02416ba46171c462dde7934537888c37661bdd3f
[TP_AA.git] / 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 i in range(X.shape[0]):
56 if Y[i] * np.dot(w, X[i]) <= 0:
57 classification_error += 1
58 w = w + Y[i] * X[i]
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()