complex eigen values in PCA calculation
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05-06-2021 - |
Question
Iam trying to calculate PCA of a matrix.
Sometimes the resulting eigen values/vectors are complex values so when trying to project a point to a lower dimension plan by multiplying the eigen vector matrix with the point coordinates i get the following Warning
ComplexWarning: Casting complex values to real discards the imaginary part
In that line of code np.dot(self.u[0:components,:],vector)
The whole code i used to calculate PCA
import numpy as np
import numpy.linalg as la
class PCA:
def __init__(self,inputData):
data = inputData.copy()
#m = no of points
#n = no of features per point
self.m = data.shape[0]
self.n = data.shape[1]
#mean center the data
data -= np.mean(data,axis=0)
# calculate the covariance matrix
c = np.cov(data, rowvar=0)
# get the eigenvalues/eigenvectors of c
eval, evec = la.eig(c)
# u = eigen vectors (transposed)
self.u = evec.transpose()
def getPCA(self,vector,components):
if components > self.n:
raise Exception("components must be > 0 and <= n")
return np.dot(self.u[0:components,:],vector)
Solution
The covariance matrix is symmetric, and thus has real eigenvalues. You may see a small imaginary part in some eigenvalues due to numerical error. The imaginary parts can generally be ignored.
OTHER TIPS
You can use scikits python library for PCA, this is an example of how to use it
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