{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learning (ML) to Predict the Stability of Planetary Systems\n",
    "One key question planetary scientists strive to understand is the longterm stability of exoplanetary systems. That is, they would like to know whether, over billions of orbits, planets will collide or be ejected from the system. Due to the [chaotic](https://en.wikipedia.org/wiki/Chaos_theory) nature of planetary systems, the \"answer\" of whether a particular planetary system is longterm stable can only be explored statistically. For example, [Laskar & Gastineau (2009)](https://www.nature.com/articles/nature08096) researched the longterm stability of the Solar System by performing 2,501 N-body simulations, each 5 billion years in length, and found that 1% of solutions lead to a large unstable increase in Mercury’s eccentricity. However, this study would have taken roughly **200 years** to complete on a standard workstation (they had access to a very large computing cluster), motivating the exploration of other methods to speed up the process. \n",
    "\n",
    "One such method is to use machine learning to predict the longterm behaviour of a planetary system based off its initial conditions. Once the model is trained, it can take as little as a second to generate new predictions, arriving at an answer quickly. Such a method is described and presented in [Tamayo, Silburt, et al. (2016)](https://arxiv.org/abs/1610.05359). In this notebook, we will explore a simplified version of this work, using a dataset of 25,000 simulated 3-planet systems to train and test a variety of machine learning models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.model_selection import KFold\n",
    "from sklearn import metrics\n",
    "from sklearn.metrics import precision_recall_curve, roc_curve\n",
    "pd.options.mode.chained_assignment = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Stable</th>\n",
       "      <th>instability_time</th>\n",
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       "      <td>1.579004</td>\n",
       "      <td>...</td>\n",
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       "      <td>0.014659</td>\n",
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       "      <td>0.000011</td>\n",
       "      <td>-2.313583</td>\n",
       "      <td>1.605318</td>\n",
       "      <td>1.576007</td>\n",
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       "      <th>24998</th>\n",
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       "      <td>1.0</td>\n",
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       "         runstring   a1        e1    omega1      inc1            m1    Omega1  \\\n",
       "24995  0024995.bin  1.0  0.001983 -0.103719  0.034756  6.384047e-07  1.891501   \n",
       "24996  0024996.bin  1.0  0.000435 -0.528805  0.009183  4.383173e-06 -1.320371   \n",
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       "24999  0024999.bin  1.0  0.000022 -0.388908  0.019481  4.806837e-05  0.756854   \n",
       "\n",
       "       true_anom1  mean_anom1        a2        ...               a3        e3  \\\n",
       "24995    2.323505    2.320607  1.171907        ...         1.387978  0.136176   \n",
       "24996    2.943623    2.943452  1.118284        ...         1.220488  0.000275   \n",
       "24997    0.520523    0.520365  1.579004        ...         1.697671  0.014659   \n",
       "24998   -2.821058   -2.793167  1.055424        ...         1.286817  0.002571   \n",
       "24999    2.089563    2.089526  1.316695        ...         1.849302  0.001253   \n",
       "\n",
       "         omega3      inc3        m3    Omega3  true_anom3  mean_anom3  Stable  \\\n",
       "24995  2.998349  0.013797  0.000001 -1.687570   -0.102447   -0.077197     0.0   \n",
       "24996  2.799539  0.006669  0.000033 -0.174781   -4.296110    1.986572     0.0   \n",
       "24997  0.939074  0.090331  0.000011 -2.313583    1.605318    1.576007     0.0   \n",
       "24998 -1.435588  0.002550  0.000011 -0.858794    1.509610    1.504478     0.0   \n",
       "24999 -2.367310  0.005140  0.000041 -0.267279    0.119263    0.118965     1.0   \n",
       "\n",
       "       instability_time  \n",
       "24995      1.843085e+04  \n",
       "24996      1.868255e+03  \n",
       "24997      6.939622e+04  \n",
       "24998      3.230627e+04  \n",
       "24999      1.000000e+09  \n",
       "\n",
       "[5 rows x 27 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the dataset\n",
    "df = pd.read_csv('Stability_Data_inial_conditions.csv', index_col=0)\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above, we have loaded the raw initial conditions for each system, using ```pandas```. For each of the three planets (identified ```1```, ```2```, ```3```):  \n",
    "- ```a``` = $a$ = semi-major axis.  \n",
    "- ```e``` = $e$ = eccentricity.  \n",
    "- ```omega``` = $\\omega$ = argument of periapsis.\n",
    "- ```Omega``` = $\\Omega$ = Longitude of ascending node.\n",
    "- ```inc``` = $i$ = inclination.  \n",
    "- ```m``` = $m$ = planet mass.\n",
    "- ```true_anom``` = $\\nu$ = true anomaly.\n",
    "- ```mean_anom``` = $M$ = mean anomaly.\n",
    "\n",
    "In addition:\n",
    "- ```runstring``` = identifier for each simulation. \n",
    "- ```Stable``` = whether the system is stable over a billion orbits of the inner planet. *This is the quantity we want to train our machine learning algorithm to predict!*\n",
    "- ```instability_time``` = The physical number of years the system was stable for. If ```instability_time```=$10^9$, then ```Stable = 1```. This is an alternative quantity we could train a *regression* model on, but we won't do that here (this is a much harder problem).\n",
    "- Stellar Mass = $M_*$ = 1 for all systems.\n",
    "\n",
    "For reference, the orbital elements are shown here:\n",
    "<img src=\"555px-Orbit1.svg.png\" style=\"width: 500px;\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting\n",
    "Let's plot the data to get a sense of what it looks like. Try and plot other variables to see if you can better separate the stable (blue) systems from the unstable (red) systems!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x103686d90>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hpqT3rTsIgE9/urjxrlDoREcZQpTXoCtkkeVxkGmFohuJkWxAyHpLmAKM2zK+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\nFuLp2NttqRuuBTwmCQnQF+/e3xXNRT5cG3pKeFPuoMuFbP4COskNQyH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sl2yMaylH7P2L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wC8AqkeP0UNRMToV5HEz/dNcur1UFFbLLAWRTjb6eMKOjjrDvGbN1aWhz4AoeUNVWVZA8ipVHmR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oct06CvDxN+FVfOmFFLMZufdoVWMb+7ZpE4GcOziAxtwbnod73cSROXEz64OxlWup6lp5L9hC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EEQBEEQBA+1J8a1hhtugNHRq9sMl+fr7RPdeLbToqq4zDRaSmJf77wzPSb7oUPx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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b091790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# x and y plot variables\n",
    "x = df['a2'].values/df['a1'].values\n",
    "y = df['a3'].values/df['a1'].values\n",
    "\n",
    "# plotting\n",
    "fig, ax = plt.subplots(figsize=(12,8))\n",
    "stable = df['Stable'] == 1\n",
    "unstable = df['Stable'] == 0\n",
    "ax.scatter(x[stable], y[stable], color='blue', s=5, label='Stable')\n",
    "ax.scatter(x[unstable], y[unstable], color='red', s=5, label='Unstable')\n",
    "ax.set_xlim([1,2.25])\n",
    "ax.set_ylim([1,3.25])\n",
    "ax.set_xlabel('a2/a1', fontsize=20)\n",
    "ax.set_ylabel('a3/a2', fontsize=20)\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Get Input and Target\n",
    "A machine learning model requires an input (features), ```X```, and ground truth output (i.e. the answer), ```y```, to train. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a1</th>\n",
       "      <th>e1</th>\n",
       "      <th>omega1</th>\n",
       "      <th>inc1</th>\n",
       "      <th>m1</th>\n",
       "      <th>Omega1</th>\n",
       "      <th>true_anom1</th>\n",
       "      <th>mean_anom1</th>\n",
       "      <th>a2</th>\n",
       "      <th>e2</th>\n",
       "      <th>...</th>\n",
       "      <th>true_anom2</th>\n",
       "      <th>mean_anom2</th>\n",
       "      <th>a3</th>\n",
       "      <th>e3</th>\n",
       "      <th>omega3</th>\n",
       "      <th>inc3</th>\n",
       "      <th>m3</th>\n",
       "      <th>Omega3</th>\n",
       "      <th>true_anom3</th>\n",
       "      <th>mean_anom3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.005031</td>\n",
       "      <td>1.400202</td>\n",
       "      <td>0.008978</td>\n",
       "      <td>3.414016e-05</td>\n",
       "      <td>1.770839</td>\n",
       "      <td>-1.534327</td>\n",
       "      <td>-1.524274</td>\n",
       "      <td>1.221502</td>\n",
       "      <td>0.059391</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.567081</td>\n",
       "      <td>-0.505606</td>\n",
       "      <td>1.589043</td>\n",
       "      <td>0.002515</td>\n",
       "      <td>1.084278</td>\n",
       "      <td>0.065498</td>\n",
       "      <td>1.826900e-06</td>\n",
       "      <td>-1.192440</td>\n",
       "      <td>-0.614709</td>\n",
       "      <td>-0.611814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.010350</td>\n",
       "      <td>-2.070391</td>\n",
       "      <td>0.001541</td>\n",
       "      <td>2.529838e-07</td>\n",
       "      <td>-1.493638</td>\n",
       "      <td>0.013233</td>\n",
       "      <td>0.012961</td>\n",
       "      <td>1.190647</td>\n",
       "      <td>0.013048</td>\n",
       "      <td>...</td>\n",
       "      <td>1.437355</td>\n",
       "      <td>1.411526</td>\n",
       "      <td>1.671403</td>\n",
       "      <td>0.072450</td>\n",
       "      <td>0.275475</td>\n",
       "      <td>0.046939</td>\n",
       "      <td>1.955797e-05</td>\n",
       "      <td>-0.619350</td>\n",
       "      <td>0.192203</td>\n",
       "      <td>0.165935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.051912</td>\n",
       "      <td>-1.710828</td>\n",
       "      <td>0.016289</td>\n",
       "      <td>7.380789e-05</td>\n",
       "      <td>2.705977</td>\n",
       "      <td>2.472633</td>\n",
       "      <td>2.406234</td>\n",
       "      <td>1.125660</td>\n",
       "      <td>0.042326</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.317958</td>\n",
       "      <td>-0.292271</td>\n",
       "      <td>1.936762</td>\n",
       "      <td>0.003395</td>\n",
       "      <td>0.624064</td>\n",
       "      <td>0.014535</td>\n",
       "      <td>1.477931e-07</td>\n",
       "      <td>2.795101</td>\n",
       "      <td>1.685406</td>\n",
       "      <td>1.678659</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000152</td>\n",
       "      <td>-2.300890</td>\n",
       "      <td>0.003301</td>\n",
       "      <td>5.174804e-07</td>\n",
       "      <td>-1.027543</td>\n",
       "      <td>2.993015</td>\n",
       "      <td>2.992970</td>\n",
       "      <td>1.216684</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>...</td>\n",
       "      <td>-2.294238</td>\n",
       "      <td>-2.294199</td>\n",
       "      <td>1.503164</td>\n",
       "      <td>0.057380</td>\n",
       "      <td>2.166845</td>\n",
       "      <td>0.098014</td>\n",
       "      <td>1.287851e-06</td>\n",
       "      <td>-2.995941</td>\n",
       "      <td>-1.625763</td>\n",
       "      <td>-1.510968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.001457</td>\n",
       "      <td>0.653565</td>\n",
       "      <td>0.033910</td>\n",
       "      <td>5.106746e-07</td>\n",
       "      <td>1.084883</td>\n",
       "      <td>0.667169</td>\n",
       "      <td>0.665367</td>\n",
       "      <td>1.034058</td>\n",
       "      <td>0.020334</td>\n",
       "      <td>...</td>\n",
       "      <td>-1.074927</td>\n",
       "      <td>-1.039417</td>\n",
       "      <td>1.059346</td>\n",
       "      <td>0.010325</td>\n",
       "      <td>0.038984</td>\n",
       "      <td>0.011840</td>\n",
       "      <td>1.542321e-06</td>\n",
       "      <td>-1.253823</td>\n",
       "      <td>1.215392</td>\n",
       "      <td>1.196085</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 24 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    a1        e1    omega1      inc1            m1    Omega1  true_anom1  \\\n",
       "0  1.0  0.005031  1.400202  0.008978  3.414016e-05  1.770839   -1.534327   \n",
       "1  1.0  0.010350 -2.070391  0.001541  2.529838e-07 -1.493638    0.013233   \n",
       "2  1.0  0.051912 -1.710828  0.016289  7.380789e-05  2.705977    2.472633   \n",
       "3  1.0  0.000152 -2.300890  0.003301  5.174804e-07 -1.027543    2.993015   \n",
       "4  1.0  0.001457  0.653565  0.033910  5.106746e-07  1.084883    0.667169   \n",
       "\n",
       "   mean_anom1        a2        e2     ...      true_anom2  mean_anom2  \\\n",
       "0   -1.524274  1.221502  0.059391     ...       -0.567081   -0.505606   \n",
       "1    0.012961  1.190647  0.013048     ...        1.437355    1.411526   \n",
       "2    2.406234  1.125660  0.042326     ...       -0.317958   -0.292271   \n",
       "3    2.992970  1.216684  0.000026     ...       -2.294238   -2.294199   \n",
       "4    0.665367  1.034058  0.020334     ...       -1.074927   -1.039417   \n",
       "\n",
       "         a3        e3    omega3      inc3            m3    Omega3  true_anom3  \\\n",
       "0  1.589043  0.002515  1.084278  0.065498  1.826900e-06 -1.192440   -0.614709   \n",
       "1  1.671403  0.072450  0.275475  0.046939  1.955797e-05 -0.619350    0.192203   \n",
       "2  1.936762  0.003395  0.624064  0.014535  1.477931e-07  2.795101    1.685406   \n",
       "3  1.503164  0.057380  2.166845  0.098014  1.287851e-06 -2.995941   -1.625763   \n",
       "4  1.059346  0.010325  0.038984  0.011840  1.542321e-06 -1.253823    1.215392   \n",
       "\n",
       "   mean_anom3  \n",
       "0   -0.611814  \n",
       "1    0.165935  \n",
       "2    1.678659  \n",
       "3   -1.510968  \n",
       "4    1.196085  \n",
       "\n",
       "[5 rows x 24 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols = df.columns.drop('runstring').drop('Stable').drop('instability_time')\n",
    "\n",
    "# input \n",
    "X = df[cols]\n",
    "\n",
    "# output (target)\n",
    "y = df['Stable']\n",
    "\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Engineering\n",
    "Good features are essential to an accurate model, which often requires domain expertise. For example, if you were trying to train a model to distinguish cars from pickup-trucks, a \"number of wheels\" feature would not be very useful since they both have 4 wheels. A better feature might be \"size\", since pickup-trucks are generally bigger than cars.  \n",
    "\n",
    "For our problem, let's create a \"Mutual Hill Radius\" feature, which describes the *dynamical* spacing between planets, and is calculated according to:\n",
    "$$ R_{Hi,j} = \\left(\\frac{a_1 + a_2}{2}\\right)\\left(\\frac{m_1 + m_2}{3M_*}\\right)^{1/3} $$\n",
    "Mutual Hill Radius can be thought of as a \"normalized\" spacing parameter - a system with two Earth-sized planets will be equally as interactive as a system with two Jupiter-sized planets if they are spaced by the same number of mutual hill radii."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a1</th>\n",
       "      <th>e1</th>\n",
       "      <th>omega1</th>\n",
       "      <th>inc1</th>\n",
       "      <th>m1</th>\n",
       "      <th>Omega1</th>\n",
       "      <th>true_anom1</th>\n",
       "      <th>mean_anom1</th>\n",
       "      <th>a2</th>\n",
       "      <th>e2</th>\n",
       "      <th>...</th>\n",
       "      <th>a3</th>\n",
       "      <th>e3</th>\n",
       "      <th>omega3</th>\n",
       "      <th>inc3</th>\n",
       "      <th>m3</th>\n",
       "      <th>Omega3</th>\n",
       "      <th>true_anom3</th>\n",
       "      <th>mean_anom3</th>\n",
       "      <th>Rhill_12</th>\n",
       "      <th>Rhill_23</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.005031</td>\n",
       "      <td>1.400202</td>\n",
       "      <td>0.008978</td>\n",
       "      <td>3.414016e-05</td>\n",
       "      <td>1.770839</td>\n",
       "      <td>-1.534327</td>\n",
       "      <td>-1.524274</td>\n",
       "      <td>1.221502</td>\n",
       "      <td>0.059391</td>\n",
       "      <td>...</td>\n",
       "      <td>1.589043</td>\n",
       "      <td>0.002515</td>\n",
       "      <td>1.084278</td>\n",
       "      <td>0.065498</td>\n",
       "      <td>1.826900e-06</td>\n",
       "      <td>-1.192440</td>\n",
       "      <td>-0.614709</td>\n",
       "      <td>-0.611814</td>\n",
       "      <td>0.028916</td>\n",
       "      <td>0.026716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.010350</td>\n",
       "      <td>-2.070391</td>\n",
       "      <td>0.001541</td>\n",
       "      <td>2.529838e-07</td>\n",
       "      <td>-1.493638</td>\n",
       "      <td>0.013233</td>\n",
       "      <td>0.012961</td>\n",
       "      <td>1.190647</td>\n",
       "      <td>0.013048</td>\n",
       "      <td>...</td>\n",
       "      <td>1.671403</td>\n",
       "      <td>0.072450</td>\n",
       "      <td>0.275475</td>\n",
       "      <td>0.046939</td>\n",
       "      <td>1.955797e-05</td>\n",
       "      <td>-0.619350</td>\n",
       "      <td>0.192203</td>\n",
       "      <td>0.165935</td>\n",
       "      <td>0.024868</td>\n",
       "      <td>0.037600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.051912</td>\n",
       "      <td>-1.710828</td>\n",
       "      <td>0.016289</td>\n",
       "      <td>7.380789e-05</td>\n",
       "      <td>2.705977</td>\n",
       "      <td>2.472633</td>\n",
       "      <td>2.406234</td>\n",
       "      <td>1.125660</td>\n",
       "      <td>0.042326</td>\n",
       "      <td>...</td>\n",
       "      <td>1.936762</td>\n",
       "      <td>0.003395</td>\n",
       "      <td>0.624064</td>\n",
       "      <td>0.014535</td>\n",
       "      <td>1.477931e-07</td>\n",
       "      <td>2.795101</td>\n",
       "      <td>1.685406</td>\n",
       "      <td>1.678659</td>\n",
       "      <td>0.038585</td>\n",
       "      <td>0.043732</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000152</td>\n",
       "      <td>-2.300890</td>\n",
       "      <td>0.003301</td>\n",
       "      <td>5.174804e-07</td>\n",
       "      <td>-1.027543</td>\n",
       "      <td>2.993015</td>\n",
       "      <td>2.992970</td>\n",
       "      <td>1.216684</td>\n",
       "      <td>0.000026</td>\n",
       "      <td>...</td>\n",
       "      <td>1.503164</td>\n",
       "      <td>0.057380</td>\n",
       "      <td>2.166845</td>\n",
       "      <td>0.098014</td>\n",
       "      <td>1.287851e-06</td>\n",
       "      <td>-2.995941</td>\n",
       "      <td>-1.625763</td>\n",
       "      <td>-1.510968</td>\n",
       "      <td>0.012972</td>\n",
       "      <td>0.016725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.001457</td>\n",
       "      <td>0.653565</td>\n",
       "      <td>0.033910</td>\n",
       "      <td>5.106746e-07</td>\n",
       "      <td>1.084883</td>\n",
       "      <td>0.667169</td>\n",
       "      <td>0.665367</td>\n",
       "      <td>1.034058</td>\n",
       "      <td>0.020334</td>\n",
       "      <td>...</td>\n",
       "      <td>1.059346</td>\n",
       "      <td>0.010325</td>\n",
       "      <td>0.038984</td>\n",
       "      <td>0.011840</td>\n",
       "      <td>1.542321e-06</td>\n",
       "      <td>-1.253823</td>\n",
       "      <td>1.215392</td>\n",
       "      <td>1.196085</td>\n",
       "      <td>0.006304</td>\n",
       "      <td>0.008739</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    a1        e1    omega1      inc1            m1    Omega1  true_anom1  \\\n",
       "0  1.0  0.005031  1.400202  0.008978  3.414016e-05  1.770839   -1.534327   \n",
       "1  1.0  0.010350 -2.070391  0.001541  2.529838e-07 -1.493638    0.013233   \n",
       "2  1.0  0.051912 -1.710828  0.016289  7.380789e-05  2.705977    2.472633   \n",
       "3  1.0  0.000152 -2.300890  0.003301  5.174804e-07 -1.027543    2.993015   \n",
       "4  1.0  0.001457  0.653565  0.033910  5.106746e-07  1.084883    0.667169   \n",
       "\n",
       "   mean_anom1        a2        e2    ...           a3        e3    omega3  \\\n",
       "0   -1.524274  1.221502  0.059391    ...     1.589043  0.002515  1.084278   \n",
       "1    0.012961  1.190647  0.013048    ...     1.671403  0.072450  0.275475   \n",
       "2    2.406234  1.125660  0.042326    ...     1.936762  0.003395  0.624064   \n",
       "3    2.992970  1.216684  0.000026    ...     1.503164  0.057380  2.166845   \n",
       "4    0.665367  1.034058  0.020334    ...     1.059346  0.010325  0.038984   \n",
       "\n",
       "       inc3            m3    Omega3  true_anom3  mean_anom3  Rhill_12  \\\n",
       "0  0.065498  1.826900e-06 -1.192440   -0.614709   -0.611814  0.028916   \n",
       "1  0.046939  1.955797e-05 -0.619350    0.192203    0.165935  0.024868   \n",
       "2  0.014535  1.477931e-07  2.795101    1.685406    1.678659  0.038585   \n",
       "3  0.098014  1.287851e-06 -2.995941   -1.625763   -1.510968  0.012972   \n",
       "4  0.011840  1.542321e-06 -1.253823    1.215392    1.196085  0.006304   \n",
       "\n",
       "   Rhill_23  \n",
       "0  0.026716  \n",
       "1  0.037600  \n",
       "2  0.043732  \n",
       "3  0.016725  \n",
       "4  0.008739  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X['Rhill_12'] = 0.5*(X['a1'] + X['a2'])*((X['m1'] + X['m2'])/3.)**(1./3.) # mutual hill spacing between planets 1, 2\n",
    "X['Rhill_23'] = 0.5*(X['a3'] + X['a2'])*((X['m3'] + X['m2'])/3.)**(1./3.) # mutual hill spacing between planets 2, 3\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Split into Train/Test data\n",
    "To test the accuracy of an algorithm, we need to see how it performs on unseen data. This is the test set, which is reserved until the model is fully trained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# use subset of data - don't need 25,000 for initial model building\n",
    "frac_data = 0.7\n",
    "\n",
    "# randomly split into train/test data\n",
