Introduction to Machine Learning

# numpy and matplotlib will be used a lot during the lecture
# if you are familiar with these libraries you may skip this part
# if not - extended comments were added to make it easier to understand

# it is kind of standard to import numpy as np and pyplot as plt
import numpy as np
import matplotlib.pyplot as plt

# used later to apply different colors in for loops
mpl_colors = ('r', 'b', 'g', 'c', 'm', 'y', 'k', 'w')

# just to overwrite default colab style
plt.style.use('default')


def generate_random_points(size=10, low=0, high=1):
  """Generate a set of random 2D points
  
  size -- number of points to generate
  low  -- min value
  high -- max value
  """
  # random_sample([size]) returns random numbers with shape defined by size
  # e.g.
  # >>> np.random.random_sample((2, 3))
  #
  # array([[ 0.44013807,  0.77358569,  0.64338619],
  #        [ 0.54363868,  0.31855232,  0.16791031]])
  #
  return (high - low) * np.random.random_sample((size, 2)) + low


def init_plot(x_range=None, y_range=None, x_label="$x_1$", y_label="$x_2$"):
  """Set axes limits and labels
  
  x_range -- [min x, max x]
  y_range -- [min y, max y]
  x_label -- string
  y_label -- string
  """
 
  # subplots returns figure and axes
  # (in general you may want many axes on one figure)
  # we do not need fig here
  # but we will apply changes (including adding points) to axes
  _, ax = plt.subplots(dpi=70)
  
  # set grid style and color
  ax.grid(c='0.70', linestyle=':')
  
  # set axes limits (x_range and y_range is a list with two elements)
  ax.set_xlim(x_range) 
  ax.set_ylim(y_range)
    
  # set axes labels
  ax.set_xlabel(x_label)
  ax.set_ylabel(y_label)
  
  # return axes so we can continue modyfing them later
  return ax


def plot_random_points(style=None, color=None):
  """Generate and plot two (separated) sets of random points
  
  style -- latter group points style (default as first)
  color -- latter group color (default as first)
  """
  
  # create a plot with x and y ranges from 0 to 2.5
  ax = init_plot([0, 2.5], [0, 2.5])

  # add two different sets of random points
  # first set = 5 points from [0.5, 1.0]x[0.5, 1.0]
  # second set = 5 points from [1.5, 2.0]x[1.5, 2.0]
  # generate_random_points return a numpy array in the format like
  # [[x1, y1], [x2, y2], ..., [xn, yn]]
  # pyplot.plt take separately arrays with X and Y, like
  # plot([x1, x2, x3], [y1, y2, y3])
  # thus, we transpose numpy array to the format
  # [[x1, x2, ..., xn], [y1, y2, ..., yn]]
  # and unpack it with *
  ax.plot(*generate_random_points(5, 0.5, 1.0).T, 'ro')
  ax.plot(*generate_random_points(5, 1.5, 2.0).T, style or 'ro')
  
  return ax


def plot_an_example(style=None, color=None, label="Class"):
  """Plot an example of supervised or unsupervised learning"""
  ax = plot_random_points(style, color)

  # circle areas related to each set of points
  # pyplot.Circle((x, y), r); (x, y) - the center of a circle; r - radius
  # lw - line width
  ax.add_artist(plt.Circle((0.75, 0.75), 0.5, fill=0, color='r', lw=2))
  ax.add_artist(plt.Circle((1.75, 1.75), 0.5, fill=0, color=color or 'r', lw=2))

  # put group labels
  # pyplot.text just put arbitrary text in given coordinates
  ax.text(0.65, 1.4, label + " I", fontdict={'color': 'r'})
  ax.text(1.65, 1.1, label + " II", fontdict={'color': color or 'r'})

plot_an_example(style='bs', color='b');

plot_an_example(label="Cluster");