Skip to content

Instantly share code, notes, and snippets.

@xiaoouwang

xiaoouwang/Tuto_plongement_lexical.ipynb

Last active March 9, 2024 18:51
Show Gist options
  • Save xiaoouwang/93a2b20df84ac2e3b5bb29ddec72df27 to your computer and use it in GitHub Desktop.
Save xiaoouwang/93a2b20df84ac2e3b5bb29ddec72df27 to your computer and use it in GitHub Desktop.
Download ZIP
Tuto_plongement_lexical.ipynb
Display the source blob
Display the rendered blob
Raw
Tuto_plongement_lexical.ipynb
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# Word vector pour les passionnés\n\n> Author: Xiaoou Wang, Master’s student (currently in Paris) in NLP looking for a phd position/contrat cifre. [linkedin](https://www.linkedin.com/in/xiaoou-wang)/[email](xiaoouwangfrance@gmail.com)"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T15:42:24.019419Z",
"start_time": "2021-01-23T15:42:24.017493Z"
}
},
"cell_type": "markdown",
"source": "## Introduction\n\nLe `plongement lexical` vise à représenter un mot par un vecteur de nombres réels. Autrement dit, le principe fondamental consiste à représenter un concept linguistique par l'intermédiaire d'une représentation mathématique. Le mot « chien » serait représenté par exemple par un vecteur à 3 dimensions [1.3, 2.2, 4,1].\n\nAu cours de la recherche d'une représentation mathématique adéquate, certaines idées ont permis d'éclairer le chemin dont entre autres l'hypothèse distributionnelle de Harris (`distributional hypothesis`) dans le domaine de la sémantique distributionnelle.\n\nOn retiendra aussi la fameuse phrase de Firth : Vous connaîtrez un mot par ses voisinages (`You shall know a word by the company it keeps` (Firth, J. R. 1957:11))."
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:44:55.465329Z",
"start_time": "2021-01-23T22:44:55.458864Z"
}
},
"cell_type": "markdown",
"source": "## Dimension, une histoire de feature (trait)\n\nTout à l'heure j'ai évoqué l'idée de dimension, pour les non-matheux ce mot peut paraître barbant, mais mine de rien cette idée de dimension est omniprésente dans notre vie des communs mortels.\n\nQuand tu dis `Jean a 39 ans`, âge est une dimension et lorsque Macron dit que [la France est devenue une nation de 66 millions de procureurs](https://www.nouvelobs.com/politique/20210121.OBS39163/pour-macron-la-france-est-devenue-une-nation-de-66-millions-de-procureurs.html), le trait qu'il utilise est le nombre d'habitants innocents considérés par lui comme des procureurs impitoyables. \n\nPuisque tu aimes bien le code, voici un exemple en Python. Cette fois-ci nous prenons les animaux comme exemples. Chaque animal constitue un dictionnaire avec 3 clés. La première indique l'espèce et les deux autres poids et taille (donc deux dimensions caractérisantes).\n\nNotons que `animals` est une liste de dictionnaire et j'ai utilisé `F-strings` pour rendre le code plus lisible."
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:46:19.167966Z",
"start_time": "2021-01-23T22:46:19.163704Z"
},
"trusted": false
},
"cell_type": "code",
"source": "## Use of dimensions in describing animals\n\nanimals = [\n {'espece': 'chat', 'poids': 40, 'taille': 15},\n {'espece': 'chien', 'poids': 45, 'taille': 20},\n {'espece': 'éléphant', 'poids': 90, 'taille': 95},\n {'espece': 'moustique', 'poids': 3, 'taille': 4}\n]\nprint(f\"L'animal {animals[0]['espece']} pèse {animals[0]['poids']} et mesure {animals[0]['taille']} sur une échelle de 0 à 100.\")",
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": "L'animal chat pèse 40 et mesure 15 sur une échelle de 0 à 100.\n"
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:45:12.381250Z",
"start_time": "2021-01-23T22:45:12.374196Z"
}
},
"cell_type": "markdown",
"source": "## Opérer une comparaison visuelle à base de features\n\nA quoi ça sert les features ? Eh bien elles servent d'un système de référence à travers qui, une fois défini, permet d'opérer des comparaisons. En l'occurence tu peux comparer différents animaux et avoir une idée sur la similarité de différentes espèces.\n\nSi tu dessines le poids sur l'abscisse et la taille sur l'ordonnée (un scatterplot), tu auras une idée assez instinctive de l'utilisation des features. \n\n* `plt.style.use('ggplot')` superpose une grille afin d'avoir un graphe plus lisible.\n* `plt.text(animal.cuteness+1, animal.size+1, animal.name)` superpose le nom d'animal en le décalant de 1 par rapport à chaque point.\n* Pour les curieux, [`itertuples`](https://stackoverflow.com/questions/16476924/how-to-iterate-over-rows-in-a-dataframe-in-pandas) est supposé être plus rapide que `iterrows`.\n\nTu vois bien que `chat` et `chien` sont très proches et que `éléphant`et `moustique` sont loin."
