{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Méthodes hiérarchiques" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "https://fr.wikipedia.org/wiki/Regroupement_hi%C3%A9rarchique\n", "\n", "Il fonctionne avec des données décrites par une distance. Il construit des classes emboîtées et peut être repéresenté par une hiérarchie (un arbre).\n", "\n", "L'intérêt de ces méthodes est :\n", "* de permettre une classification sans avoir à choisir un nombre de classe\n", "* d'avoir des classes de plus en plus grosse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Une hiérarchie est un ensemble de classes $\\mathcal{H}$ tel que pour tous $A, B \\in \\mathcal{H}$ on a : $A \\cap B \\in \\{ A, B, \\phi\\}$ (deux classes sont soit disjointes soit emboîtées).\n", "\n", "C'est une forme de généralisation d'une partition. C'est également un arbre si on considère l'inclusion : les enfants d'une classe étants les classes strictement plus petite que celle-ci (on appelle cet arbre un *dendregramme*)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## algorithme\n", "\n", "* **Entrée** : \n", " * un ensemble $X$ de $n$ éléments à classer\n", " * une distance $d$ entre les éléments\n", " * une façon de mettre à jour la distance : $f$: $X \\times X \\rightarrow \\mathbb{R}$ \n", "* **Sortie** : Un ensemble de classes formant une hiérarchie\n", "\n", "* **Algorithme** :\n", " * On considère que $\\mathcal{H}$ est l'ensemble des singletons formé avec l'ensmelbe des éléments à classer.\n", " * $\\mathcal{C} = \\mathcal{H}$\n", " * la distance entre 2 singletons est la distance entre les deux éléments.\n", " * répète $n-1$ fois :\n", " * soient $A$ et $B$ deux éléments de $\\mathcal{C}$ ayant une distance minimale\n", " * on ajoute $A \\cup B$ à $\\mathcal{C}$ et on supprime $A$ et $B$ de $C$ \n", " * pour tout $C \\in \\mathcal{C}$, la distance entre $C$ et $A\\cup B$ est $f(C, A\\cup B)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "L'algorithme dépend donc d'une fonction $f$ permettant de mettre à jour la distance. Il en existe de nombreuses, qui vont changer l'arbre solution. sklearn ensupporte 4 :\n", "* “ward” : à utiliser pour des données euclidienne : $f(A, B)$ est la perte d'inertie à regrouper $A$ et $B$ $I(A \\cup B) - I(A) - I(B)$\n", "* “average” : méthode par défaut. Basée sur des moyennes : $f(A, B) = \\frac{1}{|A| * |B|}\\sum_{x \\in A, y \\in B} d(x, y)$\n", "* “complete” : prend la plus grande distance (méthode pssimiste) : $f(A, B) = \\max_{x \\in A, y \\in B} d(x, y)$\n", "* “single” : prend la plus petite distance (méthode optimiste) : $f(A, B) = \\min_{x \\in A, y \\in B} d(x, y)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "https://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html#sklearn.cluster.AgglomerativeClustering" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " sepal_length sepal_width petal_length petal_width\n", "0 5.1 3.5 1.4 0.2\n", "1 4.9 3.0 1.4 0.2\n", "2 4.7 3.2 1.3 0.2\n", "3 4.6 3.1 1.5 0.2\n", "4 5.0 3.6 1.4 0.2\n", ".. ... ... ... ...\n", "145 6.7 3.0 5.2 2.3\n", "146 6.3 2.5 5.0 1.9\n", "147 6.5 3.0 5.2 2.0\n", "148 6.2 3.4 5.4 2.3\n", "149 5.9 3.0 5.1 1.8\n", "\n", "[150 rows x 4 columns]" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import seaborn as sns\n", "\n", "sns.set()\n", "\n", "iris = sns.load_dataset('iris').drop(columns=\"species\")\n", "iris" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On a toujours 3 espèces que l'on représentera en 3 clouleurs différentes. Les 50 premières sont de l'espèce *setosa*, les 50 suivantes de l'espèce *versicolor* et les 50 dernière de l'espèce *virginica*\n", "\n", "**Attention** : ces 3 espèces sont des *meta* données : ce sont les botanistes qui ont répartis les iris en espèces, ce n'est pas inhérent aux données." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour que nos arbres puissent être visibles, on ne va prendre qu'une partie des données, les 10 premières de chaque espèces." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " sepal_length sepal_width petal_length petal_width\n", "0 5.1 3.5 1.4 0.2\n", "1 4.9 3.0 1.4 0.2\n", "2 4.7 3.2 1.3 0.2\n", "3 4.6 3.1 1.5 0.2\n", "4 5.0 3.6 1.4 0.2\n", "5 5.4 3.9 1.7 0.4\n", "6 4.6 3.4 1.4 0.3\n", "7 5.0 3.4 1.5 0.2\n", "8 4.4 2.9 1.4 0.2\n", "9 4.9 3.1 1.5 0.1\n", "50 7.0 3.2 4.7 1.4\n", "51 6.4 3.2 4.5 1.5\n", "52 6.9 3.1 4.9 1.5\n", "53 5.5 2.3 4.0 1.3\n", "54 6.5 2.8 4.6 1.5\n", "55 5.7 2.8 4.5 1.3\n", "56 6.3 3.3 4.7 1.6\n", "57 4.9 2.4 3.3 1.0\n", "58 6.6 2.9 4.6 1.3\n", "59 5.2 2.7 3.9 1.4\n", "100 6.3 3.3 6.0 2.5\n", "101 5.8 2.7 5.1 1.9\n", "102 7.1 3.0 5.9 2.1\n", "103 6.3 2.9 5.6 1.8\n", "104 6.5 3.0 5.8 2.2\n", "105 7.6 3.0 6.6 2.1\n", "106 4.9 2.5 4.5 1.7\n", "107 7.3 2.9 6.3 1.8\n", "108 6.7 2.5 5.8 1.8\n", "109 7.2 3.6 6.1 2.5" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "iris = iris[([True] * 10 + [False] * 40) * 3]\n", "\n", "iris" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Arbre" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "import sklearn" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [], "source": [ "from sklearn.cluster import AgglomerativeClustering" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Par défaut, l'algorithme ne calcule que 2 classes (sk-learn est une bibliothèque de machine learning et ils ne savent compter que jusqu'à 2... POur répondre toujours à la question OUI/NON). Nous on veut tout l'arbre." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "# iris, on utilise ward\n", "# par défaut, la distance euclidienne est utilisée.\n", "\n", "clustering = AgglomerativeClustering(n_clusters=None, distance_threshold=0).fit(iris)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Noeuds" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Chaque nœud crée a 2 enfants, les nœuds qui ont été agrégés :" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0, 4],\n", " [ 1, 9],\n", " [ 7, 30],\n", " [14, 18],\n", " [ 2, 3],\n", " [10, 12],\n", " [11, 16],\n", " [ 6, 34],\n", " [ 8, 37],\n", " [23, 24],\n", " [13, 19],\n", " [25, 27],\n", " [31, 38],\n", " [33, 36],\n", " [28, 39],\n", " [22, 29],\n", " [ 5, 32],\n", " [15, 40],\n", " [35, 43],\n", " [26, 47],\n", " [20, 45],\n", " [21, 44],\n", " [17, 49],\n", " [41, 50],\n", " [42, 46],\n", " [51, 53],\n", " [48, 55],\n", " [52, 56],\n", " [54, 57]])" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "\n", "clustering.children_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nos données initiales sont les plus petits nœuds (ici les nœuds d'index 0 à 29). Puis chaque nœud crée va avoir un numéro plus grand. \n", "\n", "Le 1er nœud crée (qui est l'agrégation des nœuds 0 et 4) va ainsi avoir l'index 30." ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 4])" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 1er noeud crée a lié les 2 noeuds : \n", "clustering.children_[0]" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([25, 27])" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# le noeud crée à la 12ème itération a lié les noeud : \n", "clustering.children_[11]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comme on aggrège à chaque fois 2 classes, le nombre d'itération est égale à 29 (le nombre d'élément moins 1) :" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "29" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(clustering.children_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hauteur d'agrégation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La hauteur d'arégation de chaque classe pour chaque itération :" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0.14142136, 0.17320508, 0.21602469, 0.24494897, 0.24494897,\n", " 0.26457513, 0.26457513, 0.31622777, 0.5 , 0.5 ,\n", " 0.51961524, 0.52915026, 0.57445626, 0.6670832 , 0.67577116,\n", " 0.75498344, 0.77995726, 0.83066239, 0.8953584 , 0.9486833 ,\n", " 1.0082989 , 1.16332856, 1.41279864, 