05. Unsupervised/5.2 Clustering.ipynb

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   "source": [
    "# <center> Clustering\n",
    "    \n",
    "![](https://scikit-learn.org/stable/_images/sphx_glr_plot_cluster_comparison_001.png)\n",
    "\n",
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import altair as alt\n",
    "\n",
    "from scipy.cluster import hierarchy\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate sintetic data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "          x         y\n",
       "0 -3.588758 -1.679874\n",
       "1 -4.217010 -0.207285\n",
       "2 -3.505954 -2.781822\n",
       "3 -4.239929 -2.121086\n",
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   "source": [
    "np.random.seed(0)\n",
    "n_points_per_cluster = 250\n",
    "\n",
    "C1 = [-5, -2] + .8  * np.random.randn(n_points_per_cluster, 2)\n",
    "C2 = [4, -1]  + .1  * np.random.randn(n_points_per_cluster, 2)\n",
    "C3 = [1, -2]  + .2  * np.random.randn(n_points_per_cluster, 2)\n",
    "C4 = [-2, 3]  + .3  * np.random.randn(n_points_per_cluster, 2)\n",
    "C5 = [3, -2]  + 1.6 * np.random.randn(n_points_per_cluster, 2)\n",
    "C6 = [5, 6]   + 2   * np.random.randn(n_points_per_cluster, 2)\n",
    "sintetic = np.vstack((C1, C2, C3, C4, C5, C6))\n",
    "sintetic = pd.DataFrame(sintetic, columns=[\"x\", \"y\"])\n",
    "sintetic.head()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alt.Chart(sintetic).mark_circle().encode(x='x', y='y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-means (Busca centroides de los grupos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</script>"
      ],
      "text/plain": [
       "alt.LayerChart(...)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "# Do K-means\n",
    "kmeans = KMeans(n_clusters=4, random_state=0).fit(sintetic[[\"x\", \"y\"]])\n",
    "\n",
    "# Save data\n",
    "sintetic[\"kmeans4\"] = kmeans.labels_\n",
    "centers = pd.DataFrame(kmeans.cluster_centers_, columns=[\"x\", \"y\"])\n",
    "\n",
    "# Plot\n",
    "points  = alt.Chart(sintetic).mark_circle().encode(x='x', y='y', color=\"kmeans4:N\")\n",
    "centers = alt.Chart(centers).mark_circle(color='black', size=100).encode(x='x', y='y')\n",
    "points + centers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DBSCAN (Busca densidades contiguas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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{\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import DBSCAN\n",
    "\n",
    "dbscan  = DBSCAN(eps=1).fit(sintetic[[\"x\", \"y\"]])\n",
    "sintetic[\"dbscan\"] = dbscan.labels_\n",
    "\n",
    "alt.Chart(sintetic).mark_circle().encode(x='x', y='y', color=\"dbscan:N\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# OPTICS: Busca densidades (variables) contiguas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
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       "      loadScript(\"vega\")\n",
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\"y\": 5.191295560752001, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.529408563434053, \"y\": 4.732022681366558, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.213101757628674, \"y\": 6.005435079781361, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.044425329032968, \"y\": 7.086906879165451, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.279976934773718, \"y\": 5.31190874230075, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.954842916936107, \"y\": 5.385736559682632, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.101925717106069, \"y\": 6.981942110363959, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.731050381342525, \"y\": 8.548089075894168, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.404594480119165, \"y\": 6.9387444506775005, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.2106407168146487, \"y\": 6.746349436505156, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.16534456418213, 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\"y\": 4.324447481229589, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.818376990661932, \"y\": 6.161439780867734, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.925941312302616, \"y\": 3.7741882102567677, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.190823751653734, \"y\": 10.674819322956552, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.214358792907583, \"y\": 5.327452281828843, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 8.047542395234107, \"y\": 5.885437600418969, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.1030662735040235, \"y\": 2.8544070949036535, \"kmeans4\": 3, \"dbscan\": 1, \"optics\": -1}, {\"x\": 7.4533279475749605, \"y\": 7.332709084500378, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.652251416862386, \"y\": 5.884486883242574, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.5465759480344046, \"y\": 5.565673768551666, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.2720624347487535, \"y\": 4.323377688602598, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.122899819102253, \"y\": 3.480807662400557, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.334482470849553, \"y\": 