    "train_frac = 0.8\n",
    "N = int(len(X)*frac_data)\n",
    "\n",
    "# build training/test datasets\n",
    "rN = np.arange(0,N)\n",
    "np.random.shuffle(rN)  # randomly shuffle data\n",
    "train_i, test_i = rN[0: int(train_frac*N)], rN[int(train_frac*N):]\n",
    "\n",
    "Xtrain, Xtest = X.iloc[train_i], X.iloc[test_i]\n",
    "ytrain, ytest = y.iloc[train_i], y.iloc[test_i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Regression\n",
    "Algorithm: http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html\n",
    "\n",
    "In this cell we are performing:\n",
    "- cross validation (CV) using ```KFold```.\n",
    "- a grid search over hyperparameters ```C``` and ```solver```. \n",
    "- applying an \"l2\" regularization term the help prevent overfitting.\n",
    "\n",
    "In order to determine what the best set of hyperparameters are, both cross validation and grid search is necessary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "fold = KFold(n_splits=3, shuffle=False, random_state=None)\n",
    "\n",
    "# hyparameters to grid search over\n",
    "grid = {\n",
    "    'C': [1, 1e-2],   # regularization penalty term\n",
    "    'solver': ['newton-cg']\n",
    "}\n",
    "\n",
    "# initialize algorithm\n",
    "clf = LogisticRegression(penalty='l2', random_state=777, max_iter=10000, tol=10)\n",
    "\n",
    "# Search over grid\n",
    "gs = GridSearchCV(clf, grid, scoring='roc_auc', cv=fold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('gs.best_score_:', 0.87783448545759668)\n",
      "('gs.best_params_:', {'C': 1, 'solver': 'newton-cg'})\n"
     ]
    }
   ],
   "source": [
    "# perform grid search, might take a minute!\n",
    "gs.fit(Xtrain, ytrain)\n",
    "print ('gs.best_score_:', gs.best_score_)\n",
    "print ('gs.best_params_:', gs.best_params_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=10000, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=777, solver='newton-cg', tol=10,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load and train best model\n",
    "LR_best = LogisticRegression(C=gs.best_params_['C'], solver=gs.best_params_['solver'],\n",
    "                          penalty='l2', random_state=777, max_iter=10000, tol=10)\n",
    "LR_best.fit(Xtrain, ytrain)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code to generate precision-recall and receiver operating characteristic (ROC) curves\n",
    "Precision-Recall and ROC curves are both used to measure the performance of an algorithm. In particular, a classification algorithm is likely to make mistakes in the form of false positives (negative cases incorrectly classified as positive) and false negatives (positive cases incorrectly classified as negative). Most algorithms output a class probability and the user must specify what the threshold for a positive classification is. Precision-Recall and ROC curves generate performance scores for each possible threshold (between 0 and 1), giving a sense of overall performance. These are statistics calculated from the number of True Positives, $T_P$, True Negatives $T_N$, False Positives, $F_P$, and False Negatives, $F_N$.\n",
    "\n",
    "For each threshold, a False Positive Rate, $R_{FP}$ and True Positive Rate, $R_{TP}$ are calculated and plotted on an ROC curve according to:  \n",
    "$$R_{FP} = \\frac{T_P}{F_P + T_N}, \\ \\ R_{TP} = \\frac{T_P}{F_N + T_P}$$\n",
    "\n",
    "For each threshold, a Precision, $P$, and Recall, $R$, value is calculated and plotted on a precision-recall curve according to:  \n",
    "$$P = \\frac{T_P}{F_P + T_P}, \\ \\ R = \\frac{T_P}{F_N + T_P}$$\n",
    "\n",
    "The $y=x$ line on an ROC plot corresponds to random guessing (i.e. terrible performance), and the closer to the upper left corner an ROC curve lies the better the performance. By calculating the area under an ROC curve (```AUC_ROC```), one can get a measure of absolute performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def PR_ROC_curve(model, Xtest, ytest, test_i):\n",
    "    ypred = model.predict_proba(Xtest)[:,1]\n",
    "    index = np.isfinite(ypred) == True    # occasionally a prediction -> inf/nan\n",
    "    ytest, ypred = ytest[index], ypred[index]\n",
    "    precision, recall, thresholds = precision_recall_curve(ytest, ypred)\n",
    "    fpr, tpr, thresholds = roc_curve(ytest, ypred)\n",
    "    auc = metrics.roc_auc_score(ytest, ypred)\n",
    "    \n",
    "    # best model\n",
    "    best = pd.read_csv('XGB_model_preds.csv', index_col=0)\n",
    "    ytest_best, ypred_best = best['Stable'][test_i], best['preds'][test_i]\n",
    "    index = np.isfinite(ypred_best) == True    # occasionally a prediction -> inf/nan\n",
    "    ytest_best, ypred_best = ytest_best[index], ypred_best[index]\n",
    "    precision_best, recall_best, thresholds_best = precision_recall_curve(ytest_best, ypred_best)\n",
    "    fpr_best, tpr_best, thresholds_best = roc_curve(ytest_best, ypred_best)\n",
    "    auc_best = metrics.roc_auc_score(ytest_best, ypred_best)\n",
    "    \n",
    "    f, ax = plt.subplots(1, 2, figsize=(15,6))\n",
    "    ax[0].plot(recall, precision)\n",
    "    ax[0].plot(recall_best, precision_best)\n",
    "    ax[0].set_xlim([0.0, 1.0])\n",
    "    ax[0].set_ylim([0.0, 1.0])\n",
    "    ax[0].set_xlabel('Recall',fontsize=12)\n",
    "    ax[0].set_ylabel('Precision',fontsize=12)\n",
    "    ax[0].set_title(\"Precision-Recall Curve\")\n",
    "    \n",
    "    ax[1].plot(fpr, tpr, label='auc, your model: %f'%auc)\n",
    "    ax[1].plot(fpr_best, tpr_best, label='auc, best model: %f'%auc_best)\n",
    "    ax[1].plot([0, 1], [0, 1], 'k--')\n",
