Andrew Ng coursera上的《机器学习》ex8

按照课程所给的ex8的文档要求，ex8要求完成以下几个计算过程的代码编写：

一、estimateGuasssian.m

要求求出符合高斯函数的均值和方差。

function [mu sigma2] = estimateGaussian(X)%ESTIMATEGAUSSIAN This function estimates the parameters of a %Gaussian distribution using the data in X%   [mu sigma2] = estimateGaussian(X), %   The input X is the dataset with each n-dimensional data point in one row%   The output is an n-dimensional vector mu, the mean of the data set%   and the variances sigma^2, an n x 1 vector% % Useful variables[m, n] = size(X);% You should return these values correctlymu = zeros(n, 1);sigma2 = zeros(n, 1);% ====================== YOUR CODE HERE ======================% Instructions: Compute the mean of the data and the variances%               In particular, mu(i) should contain the mean of%               the data for the i-th feature and sigma2(i)%               should contain variance of the i-th feature.%mu=mean(X);sigma2=var(X,1);% =============================================================end

可以直接调用函数库里面的函数进行求值。

二、selectThresold.m

要求求出判断异常的判定边界。

function [bestEpsilon bestF1] = selectThreshold(yval, pval)%SELECTTHRESHOLD Find the best threshold (epsilon) to use for selecting%outliers%   [bestEpsilon bestF1] = SELECTTHRESHOLD(yval, pval) finds the best%   threshold to use for selecting outliers based on the results from a%   validation set (pval) and the ground truth (yval).%bestEpsilon = 0;bestF1 = 0;F1 = 0;stepsize = (max(pval) - min(pval)) / 1000;for epsilon = min(pval):stepsize:max(pval)    % ====================== YOUR CODE HERE ======================    % Instructions: Compute the F1 score of choosing epsilon as the    %               threshold and place the value in F1. The code at the    %               end of the loop will compare the F1 score for this    %               choice of epsilon and set it to be the best epsilon if    %               it is better than the current choice of epsilon.    %                   % Note: You can use predictions = (pval < epsilon) to get a binary vector    %       of 0's and 1's of the outlier predictionspredictions = (pval < epsilon);fp = sum((predictions == 1) &(yval == 0));tp = sum((predictions == 1) &(yval == 1));fn = sum((predictions == 0) &(yval == 1));pr=tp/(tp+fp);re=tp/(tp+fn);F1=2*pr*re/(pr+re);    % =============================================================    if F1 > bestF1       bestF1 = F1;       bestEpsilon = epsilon;    endendend

三、coficostFunction.m

要求是求出协同过滤等算法。

function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...                                  num_features, lambda)%COFICOSTFUNC Collaborative filtering cost function%   [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ...%   num_features, lambda) returns the cost and gradient for the%   collaborative filtering problem.%% Unfold the U and W matrices from paramsX = reshape(params(1:num_movies*num_features), num_movies, num_features);Theta = reshape(params(num_movies*num_features+1:end), ...                num_users, num_features);% You need to return the following values correctlyJ = 0;X_grad = zeros(size(X));Theta_grad = zeros(size(Theta));% ====================== YOUR CODE HERE ======================% Instructions: Compute the cost function and gradient for collaborative%               filtering. Concretely, you should first implement the cost%               function (without regularization) and make sure it is%               matches our costs. After that, you should implement the %               gradient and use the checkCostFunction routine to check%               that the gradient is correct. Finally, you should implement%               regularization.%% Notes: X - num_movies  x num_features matrix of movie features%        Theta - num_users  x num_features matrix of user features%        Y - num_movies x num_users matrix of user ratings of movies%        R - num_movies x num_users matrix, where R(i, j) = 1 if the %            i-th movie was rated by the j-th user%% You should set the following variables correctly:%%        X_grad - num_movies x num_features matrix, containing the %                 partial derivatives w.r.t. to each element of X%        Theta_grad - num_users x num_features matrix, containing the %                     partial derivatives w.r.t. to each element of Theta%M=(X*Theta'-Y).^2;J=1/2*sum(sum(R.*M));J=J+lambda/2*sum(sum(Theta.^2))+lambda/2*sum(sum(X.^2));t=(X*Theta'-Y).*R;for k=1:num_features    for i=1:num_movies           for j=1:num_users               X_grad(i,k)=X_grad(i,k)+(X(i,:)*Theta(j,:)'-Y(i,j))*Theta(j,k).*R(i,j);                                 end            endendX_grad=X_grad+lambda*X;for k=1:num_features    for j=1:num_users        for i=1:num_movies               Theta_grad(j,k)=Theta_grad(j,k)+(X(i,:)*Theta(j,:)'-Y(i,j))*X(i,k).*R(i,j);                                 end            endendTheta_grad=Theta_grad+lambda*Theta;% =============================================================grad = [X_grad(:); Theta_grad(:)];end