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:46:21.374291Z",
"start_time": "2021-01-23T22:46:21.177891Z"
},
"trusted": false
},
"cell_type": "code",
"source": "## pandas -> data processing\n## matplotlib -> data visualization\nimport pandas as pd\nimport matplotlib.pyplot as plt\nplt.style.use('ggplot')\n\ndf_animals = pd.DataFrame(animals, columns=['espece', 'poids', 'taille'])\nplt.figure(figsize=(4, 4))\nplt.scatter(df_animals.poids,\n df_animals.taille)\nplt.xlabel('Poids')\nplt.ylabel('Taille')\n## add 1 to x and y coordinates (represented by poids and taille)\nfor animal in df_animals.itertuples():\n plt.text(animal.poids+1, animal.taille+1, animal.espece, fontsize=12)\nplt.show()",
"execution_count": 2,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<Figure size 288x288 with 1 Axes>",
"image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Created with matplotlib (https://matplotlib.org/) -->\n<svg height=\"266.018591pt\" version=\"1.1\" viewBox=\"0 0 318.113084 266.018591\" width=\"318.113084pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n <defs>\n <style type=\"text/css\">\n*{stroke-linecap:butt;stroke-linejoin:round;}\n </style>\n </defs>\n <g id=\"figure_1\">\n <g id=\"patch_1\">\n <path d=\"M 0 266.018591 \nL 318.113084 266.018591 \nL 318.113084 0 \nL 0 0 \nz\n\" style=\"fill:#ffffff;\"/>\n </g>\n <g id=\"axes_1\">\n <g id=\"patch_2\">\n <path d=\"M 42.53875 226.526716 \nL 265.73875 226.526716 \nL 265.73875 9.086716 \nL 42.53875 9.086716 \nz\n\" style=\"fill:#e5e5e5;\"/>\n </g>\n <g id=\"matplotlib.axis_1\">\n <g id=\"xtick_1\">\n <g id=\"line2d_1\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 45.687339 226.526716 \nL 45.687339 9.086716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_2\">\n <defs>\n <path d=\"M 0 0 \nL 0 3.5 \n\" id=\"m3ed5c9faf2\" style=\"stroke:#555555;stroke-width:0.8;\"/>\n </defs>\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"45.687339\" xlink:href=\"#m3ed5c9faf2\" y=\"226.526716\"/>\n </g>\n </g>\n <g id=\"text_1\">\n <!-- 0 -->\n <defs>\n <path d=\"M 31.78125 66.40625 \nQ 24.171875 66.40625 20.328125 58.90625 \nQ 16.5 51.421875 16.5 36.375 \nQ 16.5 21.390625 20.328125 13.890625 \nQ 24.171875 6.390625 31.78125 6.390625 \nQ 39.453125 6.390625 43.28125 13.890625 \nQ 47.125 21.390625 47.125 36.375 \nQ 47.125 51.421875 43.28125 58.90625 \nQ 39.453125 66.40625 31.78125 66.40625 \nz\nM 31.78125 74.21875 \nQ 44.046875 74.21875 50.515625 64.515625 \nQ 56.984375 54.828125 56.984375 36.375 \nQ 56.984375 17.96875 50.515625 8.265625 \nQ 44.046875 -1.421875 31.78125 -1.421875 \nQ 19.53125 -1.421875 13.0625 8.265625 \nQ 6.59375 17.96875 6.59375 36.375 \nQ 6.59375 54.828125 13.0625 64.515625 \nQ 19.53125 74.21875 31.78125 74.21875 \nz\n\" id=\"DejaVuSans-48\"/>\n </defs>\n <g style=\"fill:#555555;\" transform=\"translate(42.506089 241.125154)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_2\">\n <g id=\"line2d_3\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 92.333107 226.526716 \nL 92.333107 9.086716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_4\">\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"92.333107\" xlink:href=\"#m3ed5c9faf2\" y=\"226.526716\"/>\n </g>\n </g>\n <g id=\"text_2\">\n <!-- 20 -->\n <defs>\n <path d=\"M 19.1875 8.296875 \nL 53.609375 8.296875 \nL 53.609375 0 \nL 7.328125 0 \nL 7.328125 8.296875 \nQ 12.9375 14.109375 22.625 23.890625 \nQ 32.328125 33.6875 34.8125 36.53125 \nQ 39.546875 41.84375 41.421875 45.53125 \nQ 43.3125 49.21875 43.3125 52.78125 \nQ 43.3125 58.59375 39.234375 62.25 \nQ 35.15625 65.921875 28.609375 65.921875 \nQ 23.96875 65.921875 18.8125 64.3125 \nQ 13.671875 62.703125 7.8125 59.421875 \nL 7.8125 69.390625 \nQ 13.765625 71.78125 18.9375 73 \nQ 24.125 74.21875 28.421875 74.21875 \nQ 39.75 74.21875 46.484375 68.546875 \nQ 53.21875 62.890625 53.21875 53.421875 \nQ 53.21875 48.921875 51.53125 44.890625 \nQ 49.859375 40.875 45.40625 35.40625 \nQ 44.1875 33.984375 37.640625 27.21875 \nQ 31.109375 20.453125 19.1875 8.296875 \nz\n\" id=\"DejaVuSans-50\"/>\n </defs>\n <g style=\"fill:#555555;\" transform=\"translate(85.970607 241.125154)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-50\"/>\n <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_3\">\n <g id=\"line2d_5\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 138.978875 226.526716 \nL 138.978875 9.086716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_6\">\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"138.978875\" xlink:href=\"#m3ed5c9faf2\" y=\"226.526716\"/>\n </g>\n </g>\n <g id=\"text_3\">\n <!