5.591984255046994, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.6179603736492627, \"y\": 1.588989289960356, \"kmeans4\": 1, \"dbscan\": 1, \"optics\": -1}, {\"x\": 5.895739328222505, \"y\": 4.488498479119466, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.651415918648743, \"y\": 5.316035444631895, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.917280823137559, \"y\": 6.1830438935577545, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.106879497260897, \"y\": 4.87318467376366, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.029475389659554, \"y\": 8.880607282035246, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.980645621311891, \"y\": 9.252862981984514, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.585292042024937, \"y\": 9.029764587786012, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 8.208652638831282, \"y\": 6.416139059259928, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.141552200855603, \"y\": 1.4755127295123884, \"kmeans4\": 1, \"dbscan\": 1, \"optics\": -1}, {\"x\": 2.3545337609564085, \"y\": 5.103434401682409, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.236529825518868, \"y\": 5.694411073195827, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.9984790195024997, \"y\": 2.808444777117372, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": -1}, {\"x\": 4.739553667066548, \"y\": 5.6211641423764185, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.3848919169002682, \"y\": 4.515695676699231, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.1196868162551867, \"y\": 5.206952521967365, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.2873943460094974, \"y\": 8.519750663034031, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.481993464090242, \"y\": 4.055364163946965, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.439104437065092, \"y\": 3.6394287872976188, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.024336590349575, \"y\": 8.76837344916164, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.504003965506063, \"y\": 3.710614737514805, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.817465960547648, \"y\": 5.196858648974168, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.1240262118283635, \"y\": 3.984180393432204, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.6482166119979667, \"y\": 5.173565943296384, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.306576938264848, \"y\": 7.388257416275772, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.342544614526784, \"y\": 7.327930151052444, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.644152713594275, \"y\": 5.573569526256358, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.508683734268806, \"y\": 3.657619329131719, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.183453950303137, \"y\": 5.047551127370661, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 1.5747413546350897, \"y\": 7.225904736366001, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.259109041092438, \"y\": 3.1880658377147433, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.358839962405291, \"y\": 7.673271974315499, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.277490502580359, \"y\": 3.451361264531166, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.195338934229434, \"y\": 5.385863026317127, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 1.5721692208994211, \"y\": 6.810160546368971, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.178353373239327, \"y\": 6.329825458509397, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.4237370945465475, \"y\": 7.423570536194088, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.1241048094770236, \"y\": 6.547458899049448, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.210319614330713, \"y\": 7.591099103538814, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.77007646744501, \"y\": 6.991701337930861, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.3589493063439355, \"y\": 6.998168551343533, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.612406792607417, \"y\": 6.727395785426726, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.625267926027972, \"y\": 5.613072234419304, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 7.482598440631982, \"y\": 5.688204028468593, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.5216615992183424, \"y\": 5.882547613262123, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.0989641091109394, \"y\": 5.072007153338312, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.645506767621202, \"y\": 5.24089175870828, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.398794145610972, \"y\": 9.891522782612654, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 6.141899679692241, \"y\": 8.144601294576184, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.992581125263527, \"y\": 4.825967422989703, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 4.243643906214021, \"y\": 7.705778194537754, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 0.7037630435382045, \"y\": 3.9336704494172654, \"kmeans4\": 3, \"dbscan\": -1, \"optics\": 3}, {\"x\": 5.204671693668439, \"y\": 5.551815265874143, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 8.935459364286093, \"y\": 6.8953664314853125, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.6756171129390385, \"y\": 2.8447858629213054, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": -1}, {\"x\": 4.318879930124275, \"y\": 3.393559834643171, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.933501300836871, \"y\": 6.322212644483357, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 5.640063864185462, \"y\": 10.158353329590074, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 3.1850680371594047, \"y\": 5.615191584408186, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}, {\"x\": 2.574968511022182, \"y\": 5.838802967699749, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import OPTICS\n",
