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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Breakout: EigenFaces\n",
      "\n",
      "In this breakout, we'll be using *Principal Component Analysis* to explore how it interacts with the *faces* dataset that we saw earlier."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy import stats\n",
      "\n",
      "# use seaborn plotting defaults\n",
      "import seaborn as sns; sns.set()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We'll use this code to load the data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.datasets import fetch_lfw_people\n",
      "faces = fetch_lfw_people(min_faces_per_person=70, resize=0.4)\n",
      "\n",
      "X, y = faces.data, faces.target"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 1. Compute a PCA of the data\n",
      "\n",
      "- Compute a Principal Component Analysis of the data, using all components\n",
      "- Plot the cumulative explained variance ratio. How many components do we need to recover 90% of the variance?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 2. Plot the \"eigenfaces\"\n",
      "\n",
      "The mean of the data (found in the ``mean_`` attribute) and each component of the data (found in the rows of the ``components_`` attribute) can be reshaped and interpreted as an image.\n",
      "\n",
      "- Display the mean face using ``plt.imshow``\n",
      "- Display the first few \"eigenfaces\" (given by the rows of the ``components_`` matrix\n",
      "\n",
      "You'll have to play around with the colormap and grid settings to make this look OK"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 3. Plot the reconstructed faces\n",
      "\n",
      "For several faces, plot the true image plus the reconstruction (computed using ``inverse_transform``) for several different values of ``n_components``. (you might even use IPython's interactive functions to make this exploration easier).\n",
      "\n",
      "Does the 90% variance choice seem to correspond to a good visual representation of each picture?\n",
      "\n",
      "**Note:** As you experiment with this, you may want to use ``RandomizedPCA`` rather than ``PCA`` for this task. ``RandomizedPCA`` is an approximate method with the same interface as ``PCA``, but operates much more quickly."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}