Principal Component Analysis in pure Numpy

pca.py

# -*- coding: utf-8 -*-
"""
Created on Sun Jan 31 11:03:57 2013
 
@author: Sukhbinder
https://sukhbinder.wordpress.com/2022/08/21/principal-component-analysis-with-numpy/
"""
 
 
import numpy as np
 
def pca1(x):
    """Determine the principal components of a vector of measurements
     
 
    Determine the principal components of a vector of measurements
    x should be a M x N numpy array composed of M observations of n variables
 
    PCA using covariance
     
    The output is:
    coeffs - the NxN correlation matrix that can be used to transform x into its components
    signals is MxN of projected data
 
    The code for this function is based on "A Tutorial on Principal Component
    Analysis", Shlens, 2005 http://www.snl.salk.edu/~shlens/pub/notes/pca.pdf
    (unpublished)
    https://www.cs.cmu.edu/~elaw/papers/pca.pdf
    """
     
    (M,N)  = x.shape
    Mean   = x.mean(0)
    y      = x - Mean
    cov    = np.dot(y.T,y) / (M-1)
    (V,PC) = np.linalg.eig(cov)
     
    order  = (-V).argsort()
    V=V[order]
    coeff  = PC[:,order]
    signals = np.dot(PC.T,y.T)
    return coeff,signals,V
 
     
def pca2(x):
    """Determine the principal components of a vector of measurements
     
    Determine the principal components of a vector of measurements
    x should be a M x N numpy array composed of M observations of n variables
    The output is:
    coeffs - the NxN correlation matrix that can be used to transform x into its components
    signals is MxN of projected data
     
    The code for this function is based on "A Tutorial on Principal Component
    Analysis", Shlens, 2005 http://www.snl.salk.edu/~shlens/pub/notes/pca.pdf
    (unpublished)
    https://www.cs.cmu.edu/~elaw/papers/pca.pdf
    """
    (M,N)  = x.shape
    Mean   = x.mean(0)
    y      = x - Mean
    yy = y.T/np.sqrt(M-1)
    u,s,pc = np.linalg.svd(yy)
    s=np.diag(s)
    v= np.dot(s,s)
    v=diag(v)
    signals = np.dot(pc.T,y)
    return pc,signals,v