-- 40 -->\n <defs>\n <path d=\"M 37.796875 64.3125 \nL 12.890625 25.390625 \nL 37.796875 25.390625 \nz\nM 35.203125 72.90625 \nL 47.609375 72.90625 \nL 47.609375 25.390625 \nL 58.015625 25.390625 \nL 58.015625 17.1875 \nL 47.609375 17.1875 \nL 47.609375 0 \nL 37.796875 0 \nL 37.796875 17.1875 \nL 4.890625 17.1875 \nL 4.890625 26.703125 \nz\n\" id=\"DejaVuSans-52\"/>\n </defs>\n <g style=\"fill:#555555;\" transform=\"translate(132.616375 241.125154)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-52\"/>\n <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_4\">\n <g id=\"line2d_7\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 185.624643 226.526716 \nL 185.624643 9.086716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_8\">\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"185.624643\" xlink:href=\"#m3ed5c9faf2\" y=\"226.526716\"/>\n </g>\n </g>\n <g id=\"text_4\">\n <!-- 60 -->\n <defs>\n <path d=\"M 33.015625 40.375 \nQ 26.375 40.375 22.484375 35.828125 \nQ 18.609375 31.296875 18.609375 23.390625 \nQ 18.609375 15.53125 22.484375 10.953125 \nQ 26.375 6.390625 33.015625 6.390625 \nQ 39.65625 6.390625 43.53125 10.953125 \nQ 47.40625 15.53125 47.40625 23.390625 \nQ 47.40625 31.296875 43.53125 35.828125 \nQ 39.65625 40.375 33.015625 40.375 \nz\nM 52.59375 71.296875 \nL 52.59375 62.3125 \nQ 48.875 64.0625 45.09375 64.984375 \nQ 41.3125 65.921875 37.59375 65.921875 \nQ 27.828125 65.921875 22.671875 59.328125 \nQ 17.53125 52.734375 16.796875 39.40625 \nQ 19.671875 43.65625 24.015625 45.921875 \nQ 28.375 48.1875 33.59375 48.1875 \nQ 44.578125 48.1875 50.953125 41.515625 \nQ 57.328125 34.859375 57.328125 23.390625 \nQ 57.328125 12.15625 50.6875 5.359375 \nQ 44.046875 -1.421875 33.015625 -1.421875 \nQ 20.359375 -1.421875 13.671875 8.265625 \nQ 6.984375 17.96875 6.984375 36.375 \nQ 6.984375 53.65625 15.1875 63.9375 \nQ 23.390625 74.21875 37.203125 74.21875 \nQ 40.921875 74.21875 44.703125 73.484375 \nQ 48.484375 72.75 52.59375 71.296875 \nz\n\" id=\"DejaVuSans-54\"/>\n </defs>\n <g style=\"fill:#555555;\" transform=\"translate(179.262143 241.125154)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-54\"/>\n <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"xtick_5\">\n <g id=\"line2d_9\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 232.270411 226.526716 \nL 232.270411 9.086716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_10\">\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"232.270411\" xlink:href=\"#m3ed5c9faf2\" y=\"226.526716\"/>\n </g>\n </g>\n <g id=\"text_5\">\n <!-- 80 -->\n <defs>\n <path d=\"M 31.78125 34.625 \nQ 24.75 34.625 20.71875 30.859375 \nQ 16.703125 27.09375 16.703125 20.515625 \nQ 16.703125 13.921875 20.71875 10.15625 \nQ 24.75 6.390625 31.78125 6.390625 \nQ 38.8125 6.390625 42.859375 10.171875 \nQ 46.921875 13.96875 46.921875 20.515625 \nQ 46.921875 27.09375 42.890625 30.859375 \nQ 38.875 34.625 31.78125 34.625 \nz\nM 21.921875 38.8125 \nQ 15.578125 40.375 12.03125 44.71875 \nQ 8.5 49.078125 8.5 55.328125 \nQ 8.5 64.0625 14.71875 69.140625 \nQ 20.953125 74.21875 31.78125 74.21875 \nQ 42.671875 74.21875 48.875 69.140625 \nQ 55.078125 64.0625 55.078125 55.328125 \nQ 55.078125 49.078125 51.53125 44.71875 \nQ 48 40.375 41.703125 38.8125 \nQ 48.828125 37.15625 52.796875 32.3125 \nQ 56.78125 27.484375 56.78125 20.515625 \nQ 56.78125 9.90625 50.3125 4.234375 \nQ 43.84375 -1.421875 31.78125 -1.421875 \nQ 19.734375 -1.421875 13.25 4.234375 \nQ 6.78125 9.90625 6.78125 20.515625 \nQ 6.78125 27.484375 10.78125 32.3125 \nQ 14.796875 37.15625 21.921875 38.8125 \nz\nM 18.3125 54.390625 \nQ 18.3125 48.734375 21.84375 45.5625 \nQ 25.390625 42.390625 31.78125 42.390625 \nQ 38.140625 42.390625 41.71875 45.5625 \nQ 45.3125 48.734375 45.3125 54.390625 \nQ 45.3125 60.0625 41.71875 63.234375 \nQ 38.140625 66.40625 31.78125 66.40625 \nQ 25.390625 66.40625 21.84375 63.234375 \nQ 18.3125 60.0625 18.3125 54.390625 \nz\n\" id=\"DejaVuSans-56\"/>\n </defs>\n <g style=\"fill:#555555;\" transform=\"translate(225.907911 241.125154)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-56\"/>\n <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"text_6\">\n <!-- Poids -->\n <defs>\n <path d=\"M 19.671875 64.796875 \nL 19.671875 37.40625 \nL 32.078125 37.40625 \nQ 38.96875 37.40625 42.71875 40.96875 \nQ 46.484375 44.53125 46.484375 51.125 \nQ 46.484375 57.671875 42.71875 61.234375 \nQ 38.96875 64.796875 32.078125 64.796875 \nz\nM 9.8125 72.90625 \nL 32.078125 72.90625 \nQ 44.34375 72.90625 50.609375 67.359375 \nQ 56.890625 61.8125 56.890625 51.125 \nQ 56.890625 40.328125 50.609375 34.8125 \nQ 44.34375 29.296875 32.078125 29.296875 \nL 19.671875 29.296875 \nL 19.671875 0 \nL 9.8125 0 \nz\n\" id=\"DejaVuSans-80\"/>\n <path d=\"M 30.609375 48.390625 \nQ 23.390625 48.390625 19.1875 42.75 \nQ 14.984375 37.109375 14.984375 27.296875 \nQ 14.984375 17.484375 19.15625 11.84375 \nQ 23.34375 6.203125 30.609375 6.203125 \nQ 37.796875 6.203125 41.984375 11.859375 \nQ 46.1875 17.53125 46.1875 27.296875 \nQ 46.1875 37.015625 41.984375 42.703125 \nQ 37.796875 48.390625 30.609375 48.390625 \nz\nM 30.609375 56 \nQ 42.328125 56 49.015625 48.375 \nQ 55.71875 40.765625 55.71875 27.296875 \nQ 55.71875 13.875 49.015625 6.21875 \nQ 42.328125 -1.421875 30.609375 -1.421875 \nQ 