Labs/lab15.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "# Initialize Otter\n",
    "import otter\n",
    "grader = otter.Notebook(\"lab14.ipynb\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "intro",
     "locked": true,
     "schema_version": 2,
     "solution": false
    }
   },
   "source": [
    "# Lab 15: Clustering\n",
    "\n",
    "In this lab you will explore K-Means, Agglomerative Clustering, and Spectral Clustering.\n",
    "\n",
    "### Due Date\n",
    "\n",
    "This assignment is due at **Tuesday, December 7th** at 11:59 pm PDT.\n",
    "\n",
    "### Collaboration Policy\n",
    "\n",
    "Data science is a collaborative activity. While you may talk with others about this assignment, we ask that you **write your solutions individually**. If you discuss the assignment with others, please **include their names** in the cell below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Collaborators:** *list names here*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "nbgrader": {
     "grade": false,
     "grade_id": "imports",
     "locked": true,
     "schema_version": 2,
     "solution": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn import cluster\n",
    "\n",
    "# more readable exceptions\n",
    "%pip install --quiet iwut\n",
    "%load_ext iwut\n",
    "%wut on"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vanilla Example\n",
    "\n",
    "Let us begin with a toy dataset with three groups that are completely separated with the variables given. There are the same number of points per group and the same variance within each group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "np.random.seed(1337)\n",
    "\n",
    "c1 = np.random.normal(size = (25, 2))\n",
    "c2 = np.array([2, 8]) + np.random.normal(size = (25, 2))\n",
    "c3 = np.array([8, 4]) + np.random.normal(size = (25, 2))\n",
    "\n",
    "x1 = np.vstack((c1, c2, c3))\n",
    "\n",
    "sns.scatterplot(x = x1[:, 0], y = x1[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running the K-Means algorithm, we can see that it is able to accurately pick out the three initial clusters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "kmeans = cluster.KMeans(n_clusters = 3, random_state = 42).fit(x1)\n",
    "sns.scatterplot(x = x1[:, 0], y = x1[:, 1], hue = kmeans.labels_)\n",
    "sns.scatterplot(x = kmeans.cluster_centers_[:, 0], \n",
    "                y = kmeans.cluster_centers_[:, 1], \n",
    "                color = 'blue', marker = 'x', s = 300, linewidth = 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "## Question 1\n",
    "\n",
    "In the previous example, the K-Means algorithm was able to accurately find the three initial clusters. However, changing the starting centers for K-Means can change the final clusters that K-Means gives us. Change the initial centers to the points `[0, 1]`, `[1, 1]`, and `[2, 2]`; and fit a [`cluster.KMeans`](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html) object called `kmeans_q1` on the toy dataset from the previous example. Keep the `random_state` parameter as 42 and the `n_clusters` parameter as 3.\n",
    "\n",
    "**Hint:** You will need to change the `init` and `n_init` parameters in `cluster.KMeans`.\n",
    "\n",
    "<!--\n",
    "BEGIN QUESTION\n",
    "name: q1\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/sklearn/cluster/_kmeans.py:1146: RuntimeWarning: Explicit initial center position passed: performing only one init in KMeans instead of n_init=10.\n",
      "  self._check_params(X)\n"
     ]
    }
   ],
   "source": [
    "init_centers = np.array([[0, 1], [1, 1], [2, 2]])\n",
    "kmeans_q1 = cluster.KMeans(n_clusters = 3, \n",
    "                           random_state = 42,\n",
    "                           init=init_centers).fit(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><strong><pre style='display: inline;'>q1</pre></strong> passed!</p>"
      ],
      "text/plain": [
       "q1 results: All test cases passed!"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grader.check(\"q1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Running the K-Means algorithm with these centers gives us a different result from before, and this particular run of K-Means was unable to accurately find the three initial clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "sns.scatterplot(x = x1[:, 0], y = x1[:, 1], hue = kmeans_q1.labels_)\n",
    "sns.scatterplot(x = kmeans_q1.cluster_centers_[:, 0], \n",
    "                y = kmeans_q1.cluster_centers_[:, 1], \n",
    "                color = 'blue', marker = 'x', s = 300, linewidth = 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2\n",
    "\n",
    "Sometimes, K-Means will have a difficult time finding the \"correct\" clusters even with ideal starting centers. For example, consider the data below. There are two groups of different sizes in two different senses. The smaller group has both smaller variability and is less numerous, and the larger of the two groups is more diffuse and populated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "np.random.seed(1337)\n",
    "\n",
    "c1 = 0.5 * np.random.normal(size = (25, 2))\n",
    "c2 = np.array([10, 10]) + 3 * np.random.normal(size = (475, 2))\n",
    "\n",
    "x2 = np.vstack((c1, c2))\n",
    "\n",
    "sns.scatterplot(x = x2[:, 0], y = x2[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "### Question 2a\n",
    "\n",
    "Fit a `cluster.KMeans` object called `kmeans_q2a` on the dataset above with two clusters and a `random_state` parameter of 42.\n",
    "\n",
    "<!--\n",
    "BEGIN QUESTION\n",
    "name: q2a\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans_q2a = cluster.KMeans(n_clusters=2,\n",
    "                            random_state=42).fit(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><strong><pre style='display: inline;'>q2a</pre></strong> passed!</p>"
