The XOR problem

Let's try to solve the XOR problem we presented earlier with a simple FFNN, by performing the following steps:

First of all, let's import everything we will need for this task and seed our random function:

import numpy as np
import pandas as pd
from sklearn.metrics import confusion_matrix
from sklearn.metrics import roc_auc_score
from sklearn.metrics import mean_squared_error
import matplotlib

matplotlib.use("TkAgg")

# initiating random number
np.random.seed(11)

To make it more similar to a real-word problem, we will add some noise to the XOR input, and we will try to predict a binary task:

#### Creating the dataset

# mean and standard deviation for the x belonging to the first class
mu_x1, sigma_x1 = 0, 0.1

# Constant to make the second distribution different from the first
# x1_mu_diff, x2_mu_diff, x3_mu_diff, x4_mu_diff = 0.5, 0.5, 0.5, 0.5
x1_mu_diff, x2_mu_diff, x3_mu_diff, x4_mu_diff = 0, 1, 0, 1

# creating the first distribution
d1 = pd.DataFrame({'x1': np.random.normal(mu_x1, sigma_x1, 
                  1000) + 0,
                  'x2': np.random.normal(mu_x1, sigma_x1,
                  1000) + 0,'type': 0})

d2 = pd.DataFrame({'x1': np.random.normal(mu_x1, sigma_x1, 
                  1000) + 1,
                  'x2': np.random.normal(mu_x1, sigma_x1,
                  1000) - 0,'type': 1})

d3 = pd.DataFrame({'x1': np.random.normal(mu_x1, sigma_x1, 
                  1000) - 0,
                  'x2': np.random.normal(mu_x1, sigma_x1, 
                  1000) - 1,'type': 0})

d4 = pd.DataFrame({'x1': np.random.normal(mu_x1, sigma_x1, 
                  1000) - 1,
                  'x2': np.random.normal(mu_x1, sigma_x1, 
                  1000) + 1, 'type': 1})

data = pd.concat([d1, d2, d3, d4], ignore_index=True)

In this way, we will get a noisy XOR, as shown in the following screenshot: