Andrew Ng机器学习笔记ex7 K-means聚类和PCA
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findClosestCentroids.m
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), for j=1:K, distance(j) =norm(X(i,:)-centroids(j,:))^2; %注意平方 end [minr,index]=min(distance); %也可用if循环 idx(i)=index;end% =============================================================end
computeCentroids.m
function centroids = computeCentroids(X, idx, K)%COMPUTECENTROIDS returns 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.%% 使用for循环for i = 1:K count = 0; for j = 1:m if idx(j) == i count = count + 1; centroids(i,:) = centroids(i,:) + X(j,:); end end centroids(i,:) = centroids(i,:) / count;end% =============================================================end
kMeansInitCentroids.m
function centroids = kMeansInitCentroids(X, K)%KMEANSINITCENTROIDS This function initializes K centroids that are to be %used in K-Means on the dataset X% centroids = KMEANSINITCENTROIDS(X, K) returns K initial centroids to be% used with the K-Means on the dataset X%% You should return this values correctlycentroids = zeros(K, size(X, 2));% ====================== YOUR CODE HERE ======================% Instructions: You should set centroids to randomly chosen examples from% the dataset X%% Randomly reorder the indices of examplesrandidx = randperm(size(X, 1));% Take the first K examples as centroidscentroids = X(randidx(1:K), :);% =============================================================end
pca.m
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).%Sigma = (1/m)*X'*X;[U,S,V] = svd(Sigma);% =========================================================================end
projectData.m
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);%U_reduced = U(:, 1:K);Z = X * U_reduced;% =============================================================end
recoverData.m
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.% U_reduced = U(:, 1:K);X_rec = Z * U_reduced';% =============================================================end
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