Python特征降维知识点总结

from sklearn.feature_selection import VarianceThreshold
# 特征选择  VarianceThreshold删除低方差的特征(删除差别不大的特征)
var = VarianceThreshold(threshold=1.0)# 将方差小于等于1.0的特征删除。 默认threshold=0.0
data = var.fit_transform([[0, 2, 0, 3], [0, 1, 4, 3], [0, 1, 1, 3]])
 
print(data)
'''
[[0]
 [4]
 [1]]
'''

def laplaEigen(dataMat,k,t): 
 m,n=shape(dataMat) 
 W=mat(zeros([m,m])) 
 D=mat(zeros([m,m])) 
 for i in range(m): 
 k_index=knn(dataMat[i,:],dataMat,k) 
 for j in range(k): 
  sqDiffVector = dataMat[i,:]-dataMat[k_index[j],:] 
  sqDiffVector=array(sqDiffVector)**2 
  sqDistances = sqDiffVector.sum() 
  W[i,k_index[j]]=math.exp(-sqDistances/t) 
  D[i,i]+=W[i,k_index[j]] 
 L=D-W 
 Dinv=np.linalg.inv(D) 
 X=np.dot(D.I,L) 
 lamda,f=np.linalg.eig(X) 
return lamda,f 
def knn(inX, dataSet, k): 
 dataSetSize = dataSet.shape[0] 
 diffMat = tile(inX, (dataSetSize,1)) - dataSet 
 sqDiffMat = array(diffMat)**2 
 sqDistances = sqDiffMat.sum(axis=1) 
 distances = sqDistances**0.5 
 sortedDistIndicies = distances.argsort() 
return sortedDistIndicies[0:k] 
dataMat, color = make_swiss_roll(n_samples=2000) 
lamda,f=laplaEigen(dataMat,11,5.0) 
fm,fn =shape(f) 
print 'fm,fn:',fm,fn 
lamdaIndicies = argsort(lamda) 
first=0 
second=0 
print lamdaIndicies[0], lamdaIndicies[1] 
for i in range(fm): 
 if lamda[lamdaIndicies[i]].real>1e-5: 
 print lamda[lamdaIndicies[i]] 
 first=lamdaIndicies[i] 
 second=lamdaIndicies[i+1] 
 break 
print first, second 
redEigVects = f[:,lamdaIndicies] 
fig=plt.figure('origin') 
ax1 = fig.add_subplot(111, projection='3d') 
ax1.scatter(dataMat[:, 0], dataMat[:, 1], dataMat[:, 2], c=color,cmap=plt.cm.Spectral) 
fig=plt.figure('lowdata') 
ax2 = fig.add_subplot(111) 
ax2.scatter(f[:,first], f[:,second], c=color, cmap=plt.cm.Spectral) 
plt.show()