UMAP_experiments.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import load_digits\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "### Import the data\n",
    "circle = pd.read_csv(\"../synthetic-data-files/circle_R1_n5000_dim20.dat\", header = None)\n",
    "gauBall = pd.read_csv(\"../synthetic-data-files/GaussianBall_mu0sd1_n5000_dim20.dat\", header = None)\n",
    "recHole = pd.read_csv(\"../synthetic-data-files/rect_hole_a6b8_n5000_dim20.dat\", header = None)\n",
    "# swissRole = pd.read_csv(\"../synthetic-data-files/swiss_hole_n5000_dim20.csv\", header = None)\n",
    "# swissRot30 = pd.read_csv(\"../synthetic-data-files/swiss_rot30Degree_hole_n5000_dim20.csv\", header = None)\n",
    "# threeDtorus = pd.read_csv(\"../synthetic-data-files/threeDTorus_r4t2d1_NormalNoise_n4913_dim20.csv\", header = None)\n",
    "# torusNormalNoise = pd.read_csv(\"../synthetic-data-files/torus_NormalNoise_R4r2_n5041_dim20.csv\", header = None)\n",
    "# torusRut = pd.read_csv(\"../synthetic-data-files/torus_rot115Degree_R4r2_n5041_dim20.csv\", header = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "d_circle = {'col1': circle.iloc[0], 'col2': circle.iloc[1]}\n",
    "circle = pd.DataFrame(data=d_circle)\n",
    "d_gauBall = {'col1': gauBall.iloc[0], 'col2': gauBall.iloc[1]}\n",
    "gauBall = pd.DataFrame(data=d_gauBall)\n",
    "d_recHole = {'col1': recHole.iloc[0], 'col2': recHole.iloc[1]}\n",
    "recHole = pd.DataFrame(data=d_recHole)\n",
    "# d_swissRole = {'col1': swissRole.iloc[0], 'col2': swissRole.iloc[1]}\n",
    "# swissRole = pd.DataFrame(data=d_swissRole)\n",
    "# d_swissRot30 = {'col1': swissRot30.iloc[0], 'col2': swissRot30.iloc[1]}\n",
    "# swissRot30 = pd.DataFrame(data=d_swissRot30)\n",
    "# d_threeDtorus = {'col1': threeDtorus.iloc[0], 'col2': threeDtorus.iloc[1]}\n",
    "# threeDtorus = pd.DataFrame(data=d_threeDtorus)\n",
    "# d_torusNormalNoise = {'col1': torusNormalNoise.iloc[0], 'col2': torusNormalNoise.iloc[1]}\n",
    "# torusNormalNoise = pd.DataFrame(data=d_torusNormalNoise)\n",
    "# d_torusRut = {'col1': torusRut.iloc[0], 'col2': torusRut.iloc[1]}\n",
    "# torusRut = pd.DataFrame(data=d_torusRut)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>col1</th>\n",
       "      <th>col2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.919281</td>\n",
       "      <td>1.023257</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.318681</td>\n",
       "      <td>-0.506675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.610181</td>\n",
       "      <td>-0.703452</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.121395</td>\n",
       "      <td>-1.414011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.450836</td>\n",
       "      <td>2.005569</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       col1      col2\n",
       "0 -0.919281  1.023257\n",
       "1  0.318681 -0.506675\n",
       "2  0.610181 -0.703452\n",
       "3  0.121395 -1.414011\n",