1.41891978, 1.4501724 ,\n", " 2.30024153, 3.74729532, 5.8080978 , 15.34672604])" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clustering.distances_" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.1414213562373093" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# hauteur de la première itération : \n", "clustering.distances_[0]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# hauteur de la 12 itérations itération : \n", "clustering.distances_[11]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La hauteur va souvent avoir une courbe *exponentielle* :" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "sns.set()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "image/png": 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2.87500 0.500000\n", "39 23.50000 0.500000\n", "40 13.50000 0.519615\n", "41 25.50000 0.529150\n", "42 1.68750 0.574456\n", "43 18.50000 0.667083\n", "44 22.75000 0.675771\n", "45 28.50000 0.754983\n", "46 6.87500 0.779957\n", "47 12.75000 0.830662\n", "48 17.00000 0.895358\n", "49 11.87500 0.948683\n", "50 27.75000 1.008299\n", "51 21.87500 1.163329\n", "52 10.93750 1.412799\n", "53 26.62500 1.418920\n", "54 4.28125 1.450172\n", "55 24.25000 2.300242\n", "56 20.62500 3.747295\n", "57 15.78125 5.808098\n", "58 10.03125 15.346726" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fils = clustering.children_\n", "hauteur = clustering.distances_\n", "n = len(clustering.labels_)\n", "\n", "\n", "node_position = pandas.DataFrame([(0, 0) for i in range(n)], \n", " columns=['x', 'y'])\n", "\n", "node_position \n", "\n", "pos = [0]\n", "def backtracking(noeud):\n", " for x in noeud:\n", " if x < n:\n", " node_position.loc[x , 'x'] = pos[0]\n", " pos[0] += 1\n", " else:\n", " backtracking(fils[x - n])\n", "\n", "backtracking(fils[-1])\n", "\n", "for i, (son1, son2) in enumerate(fils):\n", " pos = 0.5 * (node_position.loc[son1]['x'] + node_position.loc[son2]['x'])\n", " node_position = pandas.concat([node_position, pandas.DataFrame([(pos, hauteur[i])], columns=['x', 'y'])], ignore_index=True)\n", " \n", "node_position" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import matplotlib.lines as mlines" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = len(clustering.labels_)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 10))\n", "\n", "sns.scatterplot(x='x', \n", " y='y', \n", " data=node_position,\n", " legend=False,\n", " ax=ax)\n", "\n", "for i, sons in enumerate(fils):\n", " u = node_position.loc[i + n] \n", " v1 = node_position.loc[sons[0]]\n", " v2 = node_position.loc[sons[1]]\n", " \n", " l = mlines.Line2D([u['x'], v1['x']] , [u['y'], v1['y']])\n", " ax.add_line(l)\n", " l = mlines.Line2D([u['x'], v2['x']] , [u['y'], v2['y']])\n", " ax.add_line(l)\n", "\n", "\n", "for i, row in node_position.iterrows():\n", " ax.text(row['x'], row['y'], i)\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On voit bien quele 1er nœud crée est d'index 30 et à agrégé les nœuds 0 et 4 à une hauteur de .14\n", "\n", "Le noeud crée à la 12 itération est d'index 29 + 12 = 41." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut améliorer le dessin en ne légendant que les données de départ. Pour cela, on va créer un dictionnaire de correspondance entre le nœud de l'arbre et son label." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On crée le dictionnaire en itérant sur les lignes du dataframe (`iris.iterrows()`). Cette itération rend à chaque passage un couple `(index, row)` le premier correspondant à l'index (le nom) de la linge et le secon à la ligne proprement dite.\n", "\n", "Ceci ne suffit pas pour nous, puisqu'il nous faut également lenuméro de la ligne (qui est différent de l'index). Pour cela on utilise [une technique de bouble](https://docs.python.org/fr/3.5/tutorial/datastructures.html#looping-techniques) avec `enumerate`.