    "    ax[1].set_xlim([0.0, 1.0])\n",
    "    ax[1].set_ylim([0.0, 1.0])\n",
    "    ax[1].set_xlabel('False Positive Rate')\n",
    "    ax[1].set_ylabel('True Positive Rate')\n",
    "    ax[1].set_title(\"Receiver Operating Characteristic Curve\")\n",
    "    ax[1].legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wrWqv0pp/agKoVPFcRwydPn06t9xyi1vfX2sGVY1xY0wULcKCCAv2o1VECCH+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\nABiSQQAAgCEZBAAAGJJBAACAoQA23LUjj/DRkAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e5e3f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate PR/ROC curves\n",
    "PR_ROC_curve(LR_best, Xtest, ytest, test_i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Support Vector Machine (SVM)\n",
    "Algorithm: http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html  \n",
    "\n",
    "As you will notice, the training of an SVM is considerably slower than logistic regression. This is because the training time using a non-linear kernel (default for ```SVC``` is the non-linear ```rbf``` kernel) is approximately $O(\\rm{max}(n, d) * \\rm{min}(n, d)^2)$ where $n$ is the number of data points and $d$ is the number of features. Source: Chapelle, Olivier. \"Training a support vector machine in the primal.\" Neural Computation 19.5 (2007): 1155-1178."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.svm import SVC  # SVC = Support Vector for Classification\n",
    "fold = KFold(n_splits=3, shuffle=False, random_state=None)\n",
    "grid = {\n",
    "    'C': [1, 1e-3],  # regularization penalty term\n",
    "    'kernel': ['rbf','linear']\n",
    "}\n",
    "clf = SVC()\n",
    "\n",
    "# Search over grid\n",
    "gs = GridSearchCV(clf, grid, scoring='roc_auc', cv=fold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gs.best_score_: 0.885465880352\n",
      "gs.best_params_: {'C': 1, 'kernel': 'linear'}\n"
     ]
    }
   ],
   "source": [
    "# perform grid search, might take a minute!\n",
    "gs.fit(Xtrain, ytrain)\n",
    "print ('gs.best_score_:', gs.best_score_)\n",
    "print ('gs.best_params_:', gs.best_params_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape='ovr', degree=3, gamma='auto', kernel='linear',\n",
       "  max_iter=-1, probability=True, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load and train best model on full training set (no cross validation)\n",
    "SVC_best = SVC(C=gs.best_params_['C'], kernel=gs.best_params_['kernel'], probability=True)\n",
    "SVC_best.fit(Xtrain, ytrain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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fXO0xSDIobDduaDtSs/P5ct1+ps/bhlJQNzyItBwHB9NyuKxLQ85rWvFb5kKI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11af027b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate PR/ROC curves\n",
    "PR_ROC_curve(SVC_best, Xtest, ytest, test_i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Improving the models:\n",
    "Now that you know the basics of how to:  \n",
    "- Use the stability dataset.\n",
    "- Split the data into train/test sets.\n",
    "- Generate new features.\n",
    "- Train/test a model.\n",
    "- Measure it's performance.\n",
    "\n",
    "It's time to explore this notebook to try and achieve the best possible performance on the test set, and perhaps even compete with the \"best model\" performance on this dataset! This can be done by:\n",
    "1. Trying different Machine Learning algorithms. There are many easy options available here - http://scikit-learn.org/stable/supervised_learning.html#supervised-learning.\n",
    "2. Increasing the amount of training data.\n",
    "3. Perform a more thorough grid search over the hyperparameters for a model. Is there a better optimum set of values?\n",
    "4. Feature Engineering: are there better ways to express the data that could better delineate between stable/unstable systems? \n",
    "5. Ensembling: averaging the test-set predictions from many models. This tends to improve predictions since the aggregate opinions of many models generally reduces variance (i.e. less noisy) than the opinion of one model. Each algorithm has unique weaknesses which can be averaged out by the other model opinions that generally do not have the same weaknesses.\n",
    "6. Standardize features. \n",
    "\n",
    "## Questions:\n",
    "1. Does one machine learning model perform much better compared to the others? Why?\n",
    "2. Which features are most important to the performance? Does this make sense from a physics perspective?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Information About 'Best Model'\n",
    "The best model was developed by [Dan Tamayo](https://github.com/dtamayo), [Naireen Hussain](https://github.com/naireen) and [Ari Silburt](https://github.com/silburt), and uses sophisticated hand-crafted features to generate predictions using the ML algorithm XGBoost. Many of these features are generated from the early evolution of the planetary system. For example, the minimum, maximum, standard deviation and mean eccentricity of each planet over the first 10,000 orbits are used as features. As a result, 'best model' uses the initial conditions *and* the early evolution of a planetary system to generate a prediction. These sophistocated features can be found by loading \"Stability_Data_BestModel_Features.csv\" provided in the folder. Feel free to try it out!\n",
    "\n",
    "Since \"Stability_Data_inial_conditions.csv\" contains only the initial conditions, it is unlikely that you would be able to match/beat the performance of the best model. Please let us know if you even get close, as maybe you have created an important feature we didn't think of!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Clustering\n",
