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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",
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    "data = pd.DataFrame(data, columns=[\"x1\", \"x2\"])"
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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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       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
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       "    </tr>\n",
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       "      <td>-3.123062</td>\n",
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       "    </tr>\n",
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       "    </tr>\n",
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       "      <th>2</th>\n",
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       "      <td>-2.582416</td>\n",
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       "    </tr>\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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       "    </tr>\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",
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       "      <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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       "           x1        x2\n",
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       "0   -3.123062 -3.267402\n",
       "1   -2.775958 -0.929101\n",
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       "4   -0.041529  0.381166\n",
       "..        ...       ...\n",
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       "496  1.197165  1.665481\n",
       "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": 5,
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   "id": "e63b38c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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Duplicated other notebooks for new topics.
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Added first draft on PCA.  
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       "<Figure size 576x576 with 1 Axes>"
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Duplicated other notebooks for new topics.
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      ]
     },
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      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 8))\n",
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    "data.plot.scatter(x=\"x1\", y=\"x2\", alpha=0.3, ax=ax)\n",
    "ax.set(xlabel=\"$x_1$\", ylabel=r\"$x_2$\", title=\"\")\n",
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    "plt.show()"
   ]
  },
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  {
   "cell_type": "markdown",
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   "id": "bba01cd6",
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   "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",
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    "\n",
    "In Principal Component Analysis, we set ourselves the objective of maximizing the variance of the data in our new representation. That is, imagine our new representation is given by $p_1$ and $p_2$ and we define them such that $p$ is a linear combination of $x$. The criteria used to find how to make such a linear combination shall be that the variance of $p_1$ is maximal, when we want to find out how to combine $x_1$ and $x_2$ to obtain $p_1$. This can be similarly done for $p_2$ and any other component. Instead of finding $p$ directly for each sample, we will find the direction $u_1$ on which we should project $x$ using $u_1^T x$ to obtain the new space. As we are only interested in the direction of $u_1$, we define it as normalized vector, so $u_1^T u_1 = 1$.\n",
    "\n",
    "The mean data value is $\\overline{x} = \\frac{1}{N} \\sum_k x^{(k)}$, where $x^{(k)}$ refers to the vector $(x_1, x_2)$ for the $k$-th sample point. The mean of the projected data in this new dimension $u_1$ is $u_1^T \\overline{x}$. The variance of the projected data in the direction $u_1$ is:\n",
    "\n",
    "$\\frac{1}{N}\\sum_k\\left(u_1^T x^{(k)} - u_1^T \\overline{x}\\right) = u_1^T S u_1$,\n",
    "\n",
    "where $S = \\frac{1}{N}\\left(x^{(k)} - \\overline{x}\\right)\\left(x^{x(k)} - \\overline{x}\\right)^T$ is the covariance matrix of the data.\n",
    "\n",
    "We maximize the variance of the data projected in the direction $u_1$, while imposing a restriction on the maximization procedure, such that $u_1$ is normalized to 1. This can be done by maximizing the following function:\n",
    "\n",
    "$u_1^T S u_1 + \\lambda_1 (1 - u_1^T u_1)$,\n",
    "\n",
    "where $\\lambda_1$ is a Lagrange multiplier used to enforce the condition that $u_1^T u_1$ is 1.\n",
    "\n",
    "Calculating the derivative relative to $u_1$ and setting it to zero to find the maximum we see that:\n",
    "\n",
    "$S u_1 = \\lambda_1 u_1$,\n",
    "\n",
    "which is an eigenvalue problem! That is, the direction $u_1$, which maximizes the variance of the projected data is the eigenvector of the covariance matrix $S$. Moreover, if we multiply this equation by $u_1^T$ on the left and use $u_1^T u_1 = 1$, we obtain $\\lambda_1 = u_1^T S u_1$. That is, $\\lambda_1$ is the variance of the data projected in the direction $u_1$.\n",
    "\n",
    "This gives a simple recipe to find the directions with largest variance: we find the eigenvectors of the covariance matrix $S$ which have highest eigenvalues. By sorting the eigenvalues, we can easily choose which of the directions of the new representations are more important to analyse. We can also discard directions that have low eigenvalues, as they contribute little to the variations observed in the data.\n",
    "\n",
    "Naturally, we do not need to write the code to perform all those steps, as scikit-learn implements them for us:"
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   ]
  },
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  {
   "cell_type": "code",
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   "execution_count": 6,
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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": 7,
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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": 7,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
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    "pca.fit(data.loc[:, [\"x1\", \"x2\"]])"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 8,
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   "id": "cc8fc1f1",
   "metadata": {},
   "outputs": [],
   "source": [
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    "data_t = pca.transform(data.loc[:, [\"x1\", \"x2\"]])"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 10,
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   "id": "88982b21",
   "metadata": {},
   "outputs": [],
   "source": [
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    "data.loc[:, \"pca1\"] = data_t[:, 0]\n",
    "data.loc[:, \"pca2\"] = data_t[:, 1]"
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   ]
  },
  {
   "cell_type": "markdown",
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   "id": "3ac27316",
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   "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": 11,
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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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    "data.plot.scatter(x=\"pca1\", y=\"pca2\", alpha=0.3, ax=ax[0])\n",
    "data.plot.scatter(x=\"x1\", y=\"x2\", alpha=0.3, ax=ax[1])\n",
    "ax[0].set(xlabel=\"PCA component 1\", ylabel=r\"PCA component 2\", title=\"PCA representation\")\n",
    "ax[1].set(xlabel=\"$x_1$\", ylabel=r\"$x_2$\", title=\"Original data\")\n",
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    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
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   "id": "54e538c6",
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   "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",
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   "execution_count": 12,
   "id": "fa5ebbce",
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
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    "plt.barh([\"PCA 1\", \"PCA 2\"], pca.explained_variance_)\n",
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    "plt.gca().set(xlabel=\"Variance\", ylabel=\"Component\", title=\"Explained variance\")\n",
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    "plt.show()"
   ]
  },
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  {
   "cell_type": "markdown",
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   "id": "ff6b13e3",
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   "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": "markdown",
   "id": "7bcb1e2c",
   "metadata": {},
   "source": [
    "## Other representation learning methods\n",
    "\n",
    "While PCA is a great method for both data visualization and choosing a latent space to condense the information contained in the data, there are many other available, which differ on the assumptions made. Here are some of them and easy-to-read and practical references on how to use them and which assumptions they entail.\n",
    "\n",
    "  * Kernel PCA: While PCA does a great job at finding the directions where most of the variance is, it focuses on making only *linear* combinations of the features to find the new representation directions. A straightforward method to generalise this idea to non-linear transformations is to apply a non-linear transformation to the data features and after that apply PCA. This is similar to what Kernel PCA does, generalizing the PCA idea. Of course, a non-linearity transformation needs to be chosen for this and this adds extra assumptions in the model. Some more on this can be read here: https://scikit-learn.org/stable/modules/decomposition.html#kernel-pca\n",
    "  \n",
    "  * Independent Component Analysis: PCA  looks for the direction containing most of the variance, but this is not always the optimal representation of the data for all goals. In some cases, independence is much more important than decorrelation and this is where the Independent Component Analysis comes in. The ICA also assumes that the new representation can be built from a linear combination of the existing data, but it assumes additionally each observed feature comes from a linear combination of independent latent representations we want to discover. Since independence is a very strong requirement, it is imposed through various different proxy methods. One set of methods focuses on reducing the mutual information (as defined in statistics) between the new features, while an alternative imposes non-Gaussianity requirements on the underlying latent features to be discovered. Since Gaussians do not have statistical moments above the second-order moment (covariance), one can require for example, the fourth order statistical moment (kurtosis) to be maximized in the new representation. More on the scikit-learn implementation can be found here: https://scikit-learn.org/stable/modules/decomposition.html#ica .\n",
    "  \n",
    "  * t-SNE embedding: If the objective is only to visualize the data, there are many alternative solutions which focus on reducing the dimensionality of the data into a 2D representation. The t-SNE method assumes that a Gaussian probability can be used to model similarity between data points in N dimensions and that one should maintain that similarity measure when projecting the data in two dimensions, assuming however that the 2D data points' similarity can be represented with a t-Student distribution. Full details on the method can be seen here: https://jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf It can be easily tried in scikit-learn following the procedure here: https://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html"
   ]
  },
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  {
   "cell_type": "code",
   "execution_count": null,
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   "id": "b189d3af",
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   "metadata": {},
   "outputs": [],
   "source": []
  }
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