# Generate correlated data from uncorrelated data.
# Each column of X is a 3-dimensional feature vector.
Z = scipy.randn(3, 1000)
C = scipy.randn(3, 3)
X = scipy.dot(C, Z)
# Visualize the correlation among the features.
pylab.scatter(X[0,:], X[1,:])
pylab.scatter(X[0,:], X[2,:])
pylab.scatter(X[1,:], X[2,:])
# Perform PCA. It can be shown that the principal components of the
# matrix X are equivalent to the left singular vectors of X, which are
# equivalent to the eigenvectors of X X^T (up to indeterminacy in sign).
U, S, Vh = scipy.linalg.svd(X)
W, Q = scipy.linalg.eig(scipy.dot(X, X.T))
print U
print Q
# Project the original features onto the eigenspace.
Y = scipy.dot(U.T, X)
# Visualize the absence of correlation among the projected features.
pylab.scatter(Y[0,:], Y[1,:])
pylab.scatter(Y[1,:], Y[2,:])
pylab.scatter(Y[0,:], Y[2,:])
If you know Python, here is a short hands-on example:
# Generate correlated data from uncorrelated data.
# Each column of X is a 3-dimensional feature vector.
Z = scipy.randn(3, 1000)
C = scipy.randn(3, 3)
X = scipy.dot(C, Z)
# Visualize the correlation among the features.
pylab.scatter(X[0,:], X[1,:])
pylab.scatter(X[0,:], X[2,:])
pylab.scatter(X[1,:], X[2,:])
# Perform PCA. It can be shown that the principal components of the
# matrix X are equivalent to the left singular vectors of X, which are
# equivalent to the eigenvectors of X X^T (up to indeterminacy in sign).
U, S, Vh = scipy.linalg.svd(X)
W, Q = scipy.linalg.eig(scipy.dot(X, X.T))
print U
print Q
# Project the original features onto the eigenspace.
Y = scipy.dot(U.T, X)
# Visualize the absence of correlation among the projected features.
pylab.scatter(Y[0,:], Y[1,:])
pylab.scatter(Y[1,:], Y[2,:])
pylab.scatter(Y[0,:], Y[2,:])
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评论（3）
如果您了解 Python，这里有一个简短的实践示例：
If you know Python, here is a short hands-on example:
您可以检查 http://alias-i.com/lingpipe/ demos/tutorial/svd/read-me.html SVD 和 LSA 与 PCA 非常相似，都是空间缩减方法。唯一的区别在于基础评估方法。
You can check http://alias-i.com/lingpipe/demos/tutorial/svd/read-me.html SVD and LSA is very similar approach to PCA both are space reduction methods. The only difference in basis evaluation approach.
由于您要求提供可用的实践示例，此处您有一个可以玩的交互式演示。
Since you're asking for available hands-on examples, here you have an interactive demo to play with.