    "We will briefly analyze this dataset from a clustering perspective. If we plot a histograms of ```instability_time``` and ```log10(instability_time)```, we can see that clusters emerge. In particular, it appears that when binning ```instability_time``` systems cluster around $<0.1$ or $1$ billion years. Although it is very common to analyze the stability of planetary systems in terms of ```log10(instability_time)```, we will instead try to successfully cluster the two groups in ```instability_time``` space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10e652a50>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ZhFyyHnGOnPlkbi1kPkmrziRJkiRJ62GDHIBCkiRJkuabxZQkSZIk9WAxJUmS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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e0c35d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(1, 3, figsize=(14,4), sharey=True)\n",
    "ax[0].hist(np.log10(df['instability_time']));\n",
    "ax[1].hist(df['instability_time']);\n",
    "ax[2].hist(df['Stable']);\n",
    "ax[0].set_ylabel('counts');\n",
    "ax[0].set_xlabel('log10(instability_time)');\n",
    "ax[1].set_xlabel('instability_time (years)');\n",
    "ax[2].set_xlabel('Stability (binary)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Spectral Clustering\n",
    "Algorithm: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.SpectralClustering.html#sklearn.cluster.SpectralClustering\n",
    "\n",
    "From [here](http://scikit-learn.org/stable/auto_examples/cluster/plot_cluster_comparison.html) we can see that Spectral Clustering can do a good job of separating intertwined/messy classes, while the other methods do not do as well. However, from [here](http://hdbscan.readthedocs.io/en/latest/performance_and_scalability.html) we can see that spectral clustering (\"sklearn spectral\" in the first figure) is a very slow algorithm, and scales poorly with the amount of data. However, we will attempt to cluster the stable/unstable systems using this algorithm for a very small amount of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpectralClustering(affinity='rbf', assign_labels='kmeans', coef0=1, degree=3,\n",
       "          eigen_solver=None, eigen_tol=0.0, gamma=1.0, kernel_params=None,\n",
       "          n_clusters=2, n_init=10, n_jobs=1, n_neighbors=10,\n",
       "          random_state=None)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import SpectralClustering\n",
    "clf = SpectralClustering(n_clusters=2, affinity='rbf', gamma=1.0, n_init=10)\n",
    "clf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>a1</th>\n",
       "      <th>e1</th>\n",
       "      <th>omega1</th>\n",
       "      <th>inc1</th>\n",
       "      <th>m1</th>\n",
       "      <th>Omega1</th>\n",
       "      <th>true_anom1</th>\n",
       "      <th>mean_anom1</th>\n",
       "      <th>a2</th>\n",
       "      <th>e2</th>\n",
       "      <th>...</th>\n",
       "      <th>a3</th>\n",
       "      <th>e3</th>\n",
       "      <th>omega3</th>\n",
       "      <th>inc3</th>\n",
       "      <th>m3</th>\n",
       "      <th>Omega3</th>\n",
       "      <th>true_anom3</th>\n",
       "      <th>mean_anom3</th>\n",
       "      <th>Rhill_12</th>\n",
       "      <th>Rhill_23</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>744</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.005276</td>\n",
       "      <td>-2.280183</td>\n",
       "      <td>0.003580</td>\n",
       "      <td>8.450904e-07</td>\n",
       "      <td>-0.521908</td>\n",
       "      <td>4.171273</td>\n",
       "      <td>-2.102849</td>\n",
       "      <td>1.046257</td>\n",
       "      <td>0.007543</td>\n",
       "      <td>...</td>\n",
       "      <td>1.059626</td>\n",
       "      <td>0.022941</td>\n",
       "      <td>-1.575458</td>\n",
       "      <td>0.004367</td>\n",
       "      <td>1.018926e-06</td>\n",
       "      <td>2.793342</td>\n",
       "      <td>1.065387</td>\n",
       "      <td>1.025576</td>\n",
       "      <td>0.012080</td>\n",
       "      <td>0.012576</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>745</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.007163</td>\n",
       "      <td>1.572270</td>\n",
       "      <td>0.018378</td>\n",
       "      <td>4.589269e-07</td>\n",
       "      <td>-1.765554</td>\n",
       "      <td>-1.770789</td>\n",
       "      <td>-1.756734</td>\n",
       "      <td>1.414292</td>\n",
       "      <td>0.004847</td>\n",
       "      <td>...</td>\n",
       "      <td>1.454929</td>\n",
       "      <td>0.017930</td>\n",
       "      <td>-1.248724</td>\n",
       "      <td>0.072972</td>\n",
       "      <td>1.261339e-06</td>\n",
       "      <td>3.067091</td>\n",
       "      <td>1.311294</td>\n",
       "      <td>1.276756</td>\n",
       "      <td>0.018345</td>\n",
       "      <td>0.022342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>746</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.045097</td>\n",
       "      <td>1.730455</td>\n",
       "      <td>0.061635</td>\n",
       "      <td>1.867993e-06</td>\n",
       "      <td>2.250357</td>\n",
       "      <td>-3.620189</td>\n",
       "      <td>2.620180</td>\n",
       "      <td>1.155877</td>\n",
       "      <td>0.012655</td>\n",
       "      <td>...</td>\n",
       "      <td>1.671401</td>\n",
       "      <td>0.010231</td>\n",
       "      <td>-1.424115</td>\n",
       "      <td>0.002171</td>\n",