\n", "\n" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{0: 0,\n", " 1: 1,\n", " 2: 2,\n", " 3: 3,\n", " 4: 4,\n", " 5: 5,\n", " 6: 6,\n", " 7: 7,\n", " 8: 8,\n", " 9: 9,\n", " 10: 50,\n", " 11: 51,\n", " 12: 52,\n", " 13: 53,\n", " 14: 54,\n", " 15: 55,\n", " 16: 56,\n", " 17: 57,\n", " 18: 58,\n", " 19: 59,\n", " 20: 100,\n", " 21: 101,\n", " 22: 102,\n", " 23: 103,\n", " 24: 104,\n", " 25: 105,\n", " 26: 106,\n", " 27: 107,\n", " 28: 108,\n", " 29: 109}" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = iris\n", "\n", "labels = dict()\n", "\n", "for i, (index, row) in enumerate(iris.iterrows()):\n", " labels[i] = index\n", "\n", "labels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On a alors le dessin suivant :" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# données : \n", "# - clustering : issu de AgglomerativeClustering \n", "# - node_position : dataframe contenant la postion des différents nœuds du clustering (voir au-dessus pour son calcul)\n", "# - labels : le label des nœuds\n", "\n", "n = len(clustering.labels_)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 10))\n", "\n", "sns.scatterplot(x='x', \n", " y='y', \n", " data=node_position,\n", " legend=False,\n", " ax=ax)\n", "\n", "for i, sons in enumerate(fils):\n", " u = node_position.loc[i + n] \n", " v1 = node_position.loc[sons[0]]\n", " v2 = node_position.loc[sons[1]]\n", " \n", " l = mlines.Line2D([u['x'], v1['x']] , [u['y'], v1['y']])\n", " ax.add_line(l)\n", " l = mlines.Line2D([u['x'], v2['x']] , [u['y'], v2['y']])\n", " ax.add_line(l)\n", "\n", "\n", "for i, row in node_position.iterrows():\n", " if i in labels:\n", " ax.text(row['x'], row['y'], labels.get(i, i), \n", " horizontalalignment='center',\n", " verticalalignment='top', \n", " rotation=-90)\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On voit que les espèces sont bien conservées par les classes (de 0 à 9, de 50 à 59 et de 100 à 19)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## CAH comme une méthode de partitionnement" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On utilise cette méthode d partitionnement plutôt que la méthode des $k$-means si :\n", "* on a des formes non ronde de classes à trouver (après une isomap par exemple) :https://scikit-learn.org/stable/modules/clustering.html\n", "* nos données sont décrites par une distance non euclidienne\n", "\n", "**Attention** : on perd la notion d'inertie, il est donc impossible de déterminer *a priori* si une partition est meilleure qu'une autre. Il faut se créer sa propre *fonction objectif* pour déterminer la meilleure partition." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut utiliser notre méthode hiérarchique pour trouver une partition de de façon différente :\n", "- on arrète l'algorithme lorqu'il n'y a plus que $k$ classes (si on veut tout l'arbre on vueut qu'il ne reste plus qu'une seule classe)\n", "- on fixe une hauter et on coupe la hiérarchie à cette hauteur.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### nombre de classe fixé" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`sklearn` permet de faire ça grace au paramètre `n_clusters`\n", "\n", "Si on fixe le nombre de classes à 4, on arête l'algorithme de la CAH lorsqu'il ne reste que 4 classes (ce sera les classes d'index 54, 42, 48 et 55 de notre arbre complet)." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "clustering = AgglomerativeClustering(n_clusters=4).fit(iris)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On retrouve les classes dans l'attribut `labels_` :" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 0, 0,\n", " 0, 0, 0, 0, 2, 0, 0, 0])" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clustering.labels_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il y en a bien 4. On peut maintenant regarder leurs adéquation aux espèces d'iris : " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "clustering.labels_[:10]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "clustering.labels_[10:20]" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "clustering.labels_[20:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### coupe à une hauter donnée\n", "\n", "On commence par créer tout l'arbre, puis on regarde les hauteurs d'aggrégation.