Add TP3 exo3 and TP4 exo1.

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

diff --git a/TP3/exo3/learn.data b/TP3/exo3/learn.data
new file mode 100644 (file)
index 0000000..7e79164
--- /dev/null
+++ b/TP3/exo3/learn.data
@@ -0,0 +1,91 @@
+((16.695999571453935, -0.92787346122700254), 1)
+((15.850388825759982, 0.47211252902514111), -1)
+((10.622623441731935, -0.31499449528815537), -1)
+((7.0784268427453174, -0.17699681107630116), 1)
+((19.069159584397536, -0.027484910013680031), 1)
+((15.991549733559815, 0.23823004013080151), -1)
+((4.8615293559045814, 0.057468964112846743), -1)
+((14.934748753321383, 0.076892110240574185), 1)
+((4.888686399955084, 0.1430260760559372), -1)
+((0.85702943648359398, 0.15123320778307159), 1)
+((10.124866276079473, 0.85197942671311888), -1)
+((4.8958991656835487, 0.69585576409453753), -1)
+((4.8391930923249742, -0.28690936737134098), -1)
+((5.3995102888136941, 0.72744167839658624), -1)
+((9.40391434298669, 0.35725004144808126), -1)
+((12.909034200628621, -0.4232915510035673), 1)
+((0.87017159126183463, 0.75163187899954842), 1)
+((6.9562049949800713, -0.90973561718081219), 1)
+((7.1717649919440785, -0.28842490811701826), 1)
+((17.615529564829849, -0.18592723684801538), -1)
+((7.132240565453019, 0.13114464704213868), 1)
+((6.9830817325630479, -0.38151006148972355), 1)
+((8.4294369469384236, 0.13814115702916974), 1)
+((0.75557290592005, 0.28604087736928352), 1)
+((0.83922292474758242, 0.58015703686809039), 1)
+((0.70135832302924195, 0.50818652333324454), 1)
+((13.573423185282881, 0.96611173973180287), -1)
+((7.672704708982014, -0.74103813009467223), 1)
+((18.945112446592461, -0.89165104626659741), 1)
+((10.455526984693195, 0.96700036169426595), -1)
+((9.7212729427924529, -0.35321827008440287), 1)
+((10.545228385763641, 0.027840325333361893), -1)
+((11.948858391362833, 0.050800412258009686), -1)
+((4.9657521885585005, 0.18300050771400911), -1)
+((16.26401493653054, 0.30667600691224917), -1)
+((17.9245310070866, 0.94639881861859765), -1)
+((5.9247269215840763, 0.31364953306796961), -1)
+((10.345035469877903, -0.47195264308674556), -1)
+((6.8556689494737011, -0.9997647068865394), 1)
+((8.3550190383955414, 0.99922894229815107), -1)
+((3.2101466401133827, -0.64659653185031241), 1)
+((15.344817996874134, 0.51704626505728801), -1)
+((11.644537982887906, 0.49396793371846193), -1)
+((13.752898511406602, 0.76803163383677786), 1)
+((19.243862164394372, -0.92809967348090061), 1)
+((17.138430318422571, -0.39239639049625774), -1)
+((17.823828075185403, -0.11334270685581394), -1)
+((16.160613938611476, 0.54441903255144064), -1)
+((14.243439703916451, 0.72171673081152043), 1)
+((0.49394728724601711, -0.47594397141280265), 1)
+((13.254018719315731, 0.95756943670582961), -1)
+((17.684416102436089, 0.64668519761196608), -1)
+((8.8322321649974498, -0.09109729319185611), 1)
+((18.649532059529726, 0.24733323013667219), -1)
+((1.0436632280681279, -0.2521501001074713), 1)
+((11.664389239843725, 0.86732297881487663), -1)
+((16.428288200233997, -0.15358839214361608), -1)
+((2.1382085467537792, -0.50680711352825325), 1)
+((10.818139201342889, -0.12736814980256428), -1)
+((11.255868945207521, 0.66711418146243395), -1)
+((8.2998543493818016, -0.13730142331252471), 1)
