Implement PCA

ex7/pca.m

@@ -1,31 +1,29 @@
-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).
-%
-
-
-
-
-
-
-
-% =========================================================================
-
-end
+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;  % covariance matrix
+
+[U, S, V] = svd(Sigma);
+
+% =========================================================================
+
+end