       "      <td>2.352218e-05</td>\n",
       "      <td>-1.661276</td>\n",
       "      <td>0.842566</td>\n",
       "      <td>0.827372</td>\n",
       "      <td>0.009669</td>\n",
       "      <td>0.028202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>747</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.005446</td>\n",
       "      <td>-0.626045</td>\n",
       "      <td>0.081258</td>\n",
       "      <td>7.862898e-07</td>\n",
       "      <td>2.284007</td>\n",
       "      <td>2.358184</td>\n",
       "      <td>2.350475</td>\n",
       "      <td>1.125095</td>\n",
       "      <td>0.015416</td>\n",
       "      <td>...</td>\n",
       "      <td>1.503039</td>\n",
       "      <td>0.021079</td>\n",
       "      <td>-3.070809</td>\n",
       "      <td>0.007092</td>\n",
       "      <td>2.187174e-05</td>\n",
       "      <td>1.096155</td>\n",
       "      <td>2.599894</td>\n",
       "      <td>2.577860</td>\n",
       "      <td>0.014999</td>\n",
       "      <td>0.028160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>748</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.004916</td>\n",
       "      <td>-2.321251</td>\n",
       "      <td>0.013209</td>\n",
       "      <td>1.638547e-07</td>\n",
       "      <td>0.331210</td>\n",
       "      <td>0.190913</td>\n",
       "      <td>0.189054</td>\n",
       "      <td>1.349109</td>\n",
       "      <td>0.000609</td>\n",
       "      <td>...</td>\n",
       "      <td>1.761103</td>\n",
       "      <td>0.184905</td>\n",
       "      <td>-0.267640</td>\n",
       "      <td>0.020949</td>\n",
       "      <td>8.206347e-07</td>\n",
       "      <td>2.488754</td>\n",
       "      <td>-2.440396</td>\n",
       "      <td>-2.174502</td>\n",
       "      <td>0.033689</td>\n",
       "      <td>0.044742</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 26 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      a1        e1    omega1      inc1            m1    Omega1  true_anom1  \\\n",
       "744  1.0  0.005276 -2.280183  0.003580  8.450904e-07 -0.521908    4.171273   \n",
       "745  1.0  0.007163  1.572270  0.018378  4.589269e-07 -1.765554   -1.770789   \n",
       "746  1.0  0.045097  1.730455  0.061635  1.867993e-06  2.250357   -3.620189   \n",
       "747  1.0  0.005446 -0.626045  0.081258  7.862898e-07  2.284007    2.358184   \n",
       "748  1.0  0.004916 -2.321251  0.013209  1.638547e-07  0.331210    0.190913   \n",
       "\n",
       "     mean_anom1        a2        e2    ...           a3        e3    omega3  \\\n",
       "744   -2.102849  1.046257  0.007543    ...     1.059626  0.022941 -1.575458   \n",
       "745   -1.756734  1.414292  0.004847    ...     1.454929  0.017930 -1.248724   \n",
       "746    2.620180  1.155877  0.012655    ...     1.671401  0.010231 -1.424115   \n",
       "747    2.350475  1.125095  0.015416    ...     1.503039  0.021079 -3.070809   \n",
       "748    0.189054  1.349109  0.000609    ...     1.761103  0.184905 -0.267640   \n",
       "\n",
       "         inc3            m3    Omega3  true_anom3  mean_anom3  Rhill_12  \\\n",
       "744  0.004367  1.018926e-06  2.793342    1.065387    1.025576  0.012080   \n",
       "745  0.072972  1.261339e-06  3.067091    1.311294    1.276756  0.018345   \n",
       "746  0.002171  2.352218e-05 -1.661276    0.842566    0.827372  0.009669   \n",
       "747  0.007092  2.187174e-05  1.096155    2.599894    2.577860  0.014999   \n",
       "748  0.020949  8.206347e-07  2.488754   -2.440396   -2.174502  0.033689   \n",
       "\n",
       "     Rhill_23  \n",
       "744  0.012576  \n",
       "745  0.022342  \n",
       "746  0.028202  \n",
       "747  0.028160  \n",
       "748  0.044742  \n",
       "\n",
       "[5 rows x 26 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frac_data = 0.03\n",
    "\n",
    "N = len(X)\n",
    "X_clf = X[0:int(frac_data*N)]\n",
    "y_clf = y[0:int(frac_data*N)]\n",
    "\n",
    "X_clf.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This might take a minute!\n",
    "y_clf_pred = clf.fit_predict(X_clf, y_clf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0005843978451994811"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.adjusted_rand_score(y_clf, y_clf_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
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     "execution_count": 19,
     "metadata": {},
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   "source": [
    "zip(y_clf, y_clf_pred)"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the adjusted rand score and comparing the ground truth and predicted class labels with ```zip(y_clf, y_clf_pred)```, we can see that it doesn't do a great job. The clustering algorithm predicts mostly zeros, and few samples with ```y_clf=1``` have a corresponding ```y_clf_pred=1``` value. This highlights the importance of choosing the right machine learning algorithm for your problem, and also supports the (no free lunch theorem)[https://en.wikipedia.org/wiki/No_free_lunch_theorem]. It is important to choose the right algorithm for your problem!\n",
    "\n",
    "There are many other clustering algorithms [here](http://scikit-learn.org/stable/auto_examples/cluster/plot_cluster_comparison.html), try and implement a few different ones, they may perform better! For example, DBSCAN scales much better with the amount of data and uses a different algorithm to cluster. Perhaps it will better separate the two classes!"
   ]
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   "cell_type": "code",
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