###### weixin_36382721

2016-10-12 19:07 阅读 2.2k

# matlab实现牛顿法逻辑回归

clear all; close all; clc

[m, n] = size(x);

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

% Plot the training data
% Use different markers for positives and negatives
figure
pos = find(y); neg = find(y == 0);
plot(x(pos, 2), x(pos,3), '+')
hold on
plot(x(neg, 2), x(neg, 3), 'o')
hold on
xlabel('Exam 1 score')
ylabel('Exam 2 score')

% Initialize fitting parameters
theta = zeros(n+1, 1);

% Define the sigmoid function
g = inline('1.0 ./ (1.0 + exp(-z))');

% Newton's method
MAX_ITR = 10;
J = zeros(MAX_ITR, 1);

for i = 1:MAX_ITR
% Calculate the hypothesis function
z = x * theta;
h = g(z);

``````grad = (1/m).*x' * (h-y);
H = (1/m).*x' * diag(h) * diag(1-h) * x;

% Calculate J (for testing convergence)
J(i) =(1/m)*sum(-y.*log(h) - (1-y).*log(1-h));

``````

end
% Display theta
theta

% Calculate the probability that a student with
% Score 20 on exam 1 and score 80 on exam 2
prob = 1 - g([1, 20, 80]*theta)

% Plot Newton's method result
% Only need 2 points to define a line, so choose two endpoints
plot_x = [min(x(:,2)+2), max(x(:,2))+2];
% Calculate the decision boundary line
plot_y = (-1./theta(3)).*(theta(2).*plot_x +theta(1));
plot(plot_x, plot_y)
hold off

% Plot J
figure
plot(0:MAX_ITR-1, J, 'o--', 'MarkerFaceColor', 'r', 'MarkerSize', 8)
xlabel('Iteration'); ylabel('J-cost')

to=cputime();
m=length(y);
x = [ones(m, 1), x];
pos = find(y); neg = find(y == 0);
plot(x(pos, 2), x(pos,3), '*')
hold on
plot(x(neg, 2), x(neg, 3), 'o')
hold on
xlabel('Exam 1 score')
ylabel('Exam 2 score')
numfeature=size(x,2);
numtrainsam = size(x,1);
theta = zeros(numfeature, 1);
maxiterations=10;
errorperiteration=zeros(maxiterations,1);
g = inline('1.0 ./ (1.0 + exp(-z))');
prevtheta=theta;
for t=1:maxiterations
toterror=0;
for j=1:numfeature
totslope=0;
for i=1:m
z=0;

for jj=1:numfeature

``````          z=z+prevtheta(jj)*x(i,jj);
end
h=1.0/(1.0+exp(-z));
H=H+(x(i,q)*h*(1-h)*x(i,jj));

totslope=(totslope+(h-y(i))*x(i,j));
toterror=(toterror+-y(i)*log(h)-(1-y(i))*log(1-h));
end
``````

toterror=toterror/numtrainsam;
theta(j)= theta(j)-H\totslope;
end
prevtheta=theta;
errorperiteration(t)=toterror/j;
end
errorperiteration=zeros(maxiterations,1)
prevtheta=theta;
plot_x = [min(x(:,2)+2), max(x(:,2))+2];
% Calculate the decision boundary line
plot_y = (-1./theta(3)).*(theta(2).*plot_x +theta(1));
plot(plot_x, plot_y)