18.84375 -1.421875 12.171875 6.21875 \nQ 5.515625 13.875 5.515625 27.296875 \nQ 5.515625 40.765625 12.171875 48.375 \nQ 18.84375 56 30.609375 56 \nz\n\" id=\"DejaVuSans-111\"/>\n <path d=\"M 9.421875 54.6875 \nL 18.40625 54.6875 \nL 18.40625 0 \nL 9.421875 0 \nz\nM 9.421875 75.984375 \nL 18.40625 75.984375 \nL 18.40625 64.59375 \nL 9.421875 64.59375 \nz\n\" id=\"DejaVuSans-105\"/>\n <path d=\"M 45.40625 46.390625 \nL 45.40625 75.984375 \nL 54.390625 75.984375 \nL 54.390625 0 \nL 45.40625 0 \nL 45.40625 8.203125 \nQ 42.578125 3.328125 38.25 0.953125 \nQ 33.9375 -1.421875 27.875 -1.421875 \nQ 17.96875 -1.421875 11.734375 6.484375 \nQ 5.515625 14.40625 5.515625 27.296875 \nQ 5.515625 40.1875 11.734375 48.09375 \nQ 17.96875 56 27.875 56 \nQ 33.9375 56 38.25 53.625 \nQ 42.578125 51.265625 45.40625 46.390625 \nz\nM 14.796875 27.296875 \nQ 14.796875 17.390625 18.875 11.75 \nQ 22.953125 6.109375 30.078125 6.109375 \nQ 37.203125 6.109375 41.296875 11.75 \nQ 45.40625 17.390625 45.40625 27.296875 \nQ 45.40625 37.203125 41.296875 42.84375 \nQ 37.203125 48.484375 30.078125 48.484375 \nQ 22.953125 48.484375 18.875 42.84375 \nQ 14.796875 37.203125 14.796875 27.296875 \nz\n\" id=\"DejaVuSans-100\"/>\n <path d=\"M 44.28125 53.078125 \nL 44.28125 44.578125 \nQ 40.484375 46.53125 36.375 47.5 \nQ 32.28125 48.484375 27.875 48.484375 \nQ 21.1875 48.484375 17.84375 46.4375 \nQ 14.5 44.390625 14.5 40.28125 \nQ 14.5 37.15625 16.890625 35.375 \nQ 19.28125 33.59375 26.515625 31.984375 \nL 29.59375 31.296875 \nQ 39.15625 29.25 43.1875 25.515625 \nQ 47.21875 21.78125 47.21875 15.09375 \nQ 47.21875 7.46875 41.1875 3.015625 \nQ 35.15625 -1.421875 24.609375 -1.421875 \nQ 20.21875 -1.421875 15.453125 -0.5625 \nQ 10.6875 0.296875 5.421875 2 \nL 5.421875 11.28125 \nQ 10.40625 8.6875 15.234375 7.390625 \nQ 20.0625 6.109375 24.8125 6.109375 \nQ 31.15625 6.109375 34.5625 8.28125 \nQ 37.984375 10.453125 37.984375 14.40625 \nQ 37.984375 18.0625 35.515625 20.015625 \nQ 33.0625 21.96875 24.703125 23.78125 \nL 21.578125 24.515625 \nQ 13.234375 26.265625 9.515625 29.90625 \nQ 5.8125 33.546875 5.8125 39.890625 \nQ 5.8125 47.609375 11.28125 51.796875 \nQ 16.75 56 26.8125 56 \nQ 31.78125 56 36.171875 55.265625 \nQ 40.578125 54.546875 44.28125 53.078125 \nz\n\" id=\"DejaVuSans-115\"/>\n </defs>\n <g style=\"fill:#555555;\" transform=\"translate(138.465625 256.322966)scale(0.12 -0.12)\">\n <use xlink:href=\"#DejaVuSans-80\"/>\n <use x=\"56.677734\" xlink:href=\"#DejaVuSans-111\"/>\n <use x=\"117.859375\" xlink:href=\"#DejaVuSans-105\"/>\n <use x=\"145.642578\" xlink:href=\"#DejaVuSans-100\"/>\n <use x=\"209.119141\" xlink:href=\"#DejaVuSans-115\"/>\n </g>\n </g>\n </g>\n <g id=\"matplotlib.axis_2\">\n <g id=\"ytick_1\">\n <g id=\"line2d_11\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 42.53875 225.331991 \nL 265.73875 225.331991 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_12\">\n <defs>\n <path d=\"M 0 0 \nL -3.5 0 \n\" id=\"ma2fc42b70a\" style=\"stroke:#555555;stroke-width:0.8;\"/>\n </defs>\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"42.53875\" xlink:href=\"#ma2fc42b70a\" y=\"225.331991\"/>\n </g>\n </g>\n <g id=\"text_7\">\n <!-- 0 -->\n <g style=\"fill:#555555;\" transform=\"translate(29.17625 229.13121)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_2\">\n <g id=\"line2d_13\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 42.53875 181.887436 \nL 265.73875 181.887436 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_14\">\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"42.53875\" xlink:href=\"#ma2fc42b70a\" y=\"181.887436\"/>\n </g>\n </g>\n <g id=\"text_8\">\n <!-- 20 -->\n <g style=\"fill:#555555;\" transform=\"translate(22.81375 185.686654)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-50\"/>\n <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_3\">\n <g id=\"line2d_15\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 42.53875 138.44288 \nL 265.73875 138.44288 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_16\">\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"42.53875\" xlink:href=\"#ma2fc42b70a\" y=\"138.44288\"/>\n </g>\n </g>\n <g id=\"text_9\">\n <!-- 40 -->\n <g style=\"fill:#555555;\" transform=\"translate(22.81375 142.242099)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-52\"/>\n <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_4\">\n <g id=\"line2d_17\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 42.53875 94.998325 \nL 265.73875 94.998325 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_18\">\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"42.53875\" xlink:href=\"#ma2fc42b70a\" y=\"94.998325\"/>\n </g>\n </g>\n <g id=\"text_10\">\n <!