manual.py

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
from sklearn.preprocessing import StandardScaler
import pandas as pd
from numpy import linalg as LA

df = pd.read_csv("forestfires.csv")
df.drop(columns=["area"], inplace=True)

scaler = StandardScaler()
scaled_features = scaler.fit_transform(df)
df = pd.DataFrame(scaled_features, index=df.index, columns=df.columns)
df.head()

columns = df.columns
newDf = pd.DataFrame(columns=columns, index=columns)

for i in columns:
  for j in columns:
    if(i == j):
      expected_value_i = (df[i]).sum() / len(df)
      expected_value_i_square = (df[i]*df[j]).sum()/ len(df)
      square_expected_value_i = expected_value_i * expected_value_i
      newDf[i][j] =  expected_value_i_square - square_expected_value_i
    else:
      expected_value_ij = (df[i] * df[j]).sum() / len(df)
      expected_value_i = (df[i]).sum() / len(df)
      expected_value_j = (df[j]).sum() / len(df)
      newDf[i][j] = expected_value_ij - expected_value_i * expected_value_j

display(newDf) 

# Finding eigenvalues for covariance matrix with numpy
float_df = newDf.to_numpy(dtype="float")
eigenvalues, eigenvectors = LA.eig(float_df)
idx = eigenvalues.argsort()[::-1]   
eigenvalues = eigenvalues[idx]
eigenvectors = eigenvectors[:,idx]
print(eigenvalues)
print(eigenvectors)

transformed_data = np.matmul(np.array(df),eigenvectors[:,:4])
transformed_data
display(pd.DataFrame(transformed_data, columns=["pc1", "pc2", "pc3", "pc4"]))

from sklearn.decomposition import PCA
pca = PCA(n_components=4)
principalComponents = pca.fit_transform(df)
principalDf = pd.DataFrame(data = principalComponents, columns = ['pc'+ str(i+1) for i in range(4)])
display(principalDf)