- **covariance_boston.py:** Compute the covariance matrix of the Boston Housing dataset. These matrices can sometimes give faster insight into which variables are related rather than creating scatter plots.

- **Covariance Matrix:** The covariance of two variables measures how "correlated" they are. If the two variables have a positive covariance, then one when variable increases so does the other; with a negative covariance the values of the feature variables will change in opposite directions. The magnitude of the covariance determines how strongly the features are correlated. A high covariance value means that when one of the feature variables changes by an amount x, the other will change by an amount very close to x; vice versa for low covariance values.

import pandas as pd

import numpy as np

from scipy import stats

import seaborn.apionly as sns

from tabulate import tabulate

import matplotlib.pyplot as plt

from sklearn.datasets import load_boston

import helpers as helpers

boston_data = load_boston()

train_data = np.array(boston_data.data)

train_labels = np.array(boston_data.target)

num_features = boston_data.data.shape[1]

unique_labels = np.unique(train_labels)

num_classes = len(unique_labels)

print("The boston dataset has " + str(num_features) + " features")

print(boston_data.feature_names)

data = pd.DataFrame(data=np.c_[train_data], columns=boston_data.feature_names)

cov_mat_boston = np.cov(train_data.T)

print("Covariance matrix")

print(cov_mat_boston)

normalized_train_data = helpers.normalize_data(train_data)

normalized_cov_mat_boston = np.cov(normalized_train_data.T)

print("Normalized data covariance matrix")

print(normalized_cov_mat_boston)

fig = sns.pairplot(data=data, hue='CRIM')

plt.show()