import numpy as np
from sklearn.decomposition import PCA
import sys
#returns choosing how many main factors
def index_lst(lst, component=0, rate=0):
#component: numbers of main factors
#rate: rate of sum(main factors)/sum(all factors)
#rate range suggest: (0.8,1)
#if you choose rate parameter, return index = 0 or less than len(lst)
if component and rate:
print('Component and rate must choose only one!')
sys.exit(0)
if not component and not rate:
print('Invalid parameter for numbers of components!')
sys.exit(0)
elif component:
print('Choosing by component, components are %s......'%component)
return component
else:
print('Choosing by rate, rate is %s ......'%rate)
for i in range(1, len(lst)):
if sum(lst[:i])/sum(lst) >= rate:
return i
return 0
def main():
# test data
mat = [[-1,-1,0,2,1],[2,0,0,-1,-1],[2,0,1,1,0]]
# simple transform of test data
Mat = np.array(mat, dtype='float64')
print('Before PCA transforMation, data is:\n', Mat)
print('\nMethod 1: PCA by original algorithm:')
p,n = np.shape(Mat) # shape of Mat
t = np.mean(Mat, 0) # mean of each column
# substract the mean of each column
for i in range(p):
for j in range(n):
Mat[i,j] = float(Mat[i,j]-t[j])
# covariance Matrix
cov_Mat = np.dot(Mat.T, Mat)/(p-1)
# PCA by original algorithm
# eigvalues and eigenvectors of covariance Matrix with eigvalues descending
U,V = np.linalg.eigh(cov_Mat)
# Rearrange the eigenvectors and eigenvalues
U = U[::-1]
for i in range(n):
V[i,:] = V[i,:][::-1]
# choose eigenvalue by component or rate, not both of them euqal to 0
Index = index_lst(U, component=2) # choose how many main factors
if Index:
v = V[:,:Index] # subset of Unitary matrix
else: # improper rate choice may return Index=0
print('Invalid rate choice.\nPlease adjust the rate.')
print('Rate distribute follows:')
print([sum(U[:i])/sum(U) for i in range(1, len(U)+1)])
sys.exit(0)
# data transformation
T1 = np.dot(Mat, v)
# print the transformed data
print('We choose %d main factors.'%Index)
print('After PCA transformation, data becomes:\n',T1)
# PCA by original algorithm using SVD
print('\nMethod 2: PCA by original algorithm using SVD:')
# u: Unitary matrix, eigenvectors in columns
# d: list of the singular values, sorted in descending order
u,d,v = np.linalg.svd(cov_Mat)
Index = index_lst(d, rate=0.95) # choose how many main factors
T2 = np.dot(Mat, u[:,:Index]) # transformed data
print('We choose %d main factors.'%Index)
print('After PCA transformation, data becomes:\n',T2)
# PCA by Scikit-learn
pca = PCA(n_components=2) # n_components can be integer or float in (0,1)
pca.fit(mat) # fit the model
print('\nMethod 3: PCA by Scikit-learn:')
print('After PCA transformation, data becomes:')
print(pca.fit_transform(mat)) # transformed data
main()