+((16.347602957223614, -0.61805196879434399), 1)
+((18.320815963491508, -0.64466928264091661), 1)
+((13.164792547880657, -0.13380109607084556), 1)
+((0.4572122629454789, -0.38345621696307575), 1)
+((15.620961409110869, 0.45970561036366453), -1)
+((18.163225598542038, -0.7529684013103275), 1)
+((6.0100221084338257, 0.28991615155035189), -1)
+((16.815402002750851, -0.19380648631387531), -1)
+((6.97100180671743, -0.37910735915631522), 1)
+((8.8541549430877957, 0.11569878910064912), 1)
+((10.915144936112371, -0.51182807783035789), -1)
+((13.244618552298217, 0.6038180093761738), 1)
+((1.582858749571483, -0.0039123101698492757), 1)
+((1.2705975471954711, -0.49375247128526722), 1)
+((2.7510701789850112, -0.76463023088040183), 1)
+((8.3629887122557598, 0.53435800228334052), 1)
+((0.9192421784134841, -0.31942277867475077), 1)
+((4.0463017601103912, 0.11392149645586547), -1)
+((6.3720540497103739, -0.55465541087586034), 1)
+((15.290088491708588, 0.67986120735910172), -1)
+((1.5745431952965294, -0.73582714870824661), 1)
+((17.959851292975642, 0.099503634520412776), -1)
+((7.7307687650278183, 0.60567816327110124), 1)
+((17.878056546463807, 0.10820081597007536), -1)
+((12.246109090184902, -0.77100807235001345), 1)
+((2.5213015873727818, 0.084873128476091519), 1)
+((6.847971329921716, 0.82329735128559234), -1)
+((8.1535084884322178, 0.43240560983320431), 1)
+((19.237326622160804, 0.95388209408948965), -1)
+((11.041491819881665, -0.12069818862895776), -1)

diff --git a/TP3/exo3/tp3_exo3.py b/TP3/exo3/tp3_exo3.py
new file mode 100755 (executable)
index 0000000..3476f6f
--- /dev/null
+++ b/TP3/exo3/tp3_exo3.py
@@ -0,0 +1,180 @@
+#!/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 about 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
+
+
+def readData(file):
+    f = open(file, "r")
+    training_set = []
+    x = f.readline()
+    while x:
+        x_eval = eval(x)
+        training_set.append([x_eval[0][0], x_eval[0][1], x_eval[1]])
+        x = f.readline()
+    f.close()
+    return training_set
+
+
+training_set_size = 150
+# training_set = generateData3(training_set_size)
+training_set = readData("learn.data")
+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 x, y in zip(X, Y):
+            if y * np.dot(w, x) <= 0:
+                classification_error += 1
+                w = w + y * x
+        print(classification_error)
+    return w
+
+
+def complete(sample):
+    new_sample = np.insert(sample, len(sample[0]), [1], axis=1)
+    return np.array(new_sample)
+
+
+def plongement_phi(sample_element):
+    return [1, sample_element[0], sample_element[1], sample_element[0]**2,
+            sample_element[0] * sample_element[1], sample_element[1]**2]
+
+
+def apply_plongement(sample, p):
+    output = []
+    for i in range(sample.shape[0]):
+        current = p(sample[i])
+        output.append(current)
+    return np.array(output)
+
+
+def f_from_k(coeffs, support_set, k, x):
+    output = 0
+    for c, s in zip(coeffs, support_set):
+        output += c * s[1] * k(s[0], x)
+    return output
+
+
+def k1(X1, X2):
+    return 1 + X1[0] * X2[0] + X1[1] * X2[1] + X1[0]**2 * X2[0]**2 \
+             + X1[0] * X1[1] * X2[0] * X2[1] + X1[1]**2 * X2[1]**2
+
+
+def kg(x, y):
+    # sigma = 20  # do not converge
