ML - Lab 6 - PCA

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import sklearn

'''
# Create a DataFrame
X = [1, 0, -1, 0, -1, 1]
Y = [0, 1, 1, -1, 0, -1]
Z = [-1, -1, 0, 1, 1, 0]
labels = ["x1", "x2", "x3", "x4", "x5", "x6"]
pdata = pd.DataFrame({"X": X, "Y": Y, "Z": Z}, index=labels)
print("pdata = ")
print(pdata)
print()


# Plots - 3D scatter
fig = plt.figure()
ax = fig.add_subplot(projection='3d')
ax.scatter(pdata.X, pdata.Y, pdata.Z)
for i in range(len(pdata.index)):
    ax.text(pdata.loc[labels[i], "X"], pdata.loc[labels[i], "Y"], pdata.loc[labels[i], "Z"], '%s' % (str(labels[i])), size=20, zorder=1)
ax.set_xlabel('X Axis')
ax.set_ylabel('Y Axis')
ax.set_zlabel('Z Axis')
plt.show()
'''


# Read Data
engdata = pd.read_csv("./engdata.txt")
print("engdata = ")
print(engdata)
print()
print("engdata summary = ")
print(engdata.describe())
print()
# Find the Class
location = engdata.Location
engdata = engdata.drop(["Location"], axis=1)

# Plot data with different colors
plt.figure()
plt.scatter(engdata[location == "EU"].Age, engdata[location == "EU"].Salary, color="red", marker="+", label="EU")
plt.scatter(engdata[location == "US"].Age, engdata[location == "US"].Salary, color="blue", marker="o", label="US")
plt.title("Age - Salary")
plt.xlabel("Age")
plt.ylabel("Salary")
plt.legend()
plt.show()
print("Correlation Matrix (between 2 features) = ")
print(engdata.corr())
print()
print("We observe that Age and WorkExp have a high correlation.")
print("This means that also the correalation Age-FeatureX and WorkExp-FeatureX have approximately the same value.")
print("We could drop the WorkExp column, but we will continue with 4 features.")
print()
print()


# PCA: X features ---> X eigenvalues and eigenvectors. NEEDS A SCALER
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
# Scaler
scaler = StandardScaler()
scaler = scaler.fit(engdata)
transformed = pd.DataFrame(scaler.transform(engdata), columns=engdata.columns)


# PCA - 4 components
pca = PCA()
pca = pca.fit(transformed)
pca_transformed = pca.transform(transformed)
# Eigen
eigenvalues = pca.explained_variance_
eigenvectors = pca.components_
print("**************************************************************")
print("Eigenvalues = " + str(eigenvalues))
print("Eigenvectors = ")
print(eigenvectors)
print("**************************************************************")
print()
# Principal Components
plt.figure()
plt.bar(range(1, len(eigenvalues)+1), 100 * eigenvalues/sum(eigenvalues))
plt.title("Principal components with 4 features")
plt.xlabel("Eigenvalue #")
plt.ylabel("Component's weight (%)")
plt.show()


# PCA - 2 components
pca = PCA(n_components=2)
pca_transformed = pd.DataFrame(pca.fit_transform(transformed))
plt.figure()
plt.scatter(pca_transformed.loc[:, 0], pca_transformed.loc[:, 1])
plt.title("2-D data (from 4-D data)")
plt.xlabel("New var 1")
plt.ylabel("New var 2")
plt.show()


# PCA - 2 components - Go back and compare the 2-D plots
pca_inverse = pd.DataFrame(pca.inverse_transform(pca_transformed), columns=engdata.columns)
plt.figure()
plt.scatter(pca_transformed.loc[:, 0], pca_transformed.loc[:, 1])
plt.title("Inversed 2-D data (from 4-D data) can now be depicted")
plt.xlabel("New var 1")
plt.ylabel("New var 2")
plt.show()
print()
print()
print("transformed = ")
print(transformed)
print()
print("inversed (having kept 2-D instead of 4-D) = ")
print(pca_inverse)
print()


# New plot with new variables Age' and Salary'
plt.figure()
plt.scatter(pca_inverse[(location == "EU")].Age, pca_inverse[(location == "EU")].Salary, c="red", marker="+", label="EU")
plt.scatter(pca_inverse[(location == "US")].Age, pca_inverse[(location == "US")].Salary, c="blue", marker="o", label="US")
plt.title("Age' - Salary'")
plt.xlabel("Age'")
plt.ylabel("Salary'")
plt.legend()
plt.show()

# Info loss
info_loss = (eigenvalues[2] + eigenvalues[3]) / sum(eigenvalues)
print("Info loss = " + str(100 * info_loss) + " %")