I am working on principal component analysis of a matrix. I have already found the component matrix shown below
A = np.array([[-0.73465832 -0.24819766 -0.32045055]
[-0.3728976 0.58628043 -0.63433607]
[-0.72617152 0.53812819 -0.22846634]
[ 0.34042864 -0.08063226 -0.80064174]
[ 0.8804307 0.17166265 0.04381426]
[-0.66313032 0.54576874 0.37964986]
[ 0.286712 0.68305196 0.21769803]
[ 0.94651412 0.14986739 -0.06825887]
[ 0.40699665 0.73202276 -0.08462949]])
I need to perform varimax rotation in this component matrix but could not find the exact method and degree to rotate. Most of the examples are shown in R. However I need the method in python.
You can find a lot of examples with Python. Here is an example I found for Python using only numpy, on Wikipedia:
def varimax(Phi, gamma = 1, q = 20, tol = 1e-6):
from numpy import eye, asarray, dot, sum, diag
from numpy.linalg import svd
p,k = Phi.shape
R = eye(k)
d=0
for i in xrange(q):
d_old = d
Lambda = dot(Phi, R)
u,s,vh = svd(dot(Phi.T,asarray(Lambda)**3 - (gamma/p) * dot(Lambda, diag(diag(dot(Lambda.T,Lambda))))))
R = dot(u,vh)
d = sum(s)
if d/d_old < tol: break
return dot(Phi, R)
Wikipedia has an example in python here!
Lifting the example and tailoring it for numpy:
from numpy import eye, asarray, dot, sum, diag
from numpy.linalg import svd
def varimax(Phi, gamma = 1.0, q = 20, tol = 1e-6):
p,k = Phi.shape
R = eye(k)
d=0
for i in xrange(q):
d_old = d
Lambda = dot(Phi, R)
u,s,vh = svd(dot(Phi.T,asarray(Lambda)**3 - (gamma/p) * dot(Lambda, diag(diag(dot(Lambda.T,Lambda))))))
R = dot(u,vh)
d = sum(s)
if d_old!=0 and d/d_old < 1 + tol: break
return dot(Phi, R)
I've looked up solutions for doing factor analysis in python on stack-overflow so many times, that I recently made my own package, fa-kit. Even though this is an old post, I'm throwing up this link in case there's anybody else in the future that gets here via google.