+    # sigma = 10  # do not converge
+    sigma = 1  # overfitting
+    # sigma = 0.5  # overfitting
+    # sigma = 0.2  # overfitting
+    return np.exp(-((x[0] - y[0])**2 + (x[1] - y[1])**2) / sigma**2)
+
+
+def perceptron_k(X, Y, k):
+    coeffs = []
+    support_set = []
+    # Go in the loop at least one time
+    classification_error = 1
+    while not classification_error == 0:
+        classification_error = 0
+        for x, y in zip(X, Y):
+            if y * f_from_k(coeffs, support_set, k, x) <= 0:
+                if x not in support_set:
+                    support_set.append((x, y))
+                    coeffs.append(1)
+                else:
+                    coeffs[support_set.index((x, y))] += 1
+                classification_error += 1
+        print(classification_error)
+    return np.array(coeffs), np.array(support_set)
+
+
+def f(w, x, y):
+    return w[0] + w[1] * x + w[2] * y + w[3] * x**2 + w[4] * x * y + w[5] * y**2
+
+
+pl.scatter(X[:, 0], X[:, 1], c=Y)
+pl.title(u"Perceptron - prolontaged hyperplan")
+
+# k = k1
+# coeffs, support_set = perceptron_k(X, Y, k)
+k = kg
+coeffs, support_set = perceptron_k(X, Y, k)
+res = training_set_size
+for x in range(res):
+    for y in range(res):
+        if abs(f_from_k(coeffs, support_set, k, [-3 / 2 + 3 * x / res, -3 / 2 + 3 * y / res])) < 0.01:
+            pl.plot(-3 / 2 + 3 * x / res, -3 / 2 + 3 * y / res, 'xr')
+
+# X = apply_plongement(X, plongement_phi)
+# w = perceptron_nobias(X, Y)
+# for x in range(res):
+#     for y in range(res):
+#         if abs(f(w, -3 / 2 + 3 * x / res, -3 / 2 + 3 * y / res)) < 0.01:
+#             pl.plot(-3 / 2 + 3 * x / res, -3 / 2 + 3 * y / res, 'xb')
+
+pl.show()

diff --git a/TP4/exo1/dataRegLin2D.txt b/TP4/exo1/dataRegLin2D.txt
new file mode 100644 (file)
index 0000000..021ed56
--- /dev/null
+++ b/TP4/exo1/dataRegLin2D.txt
@@ -0,0 +1,100 @@
+  0.974633 -0.792363 -1.55824
+  0.322351 1.8034 1.8891
+  1.35589 0.389593 0.114214
+  0.0859725 -1.0693 -2.02948
+  -0.6436 -0.400372 -1.43223
+  -0.88582 0.602299 -0.0590777
+  -0.05727 -0.68016 -1.62127
+  1.3165 -0.570268 -1.07097
+  -1.2269 0.0372067 -0.670011
+  -0.307733 -0.217767 -1.0776
+  2.01961 -0.143457 -0.310584
+  -0.346529 -0.474998 -1.62418
+  0.624072 -0.437087 -1.24966
+  1.50335 1.33349 1.51722
+  1.00832 0.019365 -0.44385
+  2.61706 1.87667 2.59865
+  -2.26652 -0.0321358 -1.29284
+  1.30894 2.11607 2.47544
+  1.09092 1.04312 1.04046
+  1.20046 0.469415 0.352557
+  0.780383 0.0111708 -0.463614
+  -0.10054 -1.40242 -2.61138
+  1.21726 1.06692 1.17218
+  2.33033 0.0444168 -0.0603761
+  0.4038 1.44355 1.4526
+  -1.35011 -0.320975 -1.5722
+  -1.52264 -0.050186 -1.12542
+  -0.61236 -0.782373 -1.79026
+  0.0934571 0.36143 -0.192081
+  0.602785 -0.128348 -0.853118
+  1.4923 0.705827 0.486798
+  -0.973672 -0.578001 -1.71765
+  -0.0543634 -0.192952 -0.913405
+  0.0864153 -1.98039 -3.42191
+  -0.0877569 0.829806 0.395068
+  -0.16916 -0.650094 -1.53461
+  0.190051 0.590431 0.112188
+  2.24335 -0.540746 -0.834482
+  2.29005 1.75977 2.41157
+  1.19283 -0.217893 -0.618301
+  -0.0130601 -0.775068 -1.71921
+  1.50782 0.26217 -0.0075728
+  -0.495035 1.38466 1.14518
+  -2.57561 0.0101092 -1.40083
+  -0.550798 0.793548 0.314286
