5/m）?.*?（x?*?theta?-?y）‘?*?（x?*?theta?-?y）;
????????
????????%?The?gradient
????????grad?=?（1/m）?.*?x‘?*?（（x?*?theta）?-?y）;
????????
????????%?Here?is?the?actual?update
????????theta?=?theta?-?alpha（i）?.*?grad;
????end
????%?Now?plot?the?first?50?J?terms
????plot（0:49?J（1:50）?char（plotstyle（i））?‘LineWidth‘?2）
????hold?on
????
????%?After?some?trial?and?error?I?find?alpha=1
????%?is?the?best?learning?rate?and?converges
????%?before?the?100th?iteration
????%
????%?so?I?save?the?theta?for?alpha=1?as?the?result?of?
????%?gradient?descent
????if?（alpha（i）?==?1）
????????theta_grad_descent?=?theta;
????end
end
legend（‘0.01‘‘0.03‘‘0.1‘?‘0.3‘?‘1‘?‘1.3‘）
xlabel（‘Number?of?iterations‘）
ylabel（‘Cost?J‘）

%?force?Matlab?to?display?more?than?4?decimal?places
%?formatting?persists?for?rest?of?this?session
format?long

%?Display?gradient?descent‘s?result
theta_grad_descent

%?Estimate?the?price?of?a?1650?sq-ft?3?br?house
price_grad_desc?=?dot（theta_grad_descent?[1?（1650?-?mu（2））/sigma（2）...
????????????????????（3?-?mu（3））/sigma（3）]）
?
%?Calculate?the?parameters?from?the?normal?equation
theta_normal?=?（x_unscaled‘?*?x_unscaled）\x_unscaled‘?*?y

%Estimate?the?house?price?again
price_normal?=?dot（theta_normal?[1?1650?3]）

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????2248??2018-03-26?13:51??NG-Exercise3?Multivariate?Linear?Regression\ex3.m
?????文件????????1551??2010-10-14?23:26??NG-Exercise3?Multivariate?Linear?Regression\ex3x.dat
?????文件?????????799??2010-10-14?23:26??NG-Exercise3?Multivariate?Linear?Regression\ex3y.dat