主成分分析的工作示例？

Question

是否有任何可用的示例給出了數據集上主要組件分析的實例？我正在閱讀僅討論理論的文章，​​並且正在尋找能夠告訴我如何使用PCA，然後解釋結果並將原始數據集轉換爲新數據集的內容。有什麼建議嗎？

Answer 1

如果你知道的Python，這裏是一個簡短的動手例如：

# 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,:]) 

Answer 2

您可以檢查http://alias-i.com/lingpipe/demos/tutorial/svd/read-me.html SVD和LSA與PCA非常相似，都是空間縮減方法。基礎評估方法的唯一區別。

Answer 3

由於您要求提供實際操作示例，因此您可以使用一個交互式演示。