+  0.33286 -0.790275 -1.74584
+  0.600883 0.363704 -0.104026
+  -0.967231 -0.124756 -1.06134
+  0.86357 0.915796 0.880184
+  -2.00479 -1.20705 -2.73107
+  -1.5744 -1.06133 -2.49398
+  -1.24246 -0.0532174 -1.03638
+  -0.142512 0.437945 0.0117141
+  -0.190588 -1.13174 -2.02514
+  0.0717578 0.657072 0.233795
+  -0.847836 1.68174 1.39365
+  -2.61233 -0.160418 -1.47194
+  -0.150264 -0.0907573 -0.756651
+  1.01469 -1.21428 -2.01372
+  -0.123068 0.730712 0.265598
+  1.25154 -0.526393 -0.918618
+  0.572973 -0.0325019 -0.449671
+  0.744767 0.567598 0.0952907
+  0.767336 1.28563 1.1117
+  0.27401 0.0259356 -0.583271
+  0.0387451 0.863472 0.307276
+  1.37652 0.883576 0.864879
+  -0.24544 -1.50491 -2.83699
+  -1.01056 0.463139 -0.223184
+  -0.266867 -0.7196 -1.69465
+  -0.698632 0.320259 -0.451467
+  -0.487443 -0.578519 -1.78539
+  0.111006 -2.07078 -3.45287
+  -0.688077 -2.78516 -4.82784
+  -1.5226 1.12646 0.564719
+  0.717233 0.685768 0.58831
+  -0.380492 0.59173 -0.028383
+  1.00786 -0.027513 -0.314784
+  0.376207 0.463145 -0.153662
+  -1.77862 0.336624 -0.573957
+  -0.669653 0.093832 -0.678172
+  -0.478987 1.15075 0.666276
+  -0.275699 -0.811538 -1.81975
+  -0.185535 0.161834 -0.566101
+  2.39935 -0.560211 -0.890581
+  0.478475 -0.380631 -1.1044
+  0.0151748 0.413237 -0.211421
+  1.8743 -0.17471 -0.471368
+  -0.034751 0.165149 -0.764119
+  0.440518 0.61982 0.255088
+  1.41156 -0.15232 -0.397338
+  2.04356 0.799842 0.940545
+  1.96347 0.652255 0.764774
+  0.63714 0.24976 -0.142234
+  0.189887 -0.417674 -1.21615
+  -1.3693 0.262116 -0.663902
+  -1.66794 1.34258 1.03625
+  0.0747798 0.622185 0.0616578
+  -0.292759 -0.473951 -1.39402
+  0.230967 -0.255208 -1.00798  
\ No newline at end of file

diff --git a/TP4/exo1/tp4_exo1.py b/TP4/exo1/tp4_exo1.py
new file mode 100755 (executable)
index 0000000..06bc95b
--- /dev/null
+++ b/TP4/exo1/tp4_exo1.py
@@ -0,0 +1,60 @@
+#!/usr/bin/env python3
+
+# -*- coding: utf-8 -*-
+import numpy as np
+import pylab as pl
+from mpl_toolkits.mplot3d import Axes3D
+
+
+data = np.loadtxt("dataRegLin2D.txt")
+X = data[:, 0:2]
+Y = data[:, -1]
+
+
+def complete(sample):
+    if sample.ndim > 1:
+        ones = np.ones((sample.shape[0], 1))
+        new_sample = np.append(sample, ones, axis=-1)
+    else:
+        new_sample = []
+        for s in sample:
+            s = [s, 1]
+            new_sample.append(s)
+    return np.array(new_sample)
+
+
+def train_regression(X, Y):
+    X = complete(X)
+    return np.dot(np.dot(np.linalg.inv(np.dot(np.transpose(X), X)), np.transpose(X)), Y)
+
+
+def predict(x, w):
+    return np.dot(w[:len(w) - 1], x) + w[-1]
+
+
+def error(X, Y, w, idx):
+    err = 0.0
+    for i in range(len(X)):
+        y = predict(X[i, :idx], w)
+        err += (y - Y[i])**2
+    err /= len(X)
+    return err
+
+
+fig = pl.figure()
+ax = fig.add_subplot(131, projection='3d')
+ax.scatter(X[:, 0], X[:, 1], Y)
+w1 = train_regression(X, Y)
+print(error(X, Y, w1, 2))
+
+ax = fig.add_subplot(132)
+ax.scatter(X[:, 0], Y[:])
+w2 = train_regression(X[:, 0], Y)
+print(error(X[:, 0].reshape((len(X), 1)), Y, w2, 1))
+
+ax = fig.add_subplot(133)
+ax.scatter(X[:, 1], Y[:])
+w3 = train_regression(X[:, 1], Y)
+print(error(X[:, 1].reshape((len(X), 1)), Y, w3, 1))
+
+pl.show()