原
吴恩达机器学习 - 逻辑回归
先贴笔记
然后是代码
plotData.m(可视化数据)：
function plotData(X, y)
%PLOTDATA Plots the data points X and y into a new figure
% PLOTDATA(x,y) plots the data points with + for the positive examples
% and o for the negative examples. X is assumed to be a Mx2 matrix.
% Create New Figure
figure; hold on;
% ====================== YOUR CODE HERE ======================
% Instructions: Plot the positive and negative examples on a
% 2D plot, using the option 'k+' for the positive
% examples and 'ko' for the negative examples.
%
% Find Indices of Positive and Negative Examples
pos = find(y==1);
neg = find(y == 0);
% Plot Examples
plot(X(pos, 1), X(pos, 2), 'k+','LineWidth', 2, 'MarkerSize', 7);
plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y','MarkerSize', 7);
% =========================================================================
hold off;
end
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
- 23
- 24
- 25
- 26
- 27
- 28
- 29
- 30
效果图：
sigmoid.m(求g(z)的函数)：
function g = sigmoid(z)
%SIGMOID Compute sigmoid function
% g = SIGMOID(z) computes the sigmoid of z.
% You need to return the following variables correctly
g = zeros(size(z));
% ====================== YOUR CODE HERE ======================
% Instructions: Compute the sigmoid of each value of z (z can be a matrix,
% vector or scalar).
[h,w] = size(z);
for i = 1:h
for j = 1:w
g(i,j) = 1.0/(1+exp(-z(i,j)));
end
end
% =============================================================
end
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
costFunction.m(计算当前θ的代价和各方向的梯度)(使用矩阵计算精简)：
function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
% J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
% parameter for logistic regression and the gradient of the cost
% w.r.t. to the parameters.
% Initialize some useful values
m = length(y); % number of training examples
% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));
% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
% You should set J to the cost.
% Compute the partial derivatives and set grad to the partial
% derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%
J = (-y'*log(sigmoid(X*theta))-(1-y')*log(1-sigmoid(X*theta)))/m;
grad = X'*(sigmoid(X*theta)-y)./m;
% =============================================================
end
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
- 23
- 24
- 25
- 26
- 27
- 28
- 29
predict.m(预测)：
function p = predict(theta, X)
%PREDICT Predict whether the label is 0 or 1 using learned logistic
%regression parameters theta
% p = PREDICT(theta, X) computes the predictions for X using a
% threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1)
m = size(X, 1); % Number of training examples
% You need to return the following variables correctly
p = zeros(m, 1);
% ====================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
% your learned logistic regression parameters.
% You should set p to a vector of 0's and 1's
%
p = sigmoid(X*theta) >= 0.5;
% =========================================================================
end
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
- 11
- 12
- 13
- 14
- 15
- 16
- 17
- 18
- 19
- 20
- 21
- 22
- 23
- 24
- 25
问题
为什么在ex1.m中，使用高级算法时，代码写成了这样：
options = optimset('GradObj', 'on', 'MaxIter', 400);
[theta, cost] = fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
- 1
- 2
看起来很奇怪有没有，和笔记上不一样哎。。。
其实是因为笔记上传入的参数就一个theta，但是我们这里的代码需要传入theta,x,y三个参数呢，所以看一下fminunc的用法，发现可以传入一个三个参数的函数句柄。用法是这样：
第一个是Θ，然后是(X,y)。然而我们的costFunction函数参数是(X,y,theta)，发现了吧，是顺序问题
那么这么写的含义就清楚了，就是换一下参数的位置，下面是我搜到的解释，也是看这个才明白的：