-- 60 -->\n <g style=\"fill:#555555;\" transform=\"translate(22.81375 98.797544)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-54\"/>\n <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"ytick_5\">\n <g id=\"line2d_19\">\n <path clip-path=\"url(#pc50a1647ad)\" d=\"M 42.53875 51.553769 \nL 265.73875 51.553769 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-width:0.8;\"/>\n </g>\n <g id=\"line2d_20\">\n <g>\n <use style=\"fill:#555555;stroke:#555555;stroke-width:0.8;\" x=\"42.53875\" xlink:href=\"#ma2fc42b70a\" y=\"51.553769\"/>\n </g>\n </g>\n <g id=\"text_11\">\n <!-- 80 -->\n <g style=\"fill:#555555;\" transform=\"translate(22.81375 55.352988)scale(0.1 -0.1)\">\n <use xlink:href=\"#DejaVuSans-56\"/>\n <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n </g>\n </g>\n </g>\n <g id=\"text_12\">\n <!-- Taille -->\n <defs>\n <path d=\"M -0.296875 72.90625 \nL 61.375 72.90625 \nL 61.375 64.59375 \nL 35.5 64.59375 \nL 35.5 0 \nL 25.59375 0 \nL 25.59375 64.59375 \nL -0.296875 64.59375 \nz\n\" id=\"DejaVuSans-84\"/>\n <path d=\"M 34.28125 27.484375 \nQ 23.390625 27.484375 19.1875 25 \nQ 14.984375 22.515625 14.984375 16.5 \nQ 14.984375 11.71875 18.140625 8.90625 \nQ 21.296875 6.109375 26.703125 6.109375 \nQ 34.1875 6.109375 38.703125 11.40625 \nQ 43.21875 16.703125 43.21875 25.484375 \nL 43.21875 27.484375 \nz\nM 52.203125 31.203125 \nL 52.203125 0 \nL 43.21875 0 \nL 43.21875 8.296875 \nQ 40.140625 3.328125 35.546875 0.953125 \nQ 30.953125 -1.421875 24.3125 -1.421875 \nQ 15.921875 -1.421875 10.953125 3.296875 \nQ 6 8.015625 6 15.921875 \nQ 6 25.140625 12.171875 29.828125 \nQ 18.359375 34.515625 30.609375 34.515625 \nL 43.21875 34.515625 \nL 43.21875 35.40625 \nQ 43.21875 41.609375 39.140625 45 \nQ 35.0625 48.390625 27.6875 48.390625 \nQ 23 48.390625 18.546875 47.265625 \nQ 14.109375 46.140625 10.015625 43.890625 \nL 10.015625 52.203125 \nQ 14.9375 54.109375 19.578125 55.046875 \nQ 24.21875 56 28.609375 56 \nQ 40.484375 56 46.34375 49.84375 \nQ 52.203125 43.703125 52.203125 31.203125 \nz\n\" id=\"DejaVuSans-97\"/>\n <path d=\"M 9.421875 75.984375 \nL 18.40625 75.984375 \nL 18.40625 0 \nL 9.421875 0 \nz\n\" id=\"DejaVuSans-108\"/>\n <path d=\"M 56.203125 29.59375 \nL 56.203125 25.203125 \nL 14.890625 25.203125 \nQ 15.484375 15.921875 20.484375 11.0625 \nQ 25.484375 6.203125 34.421875 6.203125 \nQ 39.59375 6.203125 44.453125 7.46875 \nQ 49.3125 8.734375 54.109375 11.28125 \nL 54.109375 2.78125 \nQ 49.265625 0.734375 44.1875 -0.34375 \nQ 39.109375 -1.421875 33.890625 -1.421875 \nQ 20.796875 -1.421875 13.15625 6.1875 \nQ 5.515625 13.8125 5.515625 26.8125 \nQ 5.515625 40.234375 12.765625 48.109375 \nQ 20.015625 56 32.328125 56 \nQ 43.359375 56 49.78125 48.890625 \nQ 56.203125 41.796875 56.203125 29.59375 \nz\nM 47.21875 32.234375 \nQ 47.125 39.59375 43.09375 43.984375 \nQ 39.0625 48.390625 32.421875 48.390625 \nQ 24.90625 48.390625 20.390625 44.140625 \nQ 15.875 39.890625 15.1875 32.171875 \nz\n\" id=\"DejaVuSans-101\"/>\n </defs>\n <g style=\"fill:#555555;\" transform=\"translate(16.318125 132.850779)rotate(-90)scale(0.12 -0.12)\">\n <use xlink:href=\"#DejaVuSans-84\"/>\n <use x=\"44.583984\" xlink:href=\"#DejaVuSans-97\"/>\n <use x=\"105.863281\" xlink:href=\"#DejaVuSans-105\"/>\n <use x=\"133.646484\" xlink:href=\"#DejaVuSans-108\"/>\n <use x=\"161.429688\" xlink:href=\"#DejaVuSans-108\"/>\n <use x=\"189.212891\" xlink:href=\"#DejaVuSans-101\"/>\n </g>\n </g>\n </g>\n <g id=\"PathCollection_1\">\n <defs>\n <path d=\"M 0 3 \nC 0.795609 3 1.55874 2.683901 2.12132 2.12132 \nC 2.683901 1.55874 3 0.795609 3 0 \nC 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \nC 1.55874 -2.683901 0.795609 -3 0 -3 \nC -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \nC -2.683901 -1.55874 -3 -0.795609 -3 0 \nC -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \nC -1.55874 2.683901 -0.795609 3 0 3 \nz\n\" id=\"mda7b9764af\" style=\"stroke:#e24a33;stroke-width:0.5;\"/>\n </defs>\n <g clip-path=\"url(#pc50a1647ad)\">\n <use style=\"fill:#e24a33;stroke:#e24a33;stroke-width:0.5;\" x=\"138.978875\" xlink:href=\"#mda7b9764af\" y=\"192.748575\"/>\n <use style=\"fill:#e24a33;stroke:#e24a33;stroke-width:0.5;\" x=\"150.640317\" xlink:href=\"#mda7b9764af\" y=\"181.887436\"/>\n <use style=\"fill:#e24a33;stroke:#e24a33;stroke-width:0.5;\" x=\"255.593295\" xlink:href=\"#mda7b9764af\" y=\"18.970353\"/>\n <use style=\"fill:#e24a33;stroke:#e24a33;stroke-width:0.5;\" x=\"52.684205\" xlink:href=\"#mda7b9764af\" y=\"216.64308\"/>\n </g>\n </g>\n <g id=\"patch_3\">\n <path d=\"M 42.53875 226.526716 \nL 42.53875 9.086716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;\"/>\n </g>\n <g id=\"patch_4\">\n <path d=\"M 265.73875 226.526716 \nL 265.73875 9.086716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;\"/>\n </g>\n <g id=\"patch_5\">\n <path d=\"M 42.53875 226.526716 \nL 265.73875 226.526716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;\"/>\n </g>\n <g id=\"patch_6\">\n <path d=\"M 42.53875 9.086716 \nL 265.73875 9.086716 \n\" style=\"fill:none;stroke:#ffffff;stroke-linecap:square;stroke-linejoin:miter;\"/>\n </g>\n <g id=\"text_13\">\n <!