Andrew Ng coursera上的《机器学习》ex7

按照课程所给的ex7的文档要求，ex7要求完成以下几个计算过程的代码编写：

一、findClosestCentroids.m

要求是为每个数据点找到距离它最近的中心点。

function idx = findClosestCentroids(X, centroids)%FINDCLOSESTCENTROIDS computes the centroid memberships for every example%   idx = FINDCLOSESTCENTROIDS (X, centroids) returns the closest centroids%   in idx for a dataset X where each row is a single example. idx = m x 1 %   vector of centroid assignments (i.e. each entry in range [1..K])%% Set KK = size(centroids, 1);% You need to return the following variables correctly.idx = zeros(size(X,1), 1);% ====================== YOUR CODE HERE ======================% Instructions: Go over every example, find its closest centroid, and store%               the index inside idx at the appropriate location.%               Concretely, idx(i) should contain the index of the centroid%               closest to example i. Hence, it should be a value in the %               range 1..K%% Note: You can use a for-loop over the examples to compute this.%for i=1:size(X,1)    tmp=zeros(K,1);    for j=1:K        tmp(j)=sum((X(i,:)-centroids(j,:)).^2);    end    [~,  idx(i)]=min(tmp,[],1);end;% =============================================================end

算法的思想：外层循环是针对每个数据点，内层循环是针对每个中心点。

二、computeCentroids.m

在一的基础上进行中心点的计算，就是求属于某个中心点的所有数据点的平均值，求出的结果作为这个簇的新的中心点。

function centroids = computeCentroids(X, idx, K)%COMPUTECENTROIDS returs the new centroids by computing the means of the %data points assigned to each centroid.%   centroids = COMPUTECENTROIDS(X, idx, K) returns the new centroids by %   computing the means of the data points assigned to each centroid. It is%   given a dataset X where each row is a single data point, a vector%   idx of centroid assignments (i.e. each entry in range [1..K]) for each%   example, and K, the number of centroids. You should return a matrix%   centroids, where each row of centroids is the mean of the data points%   assigned to it.%% Useful variables[m n] = size(X);% You need to return the following variables correctly.centroids = zeros(K, n);% ====================== YOUR CODE HERE ======================% Instructions: Go over every centroid and compute mean of all points that%               belong to it. Concretely, the row vector centroids(i, :)%               should contain the mean of the data points assigned to%               centroid i.%% Note: You can use a for-loop over the centroids to compute this.%num = zeros(K,1);for k = 1:K   for i = 1:m      if idx(i) == k          centroids(k,:) = centroids(k,:) + X(i,:);          num(k) = num(k) + 1;      end    end    centroids(k,:) = centroids(k,:)/num(k);end% =============================================================end

计算平均值的公式就是直接总和除以个数的简单数学计算。

三、pca.m

要求求出数据集的特征向量，然后求出它的压缩之后的数据。

function [U, S] = pca(X)%PCA Run principal component analysis on the dataset X%   [U, S, X] = pca(X) computes eigenvectors of the covariance matrix of X%   Returns the eigenvectors U, the eigenvalues (on diagonal) in S%% Useful values[m, n] = size(X);% You need to return the following variables correctly.U = zeros(n);S = zeros(n);% ====================== YOUR CODE HERE ======================% Instructions: You should first compute the covariance matrix. Then, you%               should use the "svd" function to compute the eigenvectors%               and eigenvalues of the covariance matrix. %% Note: When computing the covariance matrix, remember to divide by m (the%       number of examples).%sig=1/m*X'*X;[U, S ,V]=svd(sig);% =========================================================================end

四、projectData.m

要求是根据上一个算法求出的U，计算出相应的压缩之后的数据。

function Z = projectData(X, U, K)%PROJECTDATA Computes the reduced data representation when projecting only %on to the top k eigenvectors%   Z = projectData(X, U, K) computes the projection of %   the normalized inputs X into the reduced dimensional space spanned by%   the first K columns of U. It returns the projected examples in Z.%% You need to return the following variables correctly.Z = zeros(size(X, 1), K);% ====================== YOUR CODE HERE ======================% Instructions: Compute the projection of the data using only the top K %               eigenvectors in U (first K columns). %               For the i-th example X(i,:), the projection on to the k-th %               eigenvector is given as follows:%                    x = X(i, :)';%                    projection_k = x' * U(:, k);%for  i=1:size(X,1)    for k=1:K    x= X(i, :)';    Z(i,k) = x' * U(:, k);    endend% =============================================================end

recoverData.m

要求是求出压缩前的原始数据。

function X_rec = recoverData(Z, U, K)%RECOVERDATA Recovers an approximation of the original data when using the %projected data%   X_rec = RECOVERDATA(Z, U, K) recovers an approximation the %   original data that has been reduced to K dimensions. It returns the%   approximate reconstruction in X_rec.%% You need to return the following variables correctly.X_rec = zeros(size(Z, 1), size(U, 1));% ====================== YOUR CODE HERE ======================% Instructions: Compute the approximation of the data by projecting back%               onto the original space using the top K eigenvectors in U.%%               For the i-th example Z(i,:), the (approximate)%               recovered data for dimension j is given as follows:%                    v = Z(i, :)';%                    recovered_j = v' * U(j, 1:K)';%%               Notice that U(j, 1:K) is a row vector.%               for i=1:size(Z,1)    for j=1:size(U,1)    v = Z(i, :)';     X_rec(i,j) = v' * U(j, 1:K)';    endend% =============================================================end