機器學習與模式識別

1、機器學習與模式識別實驗報告（二）姓名：白鵬飛 班級：計科1203 學號：0909121328 指導(dǎo)老師：梁毅雄IntroductionIn this exercise, you will implement logistic regression and apply it to two dierent datasets. Before starting on the programming exercise, we strongly recommend watching the video lectures and completing the review questions for the

2、 associated topics.Files included in this exerciseex2.m - Octave script that will help step you through the exerciseex2 reg.m - Octave script for the later parts of the exerciseex2data1.txt-Trainingsetforthe rst half of the exerciseex2data2.txt - Training set for the second half of the exercisesubmi

3、tWeb.m - Alternative submission scriptsubmit.m - Submission script that sends your solutions to our serversmapFeature.m - Function to generate polynomial featuresplotDecisionBounday.m - Function to plot classiFunction to plot 2DclassiFunction to plot 2Dclassiers decision boundary ? plotData.mcation

4、data? sigmoid.m - Sigmoid Function? costFunction.m - Logistic Regression Cost Function? predict.m - Logistic Regression Prediction Function? costFunctionReg.m - Regularized Logistic Regression Cost 1?indicatesles you will need to completeThroughout the exercise, you will be using the scripts ex2.m a

5、nd ex2 reg.m. These scripts set up the dataset for the problems and make calls to functions that you will write. You do not need to modify either of them. You are only requiredtomodifyfunctionsinotherles, by following the instructions in this assignment.補全代碼后如下：plotData.mfunction plotData(X, y)%PLOT

6、DATA 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 Figurefigure; hold on;% = YOUR CODE HERE =% Instructions: Plot the positive and negative examples

7、on a%2D plot, using the option k+ for the positive%examples and ko for the negative examples.% positive = find (y = 1);negative = find (y=0);plot (X(positive, 1), X(positive,2), k+，MarkerSize，7 , LineWidth ,2);plot (X(negative, 1), X(negative,2), ko，MarkerFaceColor，y ， MarkSize ,7);hold off;endSigmo

8、id.m function g = sigmoid(z)%SIGMOID Compute sigmoid functoon% J = SIGMOID(z) computes the sigmoid of z.% You need to return the following variables correctlyg = zeros(size(z);% = YOUR CODE HERE =% Instructions: Compute the sigmoid of each value of z (z can be a matrix,%vector or scalar).g = 1./(1+e

9、xp(-z);% =endcostFunction.mfunction 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.% In

10、itialize some useful valuesm = length(y); % number of training examples% You need to return the following variables correctlyJ = 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 derivati

11、ves and set grad to the partial%derivatives of the cost w.r.t. each parameter in theta%Hypothesis = sigmoid (X*theta);J=1/m*sum(-y.*log(hypothesis)-(1-y).*log(1-hypothesis)+0.5*lambda/m*(theta(2:end) *theta(2:end);n = size(X,2);grad(1) = 1/m*dot(hypothesis-y,X(:,1);for i =2 : ngrad(i) = 1/m*dot(hypo

12、thesis - y,X(:,i)+lambda /m * theta(i);% Note: grad should have the same dimensions as theta% =endPredict.mfunction 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%thres

13、hold 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 param

14、eters.%You should set p to a vector of 0s and 1s% p= sigmoid(X*theta) = 0.5;endcostFunctionReg.mfunction J, grad = costFunctionReg(theta, X, y, lambda)%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of

15、 using% theta as the parameter for regularized logistic regression and the% gradient of the cost w.r.t. to the parameters.% Initialize some useful valuesm = length(y); % number of training examples% You need to return the following variables correctlyJ = 0;grad = zeros(size(theta);% = YOUR CODE HERE

16、 =% 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 thetahypothesis = sigmoid (X*theta);J=1/m*sum(-y.*log(hypothesis)-(1-y).*log(1-hypothesis)+0.5*lambda/m*(theta(2:end) *theta(2:end);n = size(X,2);grad(1) = 1/m*dot(hypothesis-y,X(:,1);for i =2 : ngrad(i) = 1/m*dot(hypothesis - y,X(:,i)+lambda /m * theta(i);% =運行后結(jié)果如下：DFigure 2 nFile