    "\n",
    "optics = OPTICS(min_samples=50, xi=.05, min_cluster_size=.05).fit(sintetic[[\"x\", \"y\"]])\n",
    "sintetic[\"optics\"] = optics.labels_\n",
    "\n",
    "alt.Chart(sintetic).mark_circle().encode(x='x', y='y', color=\"optics:N\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering jerárquico\n",
    "- **Agglomerative** — Bottom up approach. Start with many small clusters and merge them together to create bigger clusters.\n",
    "- **Divisive** — Top down approach. Start with a single cluster than break it up into smaller clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = hierarchy.linkage(sintetic[[\"x\", \"y\"]], 'ward')\n",
    "plt.figure(figsize=(12,6))\n",
    "dn = hierarchy.dendrogram(Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<div id=\"altair-viz-5\"></div>\n",
       "<script type=\"text/javascript\">\n",
       "  (function(spec, embedOpt){\n",
       "    const outputDiv = document.getElementById(\"altair-viz-5\");\n",
       "    const paths = {\n",
       "      \"vega\": \"https://cdn.jsdelivr.net/npm//vega@5?noext\",\n",
       "      \"vega-lib\": \"https://cdn.jsdelivr.net/npm//vega-lib?noext\",\n",
       "      \"vega-lite\": \"https://cdn.jsdelivr.net/npm//vega-lite@4.0.0?noext\",\n",
       "      \"vega-embed\": \"https://cdn.jsdelivr.net/npm//vega-embed@6?noext\",\n",
       "    };\n",
       "\n",
       "    function loadScript(lib) {\n",
       "      return new Promise(function(resolve, reject) {\n",
       "        var s = document.createElement('script');\n",
       "        s.src = paths[lib];\n",
       "        s.async = true;\n",
       "        s.onload = () => resolve(paths[lib]);\n",
       "        s.onerror = () => reject(`Error loading script: ${paths[lib]}`);\n",
       "        document.getElementsByTagName(\"head\")[0].appendChild(s);\n",
       "      });\n",
       "    }\n",
       "\n",
       "    function showError(err) {\n",
       "      outputDiv.innerHTML = `<div class=\"error\" style=\"color:red;\">${err}</div>`;\n",
       "      throw err;\n",
       "    }\n",
       "\n",
       "    function displayChart(vegaEmbed) {\n",
       "      vegaEmbed(outputDiv, spec, embedOpt)\n",
       "        .catch(err => showError(`Javascript Error: ${err.message}<br>This usually means there's a typo in your chart specification. See the javascript console for the full traceback.`));\n",
       "    }\n",
       "\n",
       "    if(typeof define === \"function\" && define.amd) {\n",
       "      requirejs.config({paths});\n",
       "      require([\"vega-embed\"], displayChart, err => showError(`Error loading script: ${err.message}`));\n",
       "    } else if (typeof vegaEmbed === \"function\") {\n",
       "      displayChart(vegaEmbed);\n",
       "    } else {\n",
       "      loadScript(\"vega\")\n",
       "        .then(() => loadScript(\"vega-lite\"))\n",
       "        .then(() => loadScript(\"vega-embed\"))\n",
       "        .catch(showError)\n",
       "        .then(() => displayChart(vegaEmbed));\n",
       "    }\n",
       "  })({\"config\": {\"view\": {\"continuousWidth\": 400, \"continuousHeight\": 300}}, \"data\": {\"name\": \"data-cb23a249a126d696e15fe99751e1b432\"}, \"mark\": \"circle\", \"encoding\": {\"color\": {\"type\": \"nominal\", \"field\": \"hierarchical\"}, \"x\": {\"type\": \"quantitative\", \"field\": \"x\"}, \"y\": {\"type\": \"quantitative\", \"field\": \"y\"}}, \"$schema\": \"https://vega.github.io/schema/vega-lite/v4.0.0.json\", \"datasets\": {\"data-cb23a249a126d696e15fe99751e1b432\": [{\"x\": -3.588758123225869, \"y\": -1.6798742333062213, \"kmeans4\": 0, \"dbscan\": 0, \"optics\": 0, \"hierarchical\": 1}, {\"x\": -4.217009612715408, \"y\": -0.20728544063883358, \"kmeans4\": 0, \"dbscan\": 0, \"optics\": 0, \"hierarchical\": 1}, {\"x\": -3.505953607880026, \"y\": -2.7818223039011287, \"kmeans4\": 0, \"dbscan\": 0, \"optics\": 0, \"hierarchical\": 1}, {\"x\": -4.239929265979528, \"y\": -2.121085766638158, \"kmeans4\": 0, \"dbscan\": 0, \"optics\": 0, \"hierarchical\": 1}, 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\"y\": 5.838802967699749, \"kmeans4\": 2, \"dbscan\": 1, \"optics\": 3, \"hierarchical\": 0}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.Chart(...)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "hierarchical = AgglomerativeClustering().fit(sintetic[[\"x\", \"y\"]])\n",
    "sintetic[\"hierarchical\"] = hierarchical.labels_\n",
    "\n",
    "alt.Chart(sintetic).mark_circle().encode(x='x', y='y', color=\"hierarchical:N\")"
   ]
  }
 ],
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