       "4 -0.450836  2.005569"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circle.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import umap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "reducer = umap.UMAP()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "circle_data = circle[\n",
    "    [\n",
    "        \"col1\",\n",
    "        \"col2\",\n",
    "    ]\n",
    "].values\n",
    "scaled_circle_data = StandardScaler().fit_transform(circle_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "embedding = reducer.fit_transform(circle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'UMAP projection of the circle dataset')"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5kRlKvvq5k8f43icJoa83kSsvBbL9FkcplS/0EwaZZBUsEQ6JvMgcm5bMCeSD1iSc+vgdOB7RwsDCnec5As2ARF5kFr/i8dzxU1i0YXssNtQLAwwTDpoGfgaOiXApihUqmW0k8iLT+PX73rv/2ViE/tCxEzXXRxk5UmsCUdy95aEM53aav3Zb3Wsk0kUiLzKPX/dBmJQJWSJoKGmUhPGt9/QP1h2v0MBs+kjkRS7Iot+3KPoV9tr6GcjVwGz6SORFbvDj/45yZmq9Y0UZVRP3jNpqN6SwNyrlE8oPEnmRGzpnTqgbXhnlzNQkZ7nGfa4nujvOEXQi3I3Kr8Bnre5ts6K0BiJXbFoyR73IkETx5BHk2qvwSzZQT16IlMlLioYgAp/FMZRmRSIvRAiCzMqtR71skHlze0jgs0UkIk/yyyQPk3ywbNmtJAcrSgIKUQiSrHyUJ7eHBD57RNWTvx3AAo/lnzWzGe6fSsWIhqnnMghQSlZEjN/MlCJZIhl4NbN7SLZFcSxRTCZ19aLcKxE0sqOnf9BXXPZn3j4jqGmhmL92WyI97Ly4aka0EPctn5+2GcKDuKNrPkzy3QB2ArjZzH5duQHJpQCWAkBra/C84iL7VAo8AJi73I/QByksklSBimozPcMU/Jg6bqTn8YYyWldNZS750cNbsPs2rwdwbwa6Ozzbt3h2K1Z1TovERhE9cYr8vwL4JJzf8ycBfAbAeys3MrP1ANYDQHt7e3rzukVsVPtQ633YizZsz1WqgloFP2oJfd9N8zB/7bazhH7quJGRCXy1p6Dnjp/C9JVbAwu9yBexibyZHSq9JrkBwA/iOpfILkFj2met7gud8CpNn3CjtUyjEvSg1y+pMoAiPWITeZIXm9lB9+11AB6stb0oHkFT0DYi8KOHt0TuEz5vCPDy6erre/oH0Tlzgu/xgjhJsm6rF5VPXXMnj0k0AklUJxKRJ3kHgHkALiL5FICVAOaRnAHnqXwAwF9HcS6RH+oJdmUgTFiBX3f9jFh88Z9+24ya4v3pux/Dmi0Pp55qN+0ZwF5utXv3P3vGLvns0yWq6JobPBZ/KYpji+LS6DT7sLlX/NI5c0JNkR88+mJs5/ZD2r33EvXGTTbuOOCZm0e9/WTQjFeRS8aPGpab2qqLZ0cfNTbllt5IBD7NylblvX0RHxJ5kQqNxH+vu35GrmKyo3ZVrOjZUzcVgh/icnMFRUIfL8pCKVLBK5qkWrw4kJ5ft1ps+Lrra/vry7eLmrBpiUe0MFQNV5FvJPIiM8QdLx6WarHhn/vZ3prl79LuKY8fNSyRJ56hrJ9kTaQHzbLz6bS3t9vOnTvTNkNESJgZoHmi8qYEOKIXZ9k7P+6NpJ98ptzS25DQF+k7kQYkHzCzdq916smLWCn6jzftp4xKkuq9V1J+U2tkvoOIHom8EAUiCwPS1WyoNmms6B2BtJHINzGVj9hxuhm8endxx7mLbNE5c0ImonmaDYVQNilePtST5vh7G83DUkm1x3eDwuei5srlKtsgzkYi36TUGiRbtnlXpGJRzz8b9U2lmXnplOnGKc5CIi88KYlFEj3DtJN75Y3Rw1vqbtPW1Yu2rl4s2rA9AYtEllEIZZMStLfXSLy633NpAM4/jfTWszD3QESLQihFw+w9/DzaunpDTfAZP2qYr5C6Wav7MhEdUnRKn2UtlDmyOKgn36R4TeLxSxihD1LCr1GB8du2PE/zTzIDpVcKhzxfuyJSqycvkW9iGhH6MK6VMLMia4nJip49ofO4lHPeECd3fN7C+xqdZRoVEvz0kciLmoQRy7D+8yxHfuTRVx3VjS4q8ngNi4BEXvgibM8wyKSmrE95Hz28JVBh6zDEkc8nKwVESmgQPVkk8sI3Pf2D+Ptv/RdOng7+vfDbi8u60MfZG631JBOVMGah5iygXn2SxC7yJL8M4K0ADpvZ1e6yMQA2A2iDU+P17Wb261rHkchnh7BugCA/7Cy7buJIE1yvvXH1fhsZe4kC9erjJwmR/0MAvwHw1TKR/xSAZ82sm2QXgFeb2UdrHUcinz3CCHGQH3WWhT7pnnUWxLCRAinVUI6i+EnEXUOyDcAPykT+MQDzzOwgyYsBbDOzK2odQyKfbeZ2/9RX8eqgYrVow/a6xaAboVQwuqd/EJ+++zHfBbijcDcEcZ1kQeTrEdbVloe25Zm0JkONN7ODAOAK/bgqxi0FsBQAWlujL3gsouMjb7kiFl/vpiVzzno/qasXYboe9Vws5VkQ/TxBROHiyIJvPEpKk9WCzHsQ6ZL6jFczWw9gPeD05FM2R9SgJJBxC1cSj/YD3R2xR6RMX7nV97aLZ+erg1OKi89aCKc4lzgTlB1y3TRw/x+O8VwiITpnTqj56D2ihQla0xhxhkou2rDd9w1k6riRuU0hsKpzGga6O2repPLzjSgmcYr8XQBudF/fCOB7MZ5LJMxAd8c5gq6Zj6/gd4xh8ezWQoQZruqc5in0GnRNn0jcNSTvADAPwEUknwKwEkA3gG+SfB+AAwDeFsW5RHbIu6CnHdlTtMHIVZ3TcvtEUmQiEXkzu6HKqjdHcXwhosRvxEsLwzkaVvTsqbvNuutnhDq2EEFJfeBViCQJ0nu/YdbEUOeoNxA5ftSw3CVDE/lFIi+ahkkBBH4oEZvrIY2c+WHyEiktQTFQ+T/RNATRuH1r4vGXpxF91NYVLvFcqbhIHMXdRXKoJy9EBXEOiMY1WF05OakU6RRVjddlm3edNY6hSKr8IJEXoow8RbzUGkB+6ZTFOiu1VOg9T9erWZHIi6aBqO2ySUKwFm3Yfk4ahyAEmWGaRNoBCX32kciLcwgy3X8o4/NfR80T3R2eeXGSHGAMk4itp38Qt971EI6++HIMFomiI5EXAMJngjxpwcISSxkh0yILsy97+gd9h1A2Wsd17uQxsWb4BJyopUsuPB8fecsVCg3NIKoM1eRkIcFUnp4G/OBnslXlwGVchT0GujvOuYEPayE+9Vev9xTkRr8PcRRbEfVR+T/hSdoVg6qRRJ3VuEk7ZQIQneAGFX756JOnlsgrTr5JWdGzJ5MCDwDPHT+Ftq5eXPWPP1R8dkii7FGv6pymNAw5Rj75JiVtF40fXnj59Bm3R95cAAPdHYn25ocQWPv2+Fwl5QVXVDAkX6gn34QEmd6fBfJaXSlutwXppCoe6O7A42s6ErkRzl+7TQKfM9STb0KC/ETHjxrmmWulp38QH/vubrzw8unoDMsIpVqwTx99seGokdHDWyKvPpXGmEWQWrUiW0jkmwy/vfjFs1trJugqf3yvR54e7yvFbPDoiw25jHbftiAyt02S8fxhB+XHjxoWgzWiESTyTUY9qY2jkk+1HCezVvfh0LETkZ6rHj39g7jt+w/h1y8Em1i0bPOu0L35ge6OQDe6FhI3zJqYaAGOqD6LNDJsitpI5JsIP8UskpwsVBKEehOxRg9v8X3MLIQuepHFZF5Rh9BOHTcysmOJ6Ihd5EkOADgG4BSAk9ViOUX81IuoSetHWj4DtjKlQhD/c1YFPiuEndXsF+WezyZJ9eT/2MyeSehcIiRZ+JHmfRJU1giShygsRZi8VmTkrhGiICSdoiKO8RsRPUmIvAH4EUkD8EUzW5/AOUVANKOxNlmfqh+3K6acamG1IpskIfJzzexpkuMA9JF81MzuKa0kuRTAUgBobW1NwBzhRd5mlCZF1gWt0SyVflG91/wSu8ib2dPu/8Mk7wTwBgD3lK1fD2A94CQoi9seUVzCphIgAbNzi4pkXeC9cuNHgQS9WMQq8iRHAhhiZsfc138C4BNxnlOE48rlWzIZ5heUrLtVoiJKgSeAzypFcGGJuyc/HsCdJEvn+rqZbY35nCIEL52yhkvTiWSIIlR0gop8NA2xiryZPQ7g9XGeQ0THvfufRVtXrwo/ZJiwAl+0wizCPwqhFOewbPMuLNu8q2lcH3lh+spgD8GKXxeARL6pCFrvs9Rr1EBc+sxfu83XpCbFrotKJPJNxKYlc0I97u89/Dwuv6U31qIU5dSzsRmfMPzkmJHACy9UNKTJCCuQp81x48SZH6anf9DX8ZWjxhsJvPBCIt+EDHR3YCjD7x+HyE5fuVVFKargxxffjE83wh9y1zQp+9Z0RJ5qNixJzdrMK/V88XGlpPC6metmkj/Uk29i+m6ah4HuDiyenV46iUUbtkvgGySOcZJqT2tyleUPibzAqs5pGOjuwNzJYxI/d1JJtYRoViTy4gyblsxJVOx7+gdD7SeXwdmody1qIZ+8OIdSaoNq4hFVBSk/A61DiMRCN7PK1HEj646dTOrqjSy6RjeNYqGevKjKQHfHOYIe1cSoKbfUF5LRw1vw+JqOphZ4wF/FLoMjzlcu39LQuWat7mtof5E91JMXNYlrpqufwdY0p+R79WbnTh6TWgK38aOG4dCxE3W3e+mUoa2rF4tnt2JV5zTfx0+y6IhIFpplJ7Shvb3ddu7cmbYZIgGyPKu1lm1pCn0j6YWriX7QY2o8JJuQfMDM2r3WqScvMsf4UcPSNqEqafZ2nwhZFAUANu44kGj9V5EdJPIic9SrxtTTP1hz0HZEC2MtgNLW1Ztaj3bx7NbUxDrLN19RHYm8yBX1BB54xS9dIo78+GGF3ss9EiQlcMnlcsd9T+JUwq7WLJdCFNVRdI1InLDx8QDw6bsfC7xPKbHaip49oc8bBdX8388dPxUoV/yqzmnYv2ZhojOV5YvPLxJ5kTiNJCJ7+uiLoffduOMA2rp6cdU//rDmjSYuQavV7/aTK76SVZ3TYhf68aOGSeBzTuwiT3IBycdI7iPZFff5RLG55MLzGz7GCy+fPtO7X7Rhu+c2aQhbmCecUkqKqGcqj2ghBro75KIpALH65Em2APgcgPkAngLwc5J3mdnDcZ5XFJePvOWKSFMS16prO9BANEsYlm3e1dDYQWVop5/Y97gHqUX6xD3w+gYA+9yC3iD5DQDXApDIC0/qpUwoiWDUuedLdW39EqanT9R22QBO7vioJoGlFc9fi3o3nqCTuER9Yp0MRfKvACwws/e7798FYJaZfbhsm6UAlgJAa2vr7/3iF7+IzR6RPlcu34KXTlX/zoV1k8Q9YzOqoth+ngyKVIB7Rc+e0JFAI4e1YPV105o+rYUfak2Gitsn71V/6KxP28zWm1m7mbWPHTs2ZnNEmizasL2mwDdCKYOmV76dKAgzMOrF6OEtvs5Va7wgD5RKOW7ccSB0qOfzJ07FXnKyGYjbXfMUgIll7y8F8HTM5xQ+6OkfxG3ffwi/fuFlz/XDhw7BP//l9Eh7UUnNFi3Pt5M1gdh92wLfNpXGC6JKCpcU9Z7WwpDmBLS8E7fI/xzAVJKTAAwCeAeAd8Z8TlFG2B/c8ZOnz/ioGxH6FT17fM/QHNHSQOHZKpSEIYgdcTOihYE+k72Hn8+NyE1fuTW2p7We/kG5bkIQe4IykgsBrAPQAuDLZra62rZKUBYNPf2D+Mi3duHl08mcr7Kn2dM/iI9+ZzeOnwxmQFIiFibRV9R+8rBPGFkV+kZ8736ZcOH5uLfrTbEdP8/U8skrC2WBiOMxOSnSiKrwK/ZxDYQWReiTKsROILLCKEVDIl9g5q/dVrdqUB7ImnAlRdgbcxauV6MusHXXzwDgPxxWPfnqKNVwAUmq9xQ3zd47K01ECvp5zlrdl+ps1Fmr+3wVManEaxC53M9e7elmCJyJcCI4yl2TM1b07EFbVzEEfvHs1qYW+HL2rQkW+nno2AlfJRTj4MrlWwIL/OjhLRjo7qgbJTTQ3YHFs1sxpGwM/vzzhmBtDJlEmwW5a3JEliJEGiWO9L9FIagLJ0nXTRj3YN5CQPOI3DUFoVGBD/pj85O7PSgS9/o8unphoGs/f+22xEQ0iMBL3LOBRL4JCFuXtHPmBE9BDppCQD/24JSuvZ8InKQG3oPkvNdnnh0k8gUlzh5zFhNfFZWkM2FWY9GG7b5TO2Qh8ke8ggZeCwThiPtAd4dcIgWiFGqYJn6e3FRgJJuoJ18Q9OMqLp0zJ+DjPXsiS5IWFL/FTFRgJJuoJ58jqgm5BL74pJl6+O98DADrO5hd1JPPGfoxiaSpF8yZZEFxERyJvGgqqkUG6eYZHlVyyjZy14imoa2rt+oAYhYiWGqRVgGRK5dvqbleN8fso568KBxxTOJKkzST0OU1q6l4BYm8KAxx13lNgyxnGZUvPh9I5EUuyVoeHy93T6OuDL8uJD91Y+Pgvsd/lcp5RTAk8iJXhE1xGyfVxLitqxfjRw0LFT8eRODTCq/M6hOGOBuJvMg0Pf2DuPmbuxC3aziuAcRDx04EEvugGSjTjJ8X+SA2kSd5K4AlAI64iz5mZrWH6kXTkbYfPanokJLYA8DQIcS/vO31Z6WeCFMEZu7kMVGa6Mn4UcNqPjmpuHb2iS2fvCvyvzGzf/G7j/LJNwdp+9OjFva0wi+TukHVa9+IFp6pcCXSQfnkRWbwWzw7StIoEh4nWSuZ+NIpw5XLt0joM0rcIv9hku8GsBPAzWb268oNSC4FsBQAWlsVklU0whaqbpQkhT3JdMBp3LCmjhtZd5D1pVMm101GachdQ/LHAF7jsWo5gB0AnoGT+uKTAC42s/fWOp7cNfknrYlIWShSEfcNLc3ZpX7j9TUDNh1quWsSqfFKsg3AD8zs6lrbSeTzQdqDpSXChifGSRzRQFlxz/h5WkkzpLOZScUnT/JiMzvovr0OwINxnUvERxo+9Fpkocdei/KSidNXbm04B3yWxhP8uG2eO34KK3r2ZMZmEW90zdcAzIDjrhkA8Ndlou+JevLZImmBL3Iv0G9EUdZvYn7HHlSwPVlSd9f4RSKfHmmGNWZd2MTZ+BH6C88/D7tW/kkC1ghAIZSiDknGeSumOv/4iSY6+uLLCVkj6qF88k1MT/9gYgI/d/IYDHR3SOALgqJo8oN68k1KEqGO8ssWm9HDW1IrLi78I5FvUqISePnTm5c/nzkhU+mehTcS+SZk+sqtvrcdSmDfGj2ai7PJYspn4Y1Evgnx+4gtgRdeZL0erjgbibzwJO8Da15ClMUZsnkhy2UIRW0k8uIciijwgJPTfVJXbyZSBETFip492LTjQCST1ioHyhvJxTN13MgILBJRIJEXZ1H04swGx5+c5x59FOkSvFi2eVdkA/IajM8OEnlxFs2Qc+TQsRO5SoublYRwfsn7k2DR0GSoJqTaj7CZfpyfvvuxtE3wxazVfbkR+NKEN5Et1JNvUpr9xzh49MW0TahLnqJYspQtU5yNevKicPi9gWVZRLNsWwnCGawd6O6QwGcYibwoJH6FftGG7TFbEpwrl29J24S6zJ08Bk90d+RmXKOZkbtGFJaB7g5MuaUXJ2tEAWbN3z195daGSgj6nQvQ0z+Imzbvwmmfxx1CYO3blYsojyifvCg89VwfWZrZG9RNo9xBAlA+eREBXmF8eRGYoUTN3nytdUkyf+02X9sVuYKWiJ6GfPIk30byIZKnSbZXrLuF5D6Sj5F8S2NmijSpFqe99/DzmJSDAcKs9NLr4SdtwEB3hwReBKLRgdcHAfwFgHvKF5K8CsA7ALwOwAIAnyfZ0uC5RErU8lsb8hEJMnp4/r9+666fkbYJIoc0JPJm9oiZec0quRbAN8zsuJk9AWAfgDc0ci6Rbdq6etHTP5i2GVU5cdLvEGM2UQEWEZa4QignAHiy7P1T7jJRYJZt3oXLMyr2jUSsZAEJvAhLXZEn+WOSD3r8XVtrN49lnr8ykktJ7iS588iRI37tFgkyd/IY39uehiP2bV29vgcS42bW6r60TRAiNeqKvJldY2ZXe/x9r8ZuTwGYWPb+UgBPVzn+ejNrN7P2sWPHBrNeJMKmJXMwosXrvl2bvYefT92N09M/WLeCUR789VmctCXyQVzumrsAvIPkcJKTAEwFcH9M5xIJ8OjqhaHFsNSzb+vqxYqePRFbVp1FG7b7Sp2bh2iVe/c/m0k3mMg+jYZQXkfyKQBzAPSSvBsAzOwhAN8E8DCArQA+ZGYq655zdt+2IJDrxouNOw6cEfw43TnTV27N3GzWRokq17toLjTjVQSmp38wVsGZO3kMNi2ZE2rfoLnXs5Q90W9x7GbPICrOpdaMV4m8CE3e635msear3zkHEnpRTi2RVxZKEZq+m+ZhoLujYRdOGhDInMADzo3HD3mYgCaygXryIlLyIj5Z7gn7reFamTuo3pNVI24wkW3krhGJE7ffvhGyLPAl/N4s504eE3iAOUvjECIa5K4RidM5cwIGujuw7voZnjPj0mDquJG5EHjA/40oTATRxh0HEg1lFemiVMMiVjpnTjhnSr5fd0RU5DXvS5heul827jig3nyTIJEXieM1+SiuSJ289Ny92LRkTu4jmET6SORFJshD8ZE06LtpnoReNIR88kJknL6b5vkOrRSiEom8EBln/tptvmbCCuGF3DVCZBi/qQ6EqIZ68kJklBU9e2IT+DzOUhbhUE9eiAwSdw9eM1+bB/XkhcgYcfvg8xxWKoIjkRciQ6zo2eM7XHIonb8gSOCbD7lrhMgIQZK7VaZJ9jOLWALfnEjkhcgAU27xL/AjWnhOmuQ8lDAU6SB3jRAZ4GSAZLCPrl4YnyGicDRa4/VtJB8ieZpke9nyNpIvktzl/n2hcVOFEHK5iKA06q55EMBfAPiix7r9ZjajweMLIeAMsO5bI4EXwWlI5M3sEQAgs5IxXIjiIYEXjRCnT34SyX6S/07yf1XbiORSkjtJ7jxy5EiM5giRXUa0VO8oSeBFI9QVeZI/Jvmgx9+1NXY7CKDVzGYCuAnA10mO9trQzNabWbuZtY8dOzZcK4TIOY+uXniO0I9ooXzwomHqumvM7JqgBzWz4wCOu68fILkfwGsBqICrEFVQ1IyIg1jcNSTHkmxxX18OYCqAx+M4lxBCiOo0GkJ5HcmnAMwB0EvybnfVHwLYTfK/AHwbwAfMLJ5ilUIIIarSaHTNnQDu9Fj+HQDfaeTYQgghGkczXoUQosBI5IUQosDQLEDSjJgheQTAL9K2o4yLADyTthERU8Q2AcVsl9qUD7LQpsvMzDMGPVMinzVI7jSz9vpb5ocitgkoZrvUpnyQ9TbJXSOEEAVGIi+EEAVGIl+b9WkbEANFbBNQzHapTfkg022ST14IIQqMevJCCFFgJPJCCFFgJPIekPw0yUdJ7iZ5J8kLy9bdQnIfycdIviVFMwNRrVSjuy6XbQIAkgtcu/eR7ErbnrCQ/DLJwyQfLFs2hmQfyb3u/1enaWMQSE4k+TOSj7jfu791l+e2TQBAcgTJ+0n+l9uu29zlmW2XRN6bPgBXm9l0AP8N4BYAIHkVgHcAeB2ABQA+X8q2mQNKpRrvKV+Y5za5dn4OwJ8CuArADW578sjtcK5/OV0AfmJmUwH8xH2fF04CuNnMfgfAbAAfcj+bPLcJcFKov8nMXg9gBoAFJGcjw+2SyHtgZj8ys5Pu2x0ALnVfXwvgG2Z23MyeALAPwBvSsDEoZvaImT3msSq3bYJj5z4ze9zMTgD4Bpz25A4zuwdAZabWawF8xX39FQCdSdrUCGZ20Mz+n/v6GIBHAExAjtsEAObwG/ftee6fIcPtksjX570Afui+ngDgybJ1T7nL8kye25Rn2/0w3swOAo5oAhiXsj2hINkGYCaA+1CANpFsIbkLwGEAfWaW6XY1lGo4z5D8MYDXeKxabmbfc7dZDuexc1NpN4/tMxOD6qdNXrt5LMtMm+qQZ9ubApIXwEk7vszMniOr17LNC2Z2CsAMd6zuTpJXp2xSTZpW5OuVNSR5I4C3AnizvTKZ4CkAE8s2uxTA0/FYGJwwpRqR8TbVIc+2++EQyYvN7CDJi+H0HHMDyfPgCPwmM/uuuzjXbSrHzI6S3AZnLCWz7ZK7xgOSCwB8FMCfm9kLZavuAvAOksNJToJT1vD+NGyMkDy36ecAppKcRHIYnAHku1K2KUruAnCj+/pGANWexjIHnS77lwA8YmZry1bltk3AmdKmF7qvzwdwDYBHkeV2mZn+Kv7gDD4+CWCX+/eFsnXLAewH8BiAP03b1gBtug5Oz/c4gEMA7s57m1zbF8KJgNoPxy2Vuk0h23EHgIMAXnY/p/cB+G04kRp73f9j0rYzQHv+AI7rbHfZ72hhntvktms6gH63XQ8C+Li7PLPtUloDIYQoMHLXCCFEgZHICyFEgZHICyFEgZHICyFEgZHICyFEgZHICyFEgZHICyFEgfn/+lQjw1JSzE4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    embedding[:, 0],\n",
    "    embedding[:, 1],\n",
    ")\n",
    "plt.gca().set_aspect('equal', 'datalim')\n",
    "plt.title(\"UMAP projection of the circle dataset\", fontsize=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9ec400cbb0>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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URI3gUaDfzKab2XjgCmBdxTbrgD8JRg/NAV53930R9xURkRS1XCNw96Nmtgx4AOgB7nT3p83sumD9t4D1wAJgJ/DvwJ/W27fVMomIFEFSl8Mm0TSEu6+n9GUfXvat0GMHPh913yzNXLWBJ/9yfrveXkSkaS8ML0zkdQp/ZfGht461uwgiIm1V+CAQESm6QgRBIf6TIiJNKsR35K2Xz2p3EUREcqsQQbD4/KoXK4uI5NrZK7IZR1OIIBAR6URvHqt6o4XEKQiAGcuTuae3iEgnUhAAR7MJXRGRxPRPnpDYaykIRERyaMnaR+qu33jjvMTeqzBBMPesiXXXrxzZllFJREQae/i5VzN7r8IEwT3XXlR3/d2bXsqoJCIi+VKYIBARkeoUBCIiOTN9qP5IxlNO7En0/QoVBFNOHl93/ezVGzMqiYhIbY0GMiZ9x+RCBcHmFYN11+8/fCSjkoiI5EehgkBEJO+yuq1EWEtBYGYTzWyjme0I/j21yjZnmtm/mdl2M3vazP48tO4mM9tjZluDnwWtlCcJfQ3a5kRE0tTothKNhsI3o9UawRDwY3fvB34cPK90FPiCu58DzAE+b2bnhtZ/zd1nBT+pR+FVc3rTfgsRkaZEuZ6p0VD4ZrQaBIuAu4LHdwGLKzdw933u/njw+DCwHWjb7UBvXvyRhtvMXLUhg5KIiLxbu65najUIprj7Pih94QOT621sZn3A+cDm0OJlZvakmd1ZrWkptO9SMxszs7GDBw+2WOz6NH2liORRWi0aDYPAzB40s6eq/CyK80Zm9lvAvwLXu/uhYPE3gbOAWcA+4G9r7e/ua9x9wN0HJk2aFOetj7MrwoTPI1v2tPQeIiJxROmfjNKi0YxxjTZw90tqrTOz/WY21d33mdlU4ECN7d5DKQTucffvhl57f2ibtcAP4hQ+Tdfft1UT2ohIbiR9EVlYq01D64BrgsfXAN+v3MDMDPgnYLu731qxbmro6SeBp1osT2RRqliqFYhIFqJ0Eid9EVlYq0EwDAya2Q5gMHiOmZ1uZuURQHOBq4E/rDJM9BYz22ZmTwIXAze0WJ7IolSxrr9va/oFEZHCa/dNLxs2DdXj7q8AH6uyfC+wIHj8U8Bq7H91K+/fqv7JE9hx4I2626wc2ZZau5yISJQLyG67fFaqZSj0lcVRJnZod1KLSHeLMi9x2v2VhQ4CiNYBo0lrRCQNUUYKpV0bAAVBpA4Y1QpEJGlRTjBP6rFMRi8WPgiiajR/qIhIHFFOMJ9Znc3t1xQERLvALMv5Q0Wku0WpDTSaPyVJCoJAlOsKdGdSEUlClNpAo/lTkqQgCEQdIqqLzESkFTOWNz6hzPouyQqCkChVMV1kJiLNWrL2EY42Hi2a+bVLCoKQqFUxNRGJSDOi9DVm2TdQpiCoEKXjGNoznZyIdK6oJ5BZ9g2UKQiq6J88oeE2bx5z9ReISCTTI4ZA1BPRpCkIqohy6wlQf4GINLZyZBsRugUYV/WObNlQENQQNZnVXyAi9US9M8HOr7anNgAKgrqiDuFSGIhINVH7EtvVJFSmIKgjzhAudR6LSNiM5aOR7iya5sxjUbUUBGY20cw2mtmO4N+qk8+b2a5gApqtZjYWd/92iprUbx5z3aVURIBSK0GU6wUg3ZnHomq1RjAE/Njd+4EfB89rudjdZ7n7QJP7t03U28DqLqUiEuXK4bJ2NwmVtRoEi4C7gsd3AYsz3j8Ti8+fxkk90br01V8gUlwzV22IXBPISwhA60Ewxd33AQT/Tq6xnQM/MrPHzGxpE/tjZkvNbMzMxg4ePNhiseOLcztYhYFI8Qze+hCH3joWadssJpuJo2EQmNmDZvZUlZ9FMd5nrrtfAFwKfN7MPhq3oO6+xt0H3H1g0qRJcXdPRJwEVxiIFMfKkW0N5z8vO+XEnkwmm4mjYRC4+yXu/rtVfr4P7DezqQDBvwdqvMbe4N8DwPeAC4NVkfbPE4WBiIQtWftIrP7BPHQOV2q1aWgdcE3w+Brg+5UbmNkEMzu5/Bj4OPBU1P3zSGEgIlAKgTiTVuWpXyCs1SAYBgbNbAcwGDzHzE43s/LA+inAT83sCeDnwKi7b6i3fyeI08anMBDpPjNXbeiKEAAw94hd3DkyMDDgY2NjjTdMWbecDYhIPDOWR79OAPLzt29mj1UM4Qd0ZXFL7rn2okh3Ki1TzUCk881evbEjQ6AeBUGLNt44L9ZEEn1Do8xevTHFEolIWgZvfYj9h49E3r4TQgAUBInYvGIwVs1g/+EjCgORDnP2ivWRh4ganRMCoCBIzMYb58WacFphINI5+oai3UAOStcJvNBBIQAKgkTdvPgjsZqJ9h8+on4DkRxbObIt1t/oST2Wy+sEGlEQJCxuMxGUzjaWrH0kpRKJSDNmrtoQ+0aScW5FkycKghRsvHFe7PbBh597lZmrNjTeUERSN2P5aOT7BpV1Up9AJQVBiuIeGIfeOqamIpE2mx5jLoGyTg4BUBCkrpkDpG9oVJPciGRsZMse+oZGI000X3bKiT0dHwKgIMhEMwfK3ZteUu1AJCN9Q6Ncf9/WWPtcNae3IzuGq1EQZGTX8MJYw0vLFAYi6Yk7Kqhs1/DCWHOa553uNdQGzRx4U04ez+YVgymURqSYZq/eGOsq4bJObgrSvYZypJkDSdcciCRjydpH6BsajR0C46yzQ6AeBUGb7BpeSLRZkN+tb2iUs1esb7yhiBynb2g01h2Dy+aeNZGdX+3OEAAFQVu90GS/wZvHXLUDkRgGb32o6b+ZXcMLuefaixIuUb6ojyAnpscctlZ2yok9XTNyQSRpI1v2xB4NFNZtTUGp9BGY2UQz22hmO4J/T62yzYfMbGvo55CZXR+su8nM9oTWdeb12QlotnZQvghtZMueFEol0rlmrtrQdAjsGl7YdSFQT0s1AjO7BXjV3YfNbAg41d2/VGf7HmAPMNvdXzSzm4Bfu/vfxHnfbqwRhLXS7HPVnN6uGtYmEtfKkW2x7xFU1u017LRGDS0C7goe3wUsbrD9x4Dn3P3FFt+3qzV7zQGULkTr/2+qIUjxzFy1gb6h0aZDoJsuEIur1RrB/3X394eev+buxzUPhdbfCTzu7n8fPL8J+AxwCBgDvuDur9XYdymwFKC3t/f3XnyxGFnSaqdwkaq3Ukxx5w6v1O21gLBaNYKGQWBmDwIfrLJqBXBX1CAws/HAXuDD7r4/WDYF+BXgwFeAqe7+Z43+M93eNFRp5qoNse+EGDbO6Oqhb1JMrXYEG3TcBDKtqhUE4xrt6O6X1HnR/WY21d33mdlU4ECdl7qUUm1gf+i133lsZmuBHzQqTxGVz1YGb30o8lR5YUe9VLM4cdwJ/PV/nsni86clXUSRzDR7RXDYbZfP0t9BSKtNQ/8deCXUWTzR3f9rjW3vBR5w9/8RWjbV3fcFj2+g1Il8RaP3LVqNoNLZK9ZHnjavliJVh6U7tNIJXFb0477ppqEGL/oB4H6gF3gJuMzdXzWz04E73H1BsN17gZeB33H310P7/wswi1LT0C7gv5SDoZ6iBwG0Xi0uK/ofhuRfq02jUJpCslNnD0tSKkHQLgqC30iimgy6qZ3kT1LHtoZU/4aCoMslUW0uU/uptEuz/WDV9E+ewMYb5yXyWt1CQVAQSf4hqTotWUmi36tMJzK1KQgKJsmb0hnwNf1xScJmLI8/N3A9agJqTEFQUEm1s5bNPWti19+JUdKTZBNmmY7J6BQEBZdkk1GZOpgliqRGuFVSDSA+BYEArV+OX4s65iQsjTP/Mh1rzVMQyLuMbNnDjfdv5e0Ufv2qqhdXGjVPUAdwUhQEUlNaf7xlCobulXSHbyUdO8lSEEhDabXlhmlIamdLq2kxTMdIehQEEksWf/CgW1zkXRYnB6DjICsKAmla2tX/sPE9xi2fOk/twW2SZidvNer4zZaCQFqW1dlhJQ0TTMfIlj3ceN9W3s74fXX23z4KAknc9KFR2nn0aCRJdFmf6VfS5Ej5oCCQVGXZfFRPEWedCmtXra2aov8u8khBIJlJ4v7xaRl3gvE3l3VuH0S7z+wb0XDPfFMQSNvkpbbQjLTbs/N0Bt8Mtfd3lrRmKLsMuAk4B7jQ3at+O5vZfODrQA+lmcuGg+UTgfuAPkozlP2xu7/W6H0VBJ1rZMsebrhva1v7FqR5+uLvbGkFwTnA28A/Al+sFgRm1gM8CwwCu4FHgSvd/RdmdgvwamjO41Pd/UuN3ldB0F3y3JRUdBqx1V1qBcG4Vl7U3bcHL15vswuBne7+fLDtvcAi4BfBv/OC7e4CHgIaBoF0l2pnmGnf9kKOp7vJFldLQRDRNEoT15ftBmYHj6eUJ6t3931mNrnWi5jZUmApQG9vb0pFlbyodpGRag7J0YVcEtYwCMzsQeCDVVatcPfvR3iPatWF2O1R7r4GWAOlpqG4+0vnq9U2ndXtMDqRRvFIFA2DwN0vafE9dgNnhp6fAewNHu83s6lBbWAqcKDF95ICavRFN7JlD1+4fysJTYmbK7qoTpKQRdPQo0C/mU0H9gBXAJ8O1q0DrgGGg3+j1DBEYll8/rTIX5btrl2oyUbaoaUgMLNPAn8HTAJGzWyru/9HMzud0jDRBe5+1MyWAQ9QGj56p7s/HbzEMHC/mX0WeAm4rJXyiLRKzShSRLqgTESkIGoNHz2hHYUREZH8UBCIiBScgkBEpOAUBCIiBdeRncVmdhB4scndTwN+lWBxkqJyxaNyxaNyxZPXckFrZfttd59UubAjg6AVZjZWrde83VSueFSueFSuePJaLkinbGoaEhEpOAWBiEjBFTEI1rS7ADWoXPGoXPGoXPHktVyQQtkK10cgIiLvVsQagYiIhCgIREQKriuDwMwuM7OnzextM6s5zMrM5pvZL81sZzBncnn5RDPbaGY7gn9PTahcDV/XzD5kZltDP4fM7Ppg3U1mtie0bkFW5Qq222Vm24L3Hou7fxrlMrMzzezfzGx78Dv/89C6RD+vWsdLaL2Z2TeC9U+a2QVR9025XEuC8jxpZj8zs/NC66r+TjMq1zwzez30+/ly1H1TLtdfhMr0lJkdM7OJwbpUPi8zu9PMDpjZUzXWp3tsuXvX/QDnAB+iNAfyQI1teoDngN8BxgNPAOcG624BhoLHQ8BfJ1SuWK8blPH/ULoIBOAm4IspfF6RygXsAk5r9f+VZLmAqcAFweOTgWdDv8fEPq96x0tomwXADynNyjcH2Bx135TL9fvAqcHjS8vlqvc7zahc84AfNLNvmuWq2P4TwP/K4PP6KHAB8FSN9akeW11ZI3D37e7+ywabXQjsdPfn3f0IcC+wKFi3CLgreHwXsDihosV93Y8Bz7l7s1dRR9Xq/7dtn5e773P3x4PHh4HtlObJTlq94yVc3m97ySbg/VaaeS/KvqmVy91/5u6vBU83UZolMG2t/J/b+nlVuBL4TkLvXZO7/wSoNyNSqsdWVwZBRNOAl0PPd/ObL5Ap7r4PSl80wOSE3jPu617B8QfhsqBqeGdSTTAxyuXAj8zsMTNb2sT+aZULADPrA84HNocWJ/V51TteGm0TZd80yxX2WUpnlmW1fqdZlesiM3vCzH5oZh+OuW+a5cLM3gvMB/41tDitz6uRVI+tLKaqTIWZPQh8sMqqFe4eZcpLq7Ks5bG09coV83XGA38ELA8t/ibwFUrl/Arwt8CfZViuue6+18wmAxvN7JngTKZpCX5ev0XpD/Z6dz8ULG7686r2FlWWVR4vtbZJ5Vhr8J7Hb2h2MaUg+A+hxYn/TmOU63FKzZ6/DvpvRoD+iPumWa6yTwAPu3v4TD2tz6uRVI+tjg0Cd7+kxZfYDZwZen4GsDd4vN/Mprr7vqD6dSCJcplZnNe9FHjc3feHXvudx2a2FvhBluVy973BvwfM7HuUqqU/oc2fl5m9h1II3OPu3w29dtOfVxX1jpdG24yPsG+a5cLMZgJ3AJe6+yvl5XV+p6mXKxTYuPt6M/sHMzstyr5plivkuBp5ip9XI6keW0VuGnoU6Dez6cHZ9xXAumDdOuCa4PE1QJQaRhRxXve4tsngy7Dsk0DVEQZplMvMJpjZyeXHwMdD79+2z8vMDPgnYLu731qxLsnPq97xEi7vnwQjPOYArwdNWlH2Ta1cZtYLfBe42t2fDS2v9zvNolwfDH5/mNmFlL6PXomyb5rlCsrzPuAPCB1zKX9ejaR7bCXd+52HH0p/9LuBt4D9wAPB8tOB9aHtFlAaZfIcpSal8vIPAD8GdgT/TkyoXFVft0q53kvpD+J9Ffv/C7ANeDL4ZU/NqlyURiU8Efw8nZfPi1IzhwefydbgZ0Ean1e14wW4DrgueGzA7cH6bYRGrNU61hL6nBqV6w7gtdDnM9bod5pRuZYF7/sEpU7s38/D5xU8/wxwb8V+qX1elE769gH/j9J312ezPLZ0iwkRkYIrctOQiIigIBARKTwFgYhIwSkIREQKTkEgIlJwCgIRkYJTEIiIFNz/BzW1zE9fTFNDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    circle_data[:, 0],\n",
    "    circle_data[:, 1],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "gauBall_data = gauBall[\n",
    "    [\n",
    "        \"col1\",\n",
    "        \"col2\",\n",
    "    ]\n",
    "].values\n",
    "scaled_gauBall_data = StandardScaler().fit_transform(gauBall_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "embedding = reducer.fit_transform(gauBall)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'UMAP projection of the gauBall dataset')"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    embedding[:, 0],\n",
    "    embedding[:, 1],\n",
    ")\n",
    "plt.gca().set_aspect('equal', 'datalim')\n",
    "plt.title(\"UMAP projection of the gauBall dataset\", fontsize=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9ec3530af0>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    gauBall_data[:, 0],\n",
    "    gauBall_data[:, 1],\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "recHole_data = recHole[\n",
    "    [\n",
    "        \"col1\",\n",
    "        \"col2\",\n",
    "    ]\n",
    "].values\n",
    "scaled_recHole_data = StandardScaler().fit_transform(recHole_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "embedding = reducer.fit_transform(recHole)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'UMAP projection of the recHole dataset')"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    embedding[:, 0],\n",
    "    embedding[:, 1],\n",
    ")\n",
    "plt.gca().set_aspect('equal', 'datalim')\n",
    "plt.title(\"UMAP projection of the recHole dataset\", fontsize=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'(slice(None, None, None), 0)' is an invalid key",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-64-59bf6fce072f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m plt.scatter(\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0mrecHole\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m     \u001b[0mrecHole\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m )\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.8/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   2900\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnlevels\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2901\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_getitem_multilevel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2902\u001b[0;31m             \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2903\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mis_integer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2904\u001b[0m                 \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.8/site-packages/pandas/core/indexes/base.py\u001b[0m in \u001b[0;36mget_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m   2893\u001b[0m             \u001b[0mcasted_key\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_maybe_cast_indexer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2894\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2895\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcasted_key\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2896\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0merr\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2897\u001b[0m                 \u001b[0;32mraise\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0merr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: '(slice(None, None, None), 0)' is an invalid key"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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