\n", "\n", "Une fois la hauteur de coupe déterminée (juste avant la montée exponentielle si elle existe), on ré-exécute la classification avec ce paramètre. Ceci nous donnera les classes conservées." ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "clustering = AgglomerativeClustering(n_clusters=None, distance_threshold=0).fit(iris)" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 10))\n", "\n", "sns.lineplot(x=list(range(len(clustering.distances_))), \n", " y=clustering.distances_, \n", " legend=False,\n", " ax=ax)\n", "\n", "plt.axhline(2, color=\"red\")\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On va couper à 2." ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [], "source": [ "partition = AgglomerativeClustering(n_clusters=None,\n", " compute_full_tree=True,\n", " distance_threshold=2\n", " ).fit(iris)" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 1, 4,\n", " 1, 4, 4, 1, 2, 1, 4, 1])" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "partition.labels_" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0])" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "partition.labels_[:10]" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3, 3, 3, 2, 3, 2, 3, 2, 3, 2])" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "partition.labels_[10:20]" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 4, 1, 4, 4, 1, 2, 1, 4, 1])" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "partition.labels_[20:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## comme méthode d'organisation\n", "\n", "\n", "Permet d'organiser une matrice en éléments similaires. On fait une hiérarchie sur les ligne et le colonne puis on réordonne la matrice avec les hirarchies obtenues. \n", "\n", "Seaborn le fait tout seul pour nous :\n", "https://seaborn.pydata.org/examples/structured_heatmap.html\n", "\n", "Idéal pour une matrice de corrélation par exemple." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Toutes les iris\n", "\n", "Refaisons nos algorithmes avec toutes les iris en tentant de trouver une bonne partition." ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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sepal_lengthsepal_widthpetal_lengthpetal_width
05.13.51.40.2
14.93.01.40.2
24.73.21.30.2
34.63.11.50.2
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\n", "
" ], "text/plain": [ " sepal_length sepal_width petal_length petal_width\n", "0 5.1 3.5 1.4 0.2\n", "1 4.9 3.0 1.4 0.2\n", "2 4.7 3.2 1.3 0.2\n", "3 4.6 3.1 1.5 0.2\n", "4 5.0 3.6 1.4 0.2\n", ".. ... ... ... ...\n", "145 6.7 3.0 5.2 2.3\n", "146 6.3 2.5 5.0 1.9\n", "147 6.5 3.0 5.2 2.0\n", "148 6.2 3.4 5.4 2.3\n", "149 5.9 3.0 5.1 1.8\n", "\n", "[150 rows x 4 columns]" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "iris = sns.load_dataset('iris').drop(columns=\"species\")\n", "iris" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Arbre complet" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [], "source": [ "clustering = AgglomerativeClustering(n_clusters=None, distance_threshold=0).fit(iris)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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299 rows × 2 columns

\n", "
" ], "text/plain": [ " x y\n", "0 29.000000 0.000000\n", "1 2.000000 0.000000\n", "2 8.000000 0.000000\n", "3 9.000000 0.000000\n", "4 21.000000 0.000000\n", ".. ... ...\n", "294 22.992188 3.828053\n", "295 69.187500 4.847709\n", "296 109.498047 6.399407\n", "297 89.342773 12.300396\n", "298 56.167480 32.447607\n", "\n", "[299 rows x 2 columns]" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fils = clustering.children_\n", "hauteur = clustering.distances_\n", "n = len(clustering.labels_)\n", "\n", "\n", "node_position = pandas.DataFrame([(0, 0) for i in range(n)], \n", " columns=['x', 'y'])\n", "\n", "node_position \n", "\n", "pos = [0]\n", "def backtracking(noeud):\n", " for x in noeud:\n", " if x < n:\n", " node_position.loc[x , 'x'] = pos[0]\n", " pos[0] += 1\n", " else:\n", " backtracking(fils[x - n])\n", "\n", "backtracking(fils[-1])\n", "\n", "for i, (son1, son2) in enumerate(fils):\n", " pos = 0.5 * (node_position.loc[son1]['x'] + node_position.loc[son2]['x'])\n", " node_position = pandas.concat([node_position, pandas.DataFrame([(pos, hauteur[i])], columns=['x', 'y'])], ignore_index=True)\n", "node_position" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = len(clustering.labels_)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 10))\n", "\n", "sns.scatterplot(x='x', \n", " y='y', \n", " data=node_position,\n", " legend=False,\n", " ax=ax)\n", "\n", "for i, sons in enumerate(fils):\n", " u = node_position.loc[i + n] \n", " v1 = node_position.loc[sons[0]]\n", " v2 = node_position.loc[sons[1]]\n", " \n", " l = mlines.Line2D([u['x'], v1['x']] , [u['y'], v1['y']])\n", " ax.add_line(l)\n", " l = mlines.Line2D([u['x'], v2['x']] , [u['y'], v2['y']])\n", " ax.add_line(l)\n", "\n", "\n", "for i, row in node_position.iterrows():\n", " ax.text(row['x'], row['y'], i)\n", " \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### coupe à hauteur donnée" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "clustering = AgglomerativeClustering(n_clusters=None, distance_threshold=0).fit(iris)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 10))\n", "\n", "sns.lineplot(x=list(range(len(clustering.distances_))), \n", " y=clustering.distances_, \n", " legend=False,\n", " ax=ax)\n", "\n", "plt.axhline(2, color=\"red\")\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On coupe toujours à une hauteur de 2" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [], "source": [ "partition = AgglomerativeClustering(n_clusters=None,\n", " compute_full_tree=True,\n", " distance_threshold=2\n", " ).fit(iris)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Il y a 9 classes :" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max(partition.labels_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ces classes sont très homogènes avec les 3 espèces d'iris. On peut le remarquer en intersectant les classes :" ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "set()" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "set(partition.labels_[:50]).intersection(partition.labels_[50:100])" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "set()" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "set(partition.labels_[:50]).intersection(partition.labels_[100:])" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{1, 2, 4, 6}" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "set(partition.labels_[50:100]).intersection(partition.labels_[100:])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comptons le nombre d'éléments par classes" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Counter({0: 29, 5: 21, 8: 8, 6: 15, 1: 22, 7: 4, 2: 15, 4: 24, 3: 12})" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from collections import Counter\n", "\n", "Counter(partition.labels_)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour chaque éspèce :" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Counter({0: 29, 5: 21})" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Counter(partition.labels_[:50])" ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Counter({8: 8, 6: 12, 1: 21, 7: 4, 2: 4, 4: 1})" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Counter(partition.labels_[50:100])" ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Counter({4: 23, 2: 11, 3: 12, 1: 1, 6: 3})" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Counter(partition.labels_[100:])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" }, "vscode": { "interpreter": { "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49" } } }, "nbformat": 4, "nbformat_minor": 2 }