Implement PCA

ex7/pca.m

@@ -1,31 +1,29 @@
-function [U, S] = pca(X)
+function [U, S] = pca(X)
-%PCA Run principal component analysis on the dataset X
+%PCA Run principal component analysis on the dataset X
-%   [U, S, X] = pca(X) computes eigenvectors of the covariance matrix of X
+%   [U, S, X] = pca(X) computes eigenvectors of the covariance matrix of X
-%   Returns the eigenvectors U, the eigenvalues (on diagonal) in S
+%   Returns the eigenvectors U, the eigenvalues (on diagonal) in S
-%
+%
-
+
-% Useful values
+% Useful values
-[m, n] = size(X);
+[m, n] = size(X);
-
+
-% You need to return the following variables correctly.
+% You need to return the following variables correctly.
-U = zeros(n);
+U = zeros(n);
-S = zeros(n);
+S = zeros(n);
-
+
-% ====================== YOUR CODE HERE ======================
+% ====================== YOUR CODE HERE ======================
-% Instructions: You should first compute the covariance matrix. Then, you
+% Instructions: You should first compute the covariance matrix. Then, you
-%               should use the "svd" function to compute the eigenvectors
+%               should use the "svd" function to compute the eigenvectors
-%               and eigenvalues of the covariance matrix. 
+%               and eigenvalues of the covariance matrix.
-%
+%
-% Note: When computing the covariance matrix, remember to divide by m (the
+% Note: When computing the covariance matrix, remember to divide by m (the
-%       number of examples).
+%       number of examples).
-%
+%
-
+
-
+Sigma = 1/m * X'*X;  % covariance matrix
-
+
-
+[U, S, V] = svd(Sigma);
-
+
-
+% =========================================================================
-
+
-% =========================================================================
+end
-
-end