-- chat -->\n <defs>\n <path d=\"M 48.78125 52.59375 \nL 48.78125 44.1875 \nQ 44.96875 46.296875 41.140625 47.34375 \nQ 37.3125 48.390625 33.40625 48.390625 \nQ 24.65625 48.390625 19.8125 42.84375 \nQ 14.984375 37.3125 14.984375 27.296875 \nQ 14.984375 17.28125 19.8125 11.734375 \nQ 24.65625 6.203125 33.40625 6.203125 \nQ 37.3125 6.203125 41.140625 7.25 \nQ 44.96875 8.296875 48.78125 10.40625 \nL 48.78125 2.09375 \nQ 45.015625 0.34375 40.984375 -0.53125 \nQ 36.96875 -1.421875 32.421875 -1.421875 \nQ 20.0625 -1.421875 12.78125 6.34375 \nQ 5.515625 14.109375 5.515625 27.296875 \nQ 5.515625 40.671875 12.859375 48.328125 \nQ 20.21875 56 33.015625 56 \nQ 37.15625 56 41.109375 55.140625 \nQ 45.0625 54.296875 48.78125 52.59375 \nz\n\" id=\"DejaVuSans-99\"/>\n <path d=\"M 54.890625 33.015625 \nL 54.890625 0 \nL 45.90625 0 \nL 45.90625 32.71875 \nQ 45.90625 40.484375 42.875 44.328125 \nQ 39.84375 48.1875 33.796875 48.1875 \nQ 26.515625 48.1875 22.3125 43.546875 \nQ 18.109375 38.921875 18.109375 30.90625 \nL 18.109375 0 \nL 9.078125 0 \nL 9.078125 75.984375 \nL 18.109375 75.984375 \nL 18.109375 46.1875 \nQ 21.34375 51.125 25.703125 53.5625 \nQ 30.078125 56 35.796875 56 \nQ 45.21875 56 50.046875 50.171875 \nQ 54.890625 44.34375 54.890625 33.015625 \nz\n\" id=\"DejaVuSans-104\"/>\n <path d=\"M 18.3125 70.21875 \nL 18.3125 54.6875 \nL 36.8125 54.6875 \nL 36.8125 47.703125 \nL 18.3125 47.703125 \nL 18.3125 18.015625 \nQ 18.3125 11.328125 20.140625 9.421875 \nQ 21.96875 7.515625 27.59375 7.515625 \nL 36.8125 7.515625 \nL 36.8125 0 \nL 27.59375 0 \nQ 17.1875 0 13.234375 3.875 \nQ 9.28125 7.765625 9.28125 18.015625 \nL 9.28125 47.703125 \nL 2.6875 47.703125 \nL 2.6875 54.6875 \nL 9.28125 54.6875 \nL 9.28125 70.21875 \nz\n\" id=\"DejaVuSans-116\"/>\n </defs>\n <g transform=\"translate(141.311164 190.576347)scale(0.12 -0.12)\">\n <use xlink:href=\"#DejaVuSans-99\"/>\n <use x=\"54.980469\" xlink:href=\"#DejaVuSans-104\"/>\n <use x=\"118.359375\" xlink:href=\"#DejaVuSans-97\"/>\n <use x=\"179.638672\" xlink:href=\"#DejaVuSans-116\"/>\n </g>\n </g>\n <g id=\"text_14\">\n <!-- chien -->\n <defs>\n <path d=\"M 54.890625 33.015625 \nL 54.890625 0 \nL 45.90625 0 \nL 45.90625 32.71875 \nQ 45.90625 40.484375 42.875 44.328125 \nQ 39.84375 48.1875 33.796875 48.1875 \nQ 26.515625 48.1875 22.3125 43.546875 \nQ 18.109375 38.921875 18.109375 30.90625 \nL 18.109375 0 \nL 9.078125 0 \nL 9.078125 54.6875 \nL 18.109375 54.6875 \nL 18.109375 46.1875 \nQ 21.34375 51.125 25.703125 53.5625 \nQ 30.078125 56 35.796875 56 \nQ 45.21875 56 50.046875 50.171875 \nQ 54.890625 44.34375 54.890625 33.015625 \nz\n\" id=\"DejaVuSans-110\"/>\n </defs>\n <g transform=\"translate(152.972606 179.715208)scale(0.12 -0.12)\">\n <use xlink:href=\"#DejaVuSans-99\"/>\n <use x=\"54.980469\" xlink:href=\"#DejaVuSans-104\"/>\n <use x=\"118.359375\" xlink:href=\"#DejaVuSans-105\"/>\n <use x=\"146.142578\" xlink:href=\"#DejaVuSans-101\"/>\n <use x=\"207.666016\" xlink:href=\"#DejaVuSans-110\"/>\n </g>\n </g>\n <g id=\"text_15\">\n <!-- éléphant -->\n <defs>\n <path d=\"M 56.203125 29.59375 \nL 56.203125 25.203125 \nL 14.890625 25.203125 \nQ 15.484375 15.921875 20.484375 11.0625 \nQ 25.484375 6.203125 34.421875 6.203125 \nQ 39.59375 6.203125 44.453125 7.46875 \nQ 49.3125 8.734375 54.109375 11.28125 \nL 54.109375 2.78125 \nQ 49.265625 0.734375 44.1875 -0.34375 \nQ 39.109375 -1.421875 33.890625 -1.421875 \nQ 20.796875 -1.421875 13.15625 6.1875 \nQ 5.515625 13.8125 5.515625 26.8125 \nQ 5.515625 40.234375 12.765625 48.109375 \nQ 20.015625 56 32.328125 56 \nQ 43.359375 56 49.78125 48.890625 \nQ 56.203125 41.796875 56.203125 29.59375 \nz\nM 47.21875 32.234375 \nQ 47.125 39.59375 43.09375 43.984375 \nQ 39.0625 48.390625 32.421875 48.390625 \nQ 24.90625 48.390625 20.390625 44.140625 \nQ 15.875 39.890625 15.1875 32.171875 \nz\nM 38.53125 79.984375 \nL 48.25 79.984375 \nL 32.34375 61.625 \nL 24.859375 61.625 \nz\n\" id=\"DejaVuSans-233\"/>\n <path d=\"M 18.109375 8.203125 \nL 18.109375 -20.796875 \nL 9.078125 -20.796875 \nL 9.078125 54.6875 \nL 18.109375 54.6875 \nL 18.109375 46.390625 \nQ 20.953125 51.265625 25.265625 53.625 \nQ 29.59375 56 35.59375 56 \nQ 45.5625 56 51.78125 48.09375 \nQ 58.015625 40.1875 58.015625 27.296875 \nQ 58.015625 14.40625 51.78125 6.484375 \nQ 45.5625 -1.421875 35.59375 -1.421875 \nQ 29.59375 -1.421875 25.265625 0.953125 \nQ 20.953125 3.328125 18.109375 8.203125 \nz\nM 48.6875 27.296875 \nQ 48.6875 37.203125 44.609375 42.84375 \nQ 40.53125 48.484375 33.40625 48.484375 \nQ 26.265625 48.484375 22.1875 42.84375 \nQ 18.109375 37.203125 18.109375 27.296875 \nQ 18.109375 17.390625 22.1875 11.75 \nQ 26.265625 6.109375 33.40625 6.109375 \nQ 40.53125 6.109375 44.609375 11.75 \nQ 48.6875 17.390625 48.6875 27.296875 \nz\n\" id=\"DejaVuSans-112\"/>\n </defs>\n <g transform=\"translate(257.925584 16.798125)scale(0.12 -0.12)\">\n <use xlink:href=\"#DejaVuSans-233\"/>\n <use x=\"61.523438\" xlink:href=\"#DejaVuSans-108\"/>\n <use x=\"89.306641\" xlink:href=\"#DejaVuSans-233\"/>\n <use x=\"150.830078\" xlink:href=\"#DejaVuSans-112\"/>\n <use x=\"214.306641\" xlink:href=\"#DejaVuSans-104\"/>\n <use x=\"277.685547\" xlink:href=\"#DejaVuSans-97\"/>\n <use x=\"338.964844\" xlink:href=\"#DejaVuSans-110\"/>\n <use x=\"402.34375\" xlink:href=\"#DejaVuSans-116\"/>\n </g>\n </g>\n <g id=\"text_16\">\n <!