TP3/exo1/tp3_exo1.py

   1 #!/usr/bin/env python3
   2
   3 # -*- coding: utf-8 -*-
   4 import numpy as np
   5 from numpy.random import rand
   6 import pylab as pl
   7
   8
   9 def generateData(n):
  10     """
  11     Generates a 2D linearly separable dataset with 2n samples.
  12     The third element of the sample is the label
  13     """
  14     linear_offset = 0.6
  15     xb = (rand(n) * 2 - 1) / 2 - linear_offset
  16     yb = (rand(n) * 2 - 1) / 2 + linear_offset
  17     xr = (rand(n) * 2 - 1) / 2 + linear_offset
  18     yr = (rand(n) * 2 - 1) / 2 - linear_offset
  19     inputs = []
  20     for i in range(n):
  21         inputs.append([xb[i], yb[i], -1])
  22         inputs.append([xr[i], yr[i], 1])
  23     return inputs
  24
  25
  26 def generateData2(n):
  27     """
  28     Generates a 2D linearly separable dataset with 2n samples.
  29     The third element of the sample is the label
  30     """
  31     xb = (rand(n) * 2 - 1) / 2 + 0.5
  32     yb = (rand(n) * 2 - 1) / 2
  33     xr = (rand(n) * 2 - 1) / 2 + 1.5
  34     yr = (rand(n) * 2 - 1) / 2 - 0.5
  35     inputs = []
  36     for i in range(n):
  37         inputs.append([xb[i], yb[i], -1])
  38         inputs.append([xr[i], yr[i], 1])
  39     return inputs
  40
  41
  42 training_set_size = 150
  43 training_set = generateData2(training_set_size)
  44 data = np.array(training_set)
  45 X = data[:, 0:2]
  46 Y = data[:, -1]
  47
  48
  49 def perceptron_nobias(X, Y):
  50     w = np.zeros([len(X[0])])
  51     # Go in the loop at least one time
  52     classification_error = 1
  53     while not classification_error == 0:
  54         classification_error = 0
  55         for x, y in zip(X, Y):
  56             if y * np.dot(w, x) <= 0:
  57                 classification_error += 1
  58                 w = w + y * x
  59     return w
  60
  61
  62 def complete(sample):
  63     new_sample = np.insert(sample, len(sample[0]), [1], axis=1)
  64     return np.array(new_sample)
  65
  66
  67 X = complete(X)
  68 w = perceptron_nobias(X, Y)
  69 # w is orthogonal to the hyperplan
  70 # with generateData
  71 # plot arguments format is pl.plot([x1,x2],[y1,y2])
  72 # w[0]x + w[1]y = 0, so y = -w[0]x / w[1]
  73 # pl.plot([-1, 1], [w[0] / w[1], -w[0] / w[1]])
  74 # with generateData2 and complete
  75 # w[0]x + w[1]y + w[2] = 0, so y = -(w[0]x + w[2]) / w[1]
  76 x_start1 = -0.5
  77 x_start2 = 2.5
  78 pl.plot([x_start1, x_start2], [-(w[0] * x_start1 + w[2]) /
  79                                w[1], -(w[0] * x_start2 + w[2]) / w[1]])
  80 pl.scatter(X[:, 0], X[:, 1], c=Y, s=training_set_size)
  81 pl.title(u"Perceptron - hyperplan")
  82 pl.show()