Add the exo2 beginning implementation.

Signed-off-by: Jérôme Benoit <jerome.benoit@piment-noir.org>

diff --git a/TP3/exo1/tp3_exo1.py b/TP3/exo1/tp3_exo1.py
index dfd04d831840fa1024b5a45c35073325826d4ffa..73dd307de18e12ea18c25324c03142001c04c12d 100755 (executable)
--- a/TP3/exo1/tp3_exo1.py
+++ b/TP3/exo1/tp3_exo1.py
@@ -39,8 +39,8 @@ def generateData2(n):
     return inputs
 
 
-training_set_size = 100
-training_set = generateData(training_set_size)
+training_set_size = 150
+training_set = generateData2(training_set_size)
 data = np.array(training_set)
 X = data[:, 0:2]
 Y = data[:, -1]
@@ -54,17 +54,24 @@ def perceptron_nobias(X, Y):
         classification_error = 0
         for i in range(X.shape[0]):
             if Y[i] * np.dot(w, X[i]) <= 0:
-                classification_error = classification_error + 1
+                classification_error += 1
                 w = w + Y[i] * X[i]
     return w
 
 
 def complete(sample):
-    sample = np.expand_dims(sample, axis=0)
-    return sample
+    new_sample = np.insert(sample, len(sample[0]), [1], axis=1)
+    return np.array(new_sample)
 
 
+X = complete(X)
 w = perceptron_nobias(X, Y)
-pl.plot([-1, 1], [w[0] / w[1], -w[0] / w[1]])
+# w is orthogonal to the hyperplan
+# with generateData
+# pl.plot([-1, 1], [w[0] / w[1], -w[0] / w[1]])
+# with generateData2 and complete
+# FIXME: the hyperplan equation is not correct
+pl.plot([0, -1 / w[1]], [w[0] / w[1] - 1 / w[1], -w[0] / w[1] - 1 / w[1]])
 pl.scatter(X[:, 0], X[:, 1], c=Y, s=training_set_size)
+pl.title(u"Perceptron - hyperplan")
 pl.show()

diff --git a/TP3/exo2/tp3_exo2.py b/TP3/exo2/tp3_exo2.py
new file mode 100755 (executable)
index 0000000..c92d590
--- /dev/null
+++ b/TP3/exo2/tp3_exo2.py
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+
+# -*- coding: utf-8 -*-
+import numpy as np
+from numpy.random import rand
+import pylab as pl
+
+
+def generateData(n):
+    """
+    Generates a 2D linearly separable dataset with 2n samples.
+    The third element of the sample is the label
+    """
+    linear_offset = 0.6
+    xb = (rand(n) * 2 - 1) / 2 - linear_offset
+    yb = (rand(n) * 2 - 1) / 2 + linear_offset
+    xr = (rand(n) * 2 - 1) / 2 + linear_offset
+    yr = (rand(n) * 2 - 1) / 2 - linear_offset
+    inputs = []
+    for i in range(n):
+        inputs.append([xb[i], yb[i], -1])
+        inputs.append([xr[i], yr[i], 1])
+    return inputs
+
+
+def generateData2(n):
+    """
+    Generates a 2D linearly separable dataset with 2n samples.
+    The third element of the sample is the label
+    """
+    xb = (rand(n) * 2 - 1) / 2 - 0.5
+    yb = (rand(n) * 2 - 1) / 2
+    xr = (rand(n) * 2 - 1) / 2 + 1.5
+    yr = (rand(n) * 2 - 1) / 2 - 0.5
+    inputs = []
+    for i in range(n):
+        inputs.append([xb[i], yb[i], -1])
+        inputs.append([xr[i], yr[i], 1])
+    return inputs
+
+
+def generateData3(n):
+    """
+    Generates a 2D linearly separable dataset with 2n samples.
+    The third element of the sample is the label
+    """
+    # (xb, yb) est dans le carré centré à l’origine de côté 1
+    xb = (rand(n) * 2 - 1) / 2
+    yb = (rand(n) * 2 - 1) / 2
+    # (xr, yr) est dans le carré centré à l’origine de côté 3
+    xr = 3 * (rand(4 * n) * 2 - 1) / 2
+    yr = 3 * (rand(4 * n) * 2 - 1) / 2
+    inputs = []
+    for i in range(n):
+        inputs.append([xb[i], yb[i], -1])
+    for i in range(4 * n):
+        # on ne conserve que les points extérieurs au carré centré à l’origine
+        # de côté 2
+        if abs(xr[i]) >= 1 or abs(yr[i]) >= 1:
+            inputs.append([xr[i], yr[i], 1])
+    return inputs
+
+
+training_set_size = 150
+training_set = generateData2(training_set_size)
+data = np.array(training_set)
+X = data[:, 0:2]
+Y = data[:, -1]
+
+
+def perceptron_nobias(X, Y):
+    w = np.zeros([len(X[0])])
+    # Go in the loop at least one time
+    classification_error = 1
+    while not classification_error == 0:
+        classification_error = 0
+        for i in range(X.shape[0]):
+            if Y[i] * np.dot(w, X[i]) <= 0:
+                classification_error += 1
+                w = w + Y[i] * X[i]
+    return w
+
+
+def complete(sample):
+    new_sample = np.insert(sample, len(sample[0]), [1], axis=1)
+    return np.array(new_sample)
+
+
+def plongement(sample_element):
+    return [1, sample_element[0], sample_element[1], sample_element[0] * sample_element[0], sample_element[0] * sample_element[1], sample_element[1] * sample_element[1]]
+
+
+def apply_plongement(sample):
+    output = []
+    for i in range(sample.shape[0]):
+        current = plongement(sample[i])
+        output.append(current)
+    return np.array(output)
+
+
+X = apply_plongement(X)
+w = perceptron_nobias(X, Y)
+pl.scatter(X[:, 0], X[:, 1], c=Y, s=training_set_size)
+pl.title(u"Perceptron - hyperplan")
+pl.show()