-- moustique -->\n <defs>\n <path d=\"M 52 44.1875 \nQ 55.375 50.25 60.0625 53.125 \nQ 64.75 56 71.09375 56 \nQ 79.640625 56 84.28125 50.015625 \nQ 88.921875 44.046875 88.921875 33.015625 \nL 88.921875 0 \nL 79.890625 0 \nL 79.890625 32.71875 \nQ 79.890625 40.578125 77.09375 44.375 \nQ 74.3125 48.1875 68.609375 48.1875 \nQ 61.625 48.1875 57.5625 43.546875 \nQ 53.515625 38.921875 53.515625 30.90625 \nL 53.515625 0 \nL 44.484375 0 \nL 44.484375 32.71875 \nQ 44.484375 40.625 41.703125 44.40625 \nQ 38.921875 48.1875 33.109375 48.1875 \nQ 26.21875 48.1875 22.15625 43.53125 \nQ 18.109375 38.875 18.109375 30.90625 \nL 18.109375 0 \nL 9.078125 0 \nL 9.078125 54.6875 \nL 18.109375 54.6875 \nL 18.109375 46.1875 \nQ 21.1875 51.21875 25.484375 53.609375 \nQ 29.78125 56 35.6875 56 \nQ 41.65625 56 45.828125 52.96875 \nQ 50 49.953125 52 44.1875 \nz\n\" id=\"DejaVuSans-109\"/>\n <path d=\"M 8.5 21.578125 \nL 8.5 54.6875 \nL 17.484375 54.6875 \nL 17.484375 21.921875 \nQ 17.484375 14.15625 20.5 10.265625 \nQ 23.53125 6.390625 29.59375 6.390625 \nQ 36.859375 6.390625 41.078125 11.03125 \nQ 45.3125 15.671875 45.3125 23.6875 \nL 45.3125 54.6875 \nL 54.296875 54.6875 \nL 54.296875 0 \nL 45.3125 0 \nL 45.3125 8.40625 \nQ 42.046875 3.421875 37.71875 1 \nQ 33.40625 -1.421875 27.6875 -1.421875 \nQ 18.265625 -1.421875 13.375 4.4375 \nQ 8.5 10.296875 8.5 21.578125 \nz\nM 31.109375 56 \nz\n\" id=\"DejaVuSans-117\"/>\n <path d=\"M 14.796875 27.296875 \nQ 14.796875 17.390625 18.875 11.75 \nQ 22.953125 6.109375 30.078125 6.109375 \nQ 37.203125 6.109375 41.296875 11.75 \nQ 45.40625 17.390625 45.40625 27.296875 \nQ 45.40625 37.203125 41.296875 42.84375 \nQ 37.203125 48.484375 30.078125 48.484375 \nQ 22.953125 48.484375 18.875 42.84375 \nQ 14.796875 37.203125 14.796875 27.296875 \nz\nM 45.40625 8.203125 \nQ 42.578125 3.328125 38.25 0.953125 \nQ 33.9375 -1.421875 27.875 -1.421875 \nQ 17.96875 -1.421875 11.734375 6.484375 \nQ 5.515625 14.40625 5.515625 27.296875 \nQ 5.515625 40.1875 11.734375 48.09375 \nQ 17.96875 56 27.875 56 \nQ 33.9375 56 38.25 53.625 \nQ 42.578125 51.265625 45.40625 46.390625 \nL 45.40625 54.6875 \nL 54.390625 54.6875 \nL 54.390625 -20.796875 \nL 45.40625 -20.796875 \nz\n\" id=\"DejaVuSans-113\"/>\n </defs>\n <g transform=\"translate(55.016493 214.470852)scale(0.12 -0.12)\">\n <use xlink:href=\"#DejaVuSans-109\"/>\n <use x=\"97.412109\" xlink:href=\"#DejaVuSans-111\"/>\n <use x=\"158.59375\" xlink:href=\"#DejaVuSans-117\"/>\n <use x=\"221.972656\" xlink:href=\"#DejaVuSans-115\"/>\n <use x=\"274.072266\" xlink:href=\"#DejaVuSans-116\"/>\n <use x=\"313.28125\" xlink:href=\"#DejaVuSans-105\"/>\n <use x=\"341.064453\" xlink:href=\"#DejaVuSans-113\"/>\n <use x=\"404.541016\" xlink:href=\"#DejaVuSans-117\"/>\n <use x=\"467.919922\" xlink:href=\"#DejaVuSans-101\"/>\n </g>\n </g>\n </g>\n </g>\n <defs>\n <clipPath id=\"pc50a1647ad\">\n <rect height=\"217.44\" width=\"223.2\" x=\"42.53875\" y=\"9.086716\"/>\n </clipPath>\n </defs>\n</svg>\n",
"image/png": "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\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:35:25.403843Z",
"start_time": "2021-01-23T22:35:25.312462Z"
}
},
"cell_type": "markdown",
"source": "## Vers un exemple plus intéressant\n\nJ'entends certains crier déjà : ton exemple est bidon non ?\n\nD'accord d'accord, comme vous êtes exigeants, je donne ici un autre exemple tiré du [modèle de couleurs](https://www.wikiwand.com/fr/Rouge_vert_bleu) `rgb`. Ce modèle consiste à représenter la couleur en 3 nombres. Le saumon, par exemple, est représenté par le vecteur [255,204,153] signifiant 100% rouge, 80% vert et 60% bleu.\n\nLe fichier que je vais utilier est un fichier `json` danslequel chaque couleur est codée en hexadécimal. La fonction `int` convertit un hexa en son correspondant dans le système décimale : par exemple, `int(FF)` (hexa) = 255 en décimal. Pour plus de détail, regarde [ce lien](https://www.rapidtables.com/convert/number/hex-to-decimal.html). La fonction `decode_color` permet de générer les chiffres en décimal pour une couleur. Nous utilisons ensuite la [compréhension de dictionnaire](https://www.programiz.com/python-programming/dictionary-comprehension) pour créer le dictionnaire `couleurs` dont la clé est la couleur et la valeur le vecteur rgb. "
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:46:28.967480Z",
"start_time": "2021-01-23T22:46:28.740372Z"
},
"trusted": false
},
"cell_type": "code",
