PCA

PCA.py

def Reduced_data_set(dataset,final_dimension, plot = False):
    '''
    This function is used to perform pca 
    and retain final_dimension number of 
    principle component from our dataset
    '''
    
    # Centering all the features to zero mean    
    Mean_of_data=dataset.mean(0)
    centered_data=dataset-Mean_of_data
    
    # Calculating the Covariance Matrix
    covariance_matrix=np.cov(centered_data.T)
    
    # Computing the eigenvalues and eigenvectors of the Covariance Matrix 
    eigen_values,eigen_vectors=np.linalg.eig(covariance_matrix)
    
    # Sorting the eigenvalues from largest to smallest
    idx = eigen_values.argsort()[::-1]
    eigen_values = eigen_values[idx]
    eigen_vectors = eigen_vectors[:,idx]
    
    # Projecting the dataset on the final_dimension eigenvectors (selected based on higher eigenvalue)
    reduced=np.matmul(centered_data,eigen_vectors[:,:final_dimension],out=None)
    
    # If plotting the eigenvector of the covariance matrix and mean centered data is required
    if plot:
      plt.title("Mean Centered Data and the EigenVectors of Covariance Matrix (Scaled by EigenValue)")
      plt.plot(centered_data[:,0][:50], centered_data[:,1][:50], 'ro', label = ' Data A')
      plt.plot(centered_data[:,0][50:], centered_data[:,1][50:], 'go', label = ' Data B')
      plt.quiver([0,0], [0,0], *eigen_values*(eigen_vectors), label = 'Eigen Vectors of Covariance Matrix',angles='xy', scale_units='xy', scale = 2.5)
      plt.legend(loc = 'best')
      
    return reduced