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{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6a764d92",
   "metadata": {},
   "source": [
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    "# Representation Learning\n",
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    "\n",
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    "Often it is very hard either to find similarities within data or even to classify data as belonging to different labels when the data contains so many features. One particular example are images which may contain millions of pixels. Even low-dimensional data may not be easy to visualize in a 2D plane, so bringing the dominant effects in a 2D plane for visualization is in itself a very helpful starting point.\n",
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    "\n",
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    "There are different methods to obtain another view of the data, by performing linear or even non-linear combinations of the data features. The price being paid by such methods is that the new representation of the data may not be that straightforward to digest, loosing therefore some of its scientific interpretation. On the other hand, if one understands the assumptions made in such methods, one can easily imagine the mathematical process required to transform to and from this new view and gain insight from the new view without loosing track of the scientific background.\n",
    "\n",
    "We are going to go through a few methods of obtaining an alternative view of the data here and what their assumptions might be."
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "fce4d8e8",
   "metadata": {},
   "source": [
    "We start by loading the necessary Python modules. If you have not yet installed them, run the following cell to install them with pip:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "44ca341e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (1.19.2)\n",
      "Requirement already satisfied: scikit-learn in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (0.24.2)\n",
      "Requirement already satisfied: pandas in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (1.3.0)\n",
      "Requirement already satisfied: matplotlib in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (3.4.2)\n",
      "Requirement already satisfied: joblib>=0.11 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from scikit-learn) (1.0.1)\n",
      "Requirement already satisfied: scipy>=0.19.1 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from scikit-learn) (1.6.2)\n",
      "Requirement already satisfied: threadpoolctl>=2.0.0 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from scikit-learn) (2.2.0)\n",
      "Requirement already satisfied: python-dateutil>=2.7.3 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from pandas) (2.8.2)\n",
      "Requirement already satisfied: pytz>=2017.3 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from pandas) (2021.1)\n",
      "Requirement already satisfied: six>=1.5 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from python-dateutil>=2.7.3->pandas) (1.16.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from matplotlib) (1.3.1)\n",
      "Requirement already satisfied: pillow>=6.2.0 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from matplotlib) (8.3.1)\n",
      "Requirement already satisfied: pyparsing>=2.2.1 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from matplotlib) (2.4.7)\n",
      "Requirement already satisfied: cycler>=0.10 in /home/danilo/miniconda3/envs/mlmkl/lib/python3.7/site-packages (from matplotlib) (0.10.0)\n"
     ]
    }
   ],
   "source": [
    "!pip install numpy scikit-learn pandas matplotlib"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 1,
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   "id": "300cf8d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
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    "from sklearn.decomposition import PCA"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ecd6a69",
   "metadata": {},
   "source": [
    "Let's generate the fake data now to have something to cluster."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 2,
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   "id": "4959a292",
   "metadata": {},
   "outputs": [],
   "source": [
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    "rng = np.random.RandomState(0)\n",
    "n_samples = 500\n",
    "cov = [[3, 3], [3, 4]]\n",
    "data = rng.multivariate_normal(mean=[0, 0], cov=cov, size=n_samples)\n",
    "data = pd.DataFrame(data, columns=[\"x\", \"y\"])"
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   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8295e8a",
   "metadata": {},
   "source": [
    "Let's print out the dataset read first."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 3,
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   "id": "024fb65a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>-3.123062</td>\n",
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       "    </tr>\n",
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       "      <td>-2.775958</td>\n",
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       "    </tr>\n",
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       "      <td>-2.582416</td>\n",
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       "    </tr>\n",
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       "      <th>3</th>\n",
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       "      <td>-1.492453</td>\n",
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       "    </tr>\n",
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       "      <th>4</th>\n",
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       "      <td>-0.041529</td>\n",
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       "    </tr>\n",
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       "      <th>495</th>\n",
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       "    </tr>\n",
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       "      <th>496</th>\n",
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       "    </tr>\n",
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       "      <th>497</th>\n",
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       "    </tr>\n",
       "    <tr>\n",
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       "      <th>498</th>\n",
       "      <td>0.279317</td>\n",
       "      <td>0.428408</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
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       "      <th>499</th>\n",
       "      <td>2.082251</td>\n",
       "      <td>2.082815</td>\n",
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       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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       "<p>500 rows × 2 columns</p>\n",
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       "</div>"
      ],
      "text/plain": [
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       "            x         y\n",
       "0   -3.123062 -3.267402\n",
       "1   -2.775958 -0.929101\n",
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       "4   -0.041529  0.381166\n",
       "..        ...       ...\n",
       "495 -0.821492 -0.782416\n",
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       "497 -0.691309 -0.383494\n",
       "498  0.279317  0.428408\n",
       "499  2.082251  2.082815\n",
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       "\n",
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       "[500 rows x 2 columns]"
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      ]
     },
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     "execution_count": 3,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c178424",
   "metadata": {},
   "source": [
    "We can plot this fairly easily using Matplotlib."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 4,
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   "id": "e63b38c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
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       "<Figure size 576x576 with 1 Axes>"
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      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
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    "data.plot.scatter(x=\"x\", y=\"y\", alpha=0.3, ax=ax)\n",
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    "ax.set(xlabel=\"x\", ylabel=r\"y\", title=\"\")\n",
    "plt.show()"
   ]
  },
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  {
   "cell_type": "markdown",
   "id": "8312f0bc",
   "metadata": {},
   "source": [
    "Clearly there is a strong correlation in this data. One could almost predict $y$ using $x$ alone by fitting a line in the $xy$-plane. Therefore, it may be easier to provide a representation on which only one variable is present but retaining the maximum information possible. This is possible using several methods, which rely on several underlying assumptions. Let us start with Principal Component Analysis.\n",
    "\n"
   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 5,
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   "id": "0837b3ff",
   "metadata": {},
   "outputs": [],
   "source": [
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    "pca = PCA(n_components=2)"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 6,
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   "id": "8798f857",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "PCA(n_components=2)"
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      ]
     },
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     "execution_count": 6,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "pca.fit(data.loc[:, [\"x\", \"y\"]])"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 7,
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   "id": "cc8fc1f1",
   "metadata": {},
   "outputs": [],
   "source": [
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    "data_t = pca.transform(data.loc[:, [\"x\", \"y\"]])"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 8,
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   "id": "88982b21",
   "metadata": {},
   "outputs": [],
   "source": [
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    "data.loc[:, \"pca_0\"] = data_t[:, 0]\n",
    "data.loc[:, \"pca_1\"] = data_t[:, 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ec59e4a",
   "metadata": {},
   "source": [
    "We can start by plotting how the data looks like after this transformation."
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 12,
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   "id": "333581b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
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       "<Figure size 1152x1152 with 2 Axes>"
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      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(16, 16), ncols=2)\n",
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Added first draft on PCA.  
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    "data.plot.scatter(x=\"pca_0\", y=\"pca_1\", alpha=0.3, ax=ax[0])\n",
    "data.plot.scatter(x=\"x\", y=\"y\", alpha=0.3, ax=ax[1])\n",
    "ax[0].set(xlabel=\"PCA component 0\", ylabel=r\"PCA component 1\", title=\"PCA representation\")\n",
    "ax[1].set(xlabel=\"x\", ylabel=r\"y\", title=\"Original data\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d56d094",
   "metadata": {},
   "source": [
    "It is interesting to understand how many PCA components are necessary to explain the variance of the data. This is easily obtainable from the PCA object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c175e7be",
   "metadata": {},
   "outputs": [
    {
     "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.barh([\"PCA 0\", \"PCA 1\"], pca.explained_variance_)\n",
    "plt.gca().set(xlabel=\"Variance\", ylabel=\"Component\", title=\"Explained variance\")\n",
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    "plt.show()"
   ]
  },
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  {
   "cell_type": "markdown",
   "id": "273619cf",
   "metadata": {},
   "source": [
    "Clearly the zeroth PCA component holds most of the variance and we could therefore use this component to closely determine where a data sample point should be if we dropped the other component. This is equivalent to fitting a line and using the projection of the point in the line to characterize the data, instead of using the two coordinates.\n",
    "\n",
    "While this may seem superfluous in this simple case, if one has hundreds of variables, PCA provides a simple and almost automatic way to reduce the amount of features being examined, by concentrating most of the variance in a few variables. Which variables to choose, can be decided from the `explained_variance_` attribute."
   ]
  },
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  {
   "cell_type": "code",
   "execution_count": null,
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   "id": "04ed9567",
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   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}

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