"source": "import urllib.request, json \nimport numpy as np\nfichier_couleurs = \"https://raw.githubusercontent.com/dariusk/corpora/master/data/colors/xkcd.json\"\n\nwith urllib.request.urlopen(fichier_couleurs) as url:\n json_couleurs = json.loads(url.read())\n\ndef decode_color(hexa):\n hexa = hexa.strip(\"#\")\n return np.array([int(hexa[:2], 16), int(hexa[2:4], 16), int(hexa[4:6], 16)])\n\n# create the color data\ncouleurs = {c[\"color\"]: decode_color(c[\"hex\"]) for c in json_couleurs['colors']}\ncouleurs['red']",
"execution_count": 8,
"outputs": [
{
"data": {
"text/plain": "array([229, 0, 0])"
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:35:25.452719Z",
"start_time": "2021-01-23T22:35:25.449639Z"
}
},
"cell_type": "markdown",
"source": "## Visualisation à trois dimensions, une aventure périlleuse\n\nUne visualisation à trois dimension, comme c'est le cas pour les couleurs, peut paraître chouette mais difficile à appréhender pour la plupart des gens, d'autant plus que le nombre de dimensions augmente. Quand la géométrie n'aide pas, l'algèbre prend le relais. Tu te souviens de la formule qu'on utilise pour calculer la distance entre deux points ? Ou bien sais-tu encore utiliser le jargon mathématique `distance euclidienne` ? Non ? Voici les formules :\n\nDistance entre deux points à deux dimensions\n\n$$d=\\sqrt{(\\Delta x)^2+(\\Delta y)^2}=\\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$\n\nDistance entre deux points à n dimensions\n\n$$\\left( \\sum_{i=1}^n \\left| x_i - y_i \\right|^2 \\right)^{1/2}$$\n\nEn python ça se fait en un tour de main avec `numpy`."
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:46:36.004004Z",
"start_time": "2021-01-23T22:46:35.999776Z"
},
"trusted": false
},
"cell_type": "code",
"source": "from numpy import linalg as LA\ndistance_rougerose = LA.norm(couleurs['red'] - couleurs['rose'])\nprint(f\"La distance entre rouge et le rose est {distance_rougerose}.\")",
"execution_count": 9,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "La distance entre rouge et le rose est 154.19792475905763.\n"
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:35:25.576273Z",
"start_time": "2021-01-23T22:35:25.572958Z"
}
},
"cell_type": "markdown",
"source": "Cet outil est extrêmement pratique car désormais nous pouvons formuler des affirmations de l'ordre suivant :\n1. Est-ce que la distance entre rouge et vert est plus grande que celle entre rouge et rose ?"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:46:40.831688Z",
"start_time": "2021-01-23T22:46:40.828036Z"
},
"lang": "en",
"trusted": false
},
"cell_type": "code",
"source": "distance_rougevert = LA.norm(couleurs['red'] - couleurs['green'])\nprint(\"Vrai\") if distance_rougevert>distance_rougerose else print(\"Faux\")",
"execution_count": 10,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "Vrai\n"
}
]
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:46:49.993665Z",
"start_time": "2021-01-23T22:46:49.989785Z"
}
},
"cell_type": "markdown",
"source": "2. Le rouge est au rose comme le bleu est au ?\n\nTo be continued"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "## Références\n[Tuto intéressant en anglais qui a inspiré le présent notebook](https://github.com/aparrish/rwet/blob/master/understanding-word-vectors.ipynb)\n\n[Page wikipédia de word embedding en français](https://www.wikiwand.com/fr/Word_embedding)"
},
{
"metadata": {
"ExecuteTime": {
"end_time": "2021-01-23T22:47:26.375034Z",
"start_time": "2021-01-23T22:47:26.370680Z"
}
},
"cell_type": "markdown",
"source": "> Author: Xiaoou Wang, Master’s student (currently in Paris) in NLP looking for a phd position/contrat cifre. [linkedin](https://www.linkedin.com/in/xiaoou-wang)/[email](xiaoouwangfrance@gmail.com)\n\nDernière mise à jour : 2021-01-23"
}
],
"metadata": {
"_draft": {
"nbviewer_url": "https://gist.github.com/93a2b20df84ac2e3b5bb29ddec72df27"
},
"gist": {
"id": "93a2b20df84ac2e3b5bb29ddec72df27",
"data": {
"description": "Tuto_plongement_lexical.ipynb",
"public": true
}
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"name": "python",
"version": "3.7.6",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"nbTranslate": {
"hotkey": "alt-t",
"sourceLang": "en",
"targetLang": "fr",
"displayLangs": [
"en"
],
"langInMainMenu": true,
"useGoogleTranslate": true
},
"toc": {
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": true,
"base_numbering": 1,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {
"height": "calc(100% - 180px)",
"left": "10px",
"top": "150px",
"width": "268.797px"
},
"toc_section_display": true,
"toc_window_display": true
},
"varInspector": {
"window_display": false,
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"library": "var_list.py",
"delete_cmd_prefix": "del ",
"delete_cmd_postfix": "",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"library": "var_list.r",
"delete_cmd_prefix": "rm(",
"delete_cmd_postfix": ") ",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
]
}
},
"nbformat": 4,
"nbformat_minor": 4
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment