In [6]:

    

import time
print('Last updated:', time.strftime('%m/%d/%Y'))


    

    




Last updated: 06/12/2014

In [7]:

    

%matplotlib inline


    

In [8]:

    

from matplotlib import pyplot as plt
import numpy as np

# Generating a Gaussion dataset:
# creating random vectors from the multivariate normal distribution 
# given mean and covariance 
mu_vec1 = np.array([0,0])
cov_mat1 = np.array([[2,0],[0,2]])

x1_samples = np.random.multivariate_normal(mu_vec1, cov_mat1, 100)
x2_samples = np.random.multivariate_normal(mu_vec1+0.2, cov_mat1+0.2, 100)
x3_samples = np.random.multivariate_normal(mu_vec1+0.4, cov_mat1+0.4, 100)

# x1_samples.shape -> (100, 2), 100 rows, 2 columns

plt.figure(figsize=(8,6))
    
plt.scatter(x1_samples[:,0], x1_samples[:,1], marker='x', 
            color='blue', alpha=0.7, label='x1 samples')
plt.scatter(x2_samples[:,0], x1_samples[:,1], marker='o', 
            color='green', alpha=0.7, label='x2 samples')
plt.scatter(x3_samples[:,0], x1_samples[:,1], marker='^', 
            color='red', alpha=0.7, label='x3 samples')
plt.title('Basic scatter plot')
plt.ylabel('variable X')
plt.xlabel('Variable Y')
plt.legend(loc='upper right')

plt.show()


    

In [5]:

    

# 2-category classification with random 2D-sample data 
# from a multivariate normal distribution 

import numpy as np
from matplotlib import pyplot as plt

def decision_boundary(x_1):
    """ Calculates the x_2 value for plotting the decision boundary."""
    return 4 - np.sqrt(-x_1**2 + 4*x_1 + 6 + np.log(16))

# Generating a Gaussion dataset:
# creating random vectors from the multivariate normal distribution 
# given mean and covariance 
mu_vec1 = np.array([0,0])
cov_mat1 = np.array([[2,0],[0,2]])
x1_samples = np.random.multivariate_normal(mu_vec1, cov_mat1, 100)
mu_vec1 = mu_vec1.reshape(1,2).T # to 1-col vector

mu_vec2 = np.array([1,2])
cov_mat2 = np.array([[1,0],[0,1]])
x2_samples = np.random.multivariate_normal(mu_vec2, cov_mat2, 100)
mu_vec2 = mu_vec2.reshape(1,2).T # to 1-col vector

# Main scatter plot and plot annotation
f, ax = plt.subplots(figsize=(7, 7))
ax.scatter(x1_samples[:,0], x1_samples[:,1], marker='o', color='green', s=40, alpha=0.5)
ax.scatter(x2_samples[:,0], x2_samples[:,1], marker='^', color='blue', s=40, alpha=0.5)
plt.legend(['Class1 (w1)', 'Class2 (w2)'], loc='upper right') 
plt.title('Densities of 2 classes with 25 bivariate random patterns each')
plt.ylabel('x2')
plt.xlabel('x1')
ftext = 'p(x|w1) ~ N(mu1=(0,0)^t, cov1=I)\np(x|w2) ~ N(mu2=(1,1)^t, cov2=I)'
plt.figtext(.15,.8, ftext, fontsize=11, ha='left')

# Adding decision boundary to plot
x_1 = np.arange(-5, 5, 0.1)
bound = decision_boundary(x_1)
plt.plot(x_1, bound, 'r--', lw=3)

x_vec = np.linspace(*ax.get_xlim())
x_1 = np.arange(0, 100, 0.05)

plt.show()