      ],
      "text/plain": [
       "q2a results: All test cases passed!"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grader.check(\"q2a\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(For notational simplicity we will call the initial cluster on the bottom left $A$ and the initial cluster on the top right $B$. We will call the bottom left cluster found by K-Means as cluster $a$ and the top right cluster found by K-Means as cluster $b$.) \n",
    "\n",
    "As seen below, K-Means is unable to find the two intial clusters because cluster $A$ includes points from cluster $B$. Recall that K-Means attempts to minimize inertia, so it makes sense that points in the bottom left of cluster $B$ would prefer to be in cluster $A$ rather than cluster $B$. If these points were in cluster $B$ instead, then the resulting cluster assignments would have a larger distortion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
    "sns.scatterplot(x = x2[:, 0], y = x2[:, 1], hue = kmeans_q2a.labels_)\n",
    "sns.scatterplot(x = kmeans_q2a.cluster_centers_[:, 0], \n",
    "                y = kmeans_q2a.cluster_centers_[:, 1], \n",
    "                color = 'red', marker = 'x', s = 300, linewidth = 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2b\n",
    "\n",
    "It turns out agglomerative clustering works better for this task, as long as we choose the right definition of distance between two clusters. Recall that agglomerative clustering starts with every data point in its own cluster and iteratively joins the two closest clusters until there are $k$ clusters remaining. However, the \"distance\" between two clusters is ambiguous. \n",
    "\n",
    "In Lecture 24 we used the maximum distance between a point in the first cluster and a point in the second as this notion of distance, but there are other ways to define the distance between two clusters. \n",
    "\n",
    "Our choice of definition for the distance is sometimes called the \"linkage criterion.\" We will discuss three linkage criteria, each of which is a different definition of \"distance\" between two clusters:\n",
    "\n",
    "- **Complete linkage** considers the distance between two clusters as the **maximum** distance between a point in the first cluster and a point in the second. This is what you will see in Lecture 26.\n",
    "- **Single linkage** considers the distance between two clusters as the **minimum** distance between a point in the first cluster and a point in the second.\n",
    "- **Average linkage** considers the distance between two clusters as the **average** distance between a point in the first cluster and a point in the second.\n",
    "\n",
    "Below, we fit a [`cluster.AgglomerativeClustering`](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.AgglomerativeClustering.html) object called `agg_complete` on the dataset above with two clusters, using the **complete linkage criterion**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "agg_complete = cluster.AgglomerativeClustering(n_clusters = 2, linkage = 'complete').fit(x2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we visualize the results of your model. Note that complete linkage agglomerative clustering has the same issue as k-Means in that the bottom left cluster found by complete linkage agglomerative clustering includes points from the top right cluster. However, we can remedy this by picking a different linkage criterion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [
    "sns.scatterplot(x = x2[:, 0], y = x2[:, 1], hue = agg_complete.labels_);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "### Question 2b\n",
    "\n",
    "Now, use the **single linkage criterion** to fit a `cluster.AgglomerativeClustering` object called `agg_single` on the dataset above with two clusters.\n",
    "\n",
    "<!--\n",
    "BEGIN QUESTION\n",
    "name: q2b\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "agg_single = cluster.AgglomerativeClustering(n_clusters = 2, linkage = 'single').fit(x2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><strong><pre style='display: inline;'>q2b</pre></strong> passed!</p>"
      ],
      "text/plain": [
       "q2b results: All test cases passed!"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grader.check(\"q2b\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we see that single linkage agglomerative clustering is able to find the two initial clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": [
    "sns.scatterplot(x = x2[:, 0], y = x2[:, 1], hue = agg_single.labels_);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You might be curious why single linkage \"works\" while complete linkage does not in this scenario; we will leave this as an exercise for students who are interested."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 3\n",
    "\n",
    "Another example when k-means fails is when the clusters have odd shapes. For example, look at the following dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "np.random.seed(100)\n",
    "\n",
    "data = np.random.normal(0, 7, size = (1000, 2))\n",
    "lengths = np.linalg.norm(data, axis = 1, ord = 2)\n",
    "x3 = data[(lengths < 2) | ((lengths > 5) & (lengths < 7)) | ((lengths > 11) & (lengths < 15))]\n",
    "\n",
    "sns.scatterplot(x = x3[:, 0], y = x3[:, 1]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at this data, we might say there are 3 clusters, corresponding to each of the 3 concentric circles, with the same center. However, k-means will fail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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": [
    "kmeans_q3 = cluster.KMeans(n_clusters = 3, random_state = 42).fit(x3)\n",
    "sns.scatterplot(x = x3[:, 0], y = x3[:, 1], hue = kmeans_q3.labels_)\n",
    "sns.scatterplot(x = kmeans_q3.cluster_centers_[:, 0], \n",
    "                y = kmeans_q3.cluster_centers_[:, 1], \n",
    "                color = 'red', marker = 'x', s = 300, linewidth = 5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "Let's try spectral clustering instead. \n",
    "\n",
    "In the cell below, create and fit a [`cluster.SpectralClustering`](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.SpectralClustering.html) object, and assign it to `spectral`. Use 3 clusters, and make sure you set `affinity` to `\"nearest_neighbors\"` and a `random_state` of 10.\n",
    "\n",
    "**Note:** Ignore any warnings about the graph not being fully connected.\n",
    "\n",
    "<!--\n",
    "BEGIN QUESTION\n",
    "name: q3\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/sklearn/manifold/_spectral_embedding.py:260: UserWarning: Graph is not fully connected, spectral embedding may not work as expected.\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "spectral = cluster.SpectralClustering(n_clusters = 3, \n",
    "                                      affinity = 'nearest_neighbors',\n",
    "                                      random_state = 10).fit(x3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><strong><pre style='display: inline;'>q3</pre></strong> passed!</p>"
      ],
      "text/plain": [
       "q3 results: All test cases passed!"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grader.check(\"q3\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, we see that spectral clustering is able to find the three rings, when k-means does not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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": [
    "sns.scatterplot(x = x3[:, 0], y = x3[:, 1], hue = spectral.labels_);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 4\n",
    "\n",
    "In the previous three questions, we looked at clustering on two dimensional datasets. However, we can easily use clustering on data which have more than two dimensions. For this, let us turn to a World Bank dataset, containing various features for the world's countries.\n",
    "\n",
    "This data comes from https://databank.worldbank.org/source/world-development-indicators#.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Age dependency ratio (% of working-age population)</th>\n",
       "      <th>Age dependency ratio, old (% of working-age population)</th>\n",
       "      <th>Age dependency ratio, young (% of working-age population)</th>\n",
       "      <th>Bird species, threatened</th>\n",
       "      <th>Business extent of disclosure index (0=less disclosure to 10=more disclosure)</th>\n",
       "      <th>Contributing family workers, female (% of female employment) (modeled ILO estimate)</th>\n",
       "      <th>Contributing family workers, male (% of male employment) (modeled ILO estimate)</th>\n",
       "      <th>Contributing family workers, total (% of total employment) (modeled ILO estimate)</th>\n",
       "      <th>Cost of business start-up procedures (% of GNI per capita)</th>\n",
       "      <th>Cost of business start-up procedures, female (% of GNI per capita)</th>\n",
       "      <th>...</th>\n",
       "      <th>Unemployment, youth total (% of total labor force ages 15-24) (modeled ILO estimate)</th>\n",
       "      <th>Urban population</th>\n",
       "      <th>Urban population (% of total population)</th>\n",
       "      <th>Urban population growth (annual %)</th>\n",
       "      <th>Vulnerable employment, female (% of female employment) (modeled ILO estimate)</th>\n",
       "      <th>Vulnerable employment, male (% of male employment) (modeled ILO estimate)</th>\n",
       "      <th>Vulnerable employment, total (% of total employment) (modeled ILO estimate)</th>\n",
       "      <th>Wage and salaried workers, female (% of female employment) (modeled ILO estimate)</th>\n",
       "      <th>Wage and salaried workers, male (% of male employment) (modeled ILO estimate)</th>\n",
       "      <th>Wage and salaried workers, total (% of total employment) (modeled ILO estimate)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Algeria</th>\n",
       "      <td>57.508032</td>\n",
       "      <td>10.021442</td>\n",
       "      <td>47.486590</td>\n",
       "      <td>15.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.720000</td>\n",
       "      <td>1.836</td>\n",
       "      <td>1.978000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.8</td>\n",
       "      <td>...</td>\n",
       "      <td>29.952999</td>\n",
       "      <td>30670086.0</td>\n",
       "      <td>72.629</td>\n",
       "      <td>2.804996</td>\n",
       "      <td>24.337001</td>\n",
       "      <td>27.227001</td>\n",
       "      <td>26.762000</td>\n",
       "      <td>73.734001</td>\n",
       "      <td>68.160004</td>\n",
       "      <td>69.056000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Afghanistan</th>\n",
       "      <td>84.077656</td>\n",
       "      <td>4.758273</td>\n",
       "      <td>79.319383</td>\n",
       "      <td>16.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>71.780998</td>\n",
       "      <td>9.606</td>\n",
       "      <td>31.577999</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.4</td>\n",
       "      <td>...</td>\n",
       "      <td>2.639000</td>\n",
       "      <td>9477100.0</td>\n",
       "      <td>25.495</td>\n",
       "      <td>3.350383</td>\n",
       "      <td>95.573997</td>\n",
       "      <td>85.993001</td>\n",
       "      <td>89.378998</td>\n",
       "      <td>4.282000</td>\n",
       "      <td>13.292000</td>\n",
       "      <td>10.108000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Albania</th>\n",
       "      <td>45.810037</td>\n",
       "      <td>20.041214</td>\n",
       "      <td>25.768823</td>\n",
       "      <td>8.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>37.987000</td>\n",
       "      <td>20.795</td>\n",
       "      <td>28.076000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.3</td>\n",
       "      <td>...</td>\n",
       "      <td>30.979000</td>\n",
       "      <td>1728969.0</td>\n",
       "      <td>60.319</td>\n",
       "      <td>1.317162</td>\n",
       "      <td>54.663000</td>\n",
       "      <td>54.994001</td>\n",
       "      <td>54.854000</td>\n",
       "      <td>44.320999</td>\n",
       "      <td>41.542999</td>\n",
       "      <td>42.720001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>American Samoa</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>8.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>48339.0</td>\n",
       "      <td>87.153</td>\n",
       "      <td>-0.299516</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Andorra</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>67813.0</td>\n",
       "      <td>88.062</td>\n",
       "      <td>-0.092859</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 209 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Age dependency ratio (% of working-age population)  \\\n",
       "country                                                              \n",
       "Algeria                                                 57.508032    \n",
       "Afghanistan                                             84.077656    \n",
       "Albania                                                 45.810037    \n",
       "American Samoa                                                NaN    \n",
       "Andorra                                                       NaN    \n",
       "\n",
       "                Age dependency ratio, old (% of working-age population)  \\\n",
       "country                                                                   \n",
       "Algeria                                                 10.021442         \n",
       "Afghanistan                                              4.758273         \n",
       "Albania                                                 20.041214         \n",
       "American Samoa                                                NaN         \n",
       "Andorra                                                       NaN         \n",
       "\n",
       "                Age dependency ratio, young (% of working-age population)  \\\n",
       "country                                                                     \n",
       "Algeria                                                 47.486590           \n",
       "Afghanistan                                             79.319383           \n",
       "Albania                                                 25.768823           \n",
       "American Samoa                                                NaN           \n",
       "Andorra                                                       NaN           \n",
       "\n",
       "                Bird species, threatened  \\\n",
       "country                                    \n",
       "Algeria                             15.0   \n",
       "Afghanistan                         16.0   \n",
       "Albania                              8.0   \n",
       "American Samoa                       8.0   \n",
       "Andorra                              3.0   \n",
       "\n",
       "                Business extent of disclosure index (0=less disclosure to 10=more disclosure)  \\\n",
       "country                                                                                         \n",
       "Algeria                                                       4.0                               \n",
       "Afghanistan                                                   8.0                               \n",
       "Albania                                                       9.0                               \n",
       "American Samoa                                                NaN                               \n",
       "Andorra                                                       NaN                               \n",
       "\n",
       "                Contributing family workers, female (% of female employment) (modeled ILO estimate)  \\\n",
       "country                                                                                               \n",
       "Algeria                                                  2.720000                                     \n",
       "Afghanistan                                             71.780998                                     \n",
       "Albania                                                 37.987000                                     \n",
       "American Samoa                                                NaN                                     \n",
       "Andorra                                                       NaN                                     \n",
       "\n",
       "                Contributing family workers, male (% of male employment) (modeled ILO estimate)  \\\n",
       "country                                                                                           \n",
       "Algeria                                                     1.836                                 \n",
       "Afghanistan                                                 9.606                                 \n",
       "Albania                                                    20.795                                 \n",
       "American Samoa                                                NaN                                 \n",
       "Andorra                                                       NaN                                 \n",
       "\n",
       "                Contributing family workers, total (% of total employment) (modeled ILO estimate)  \\\n",
       "country                                                                                             \n",
       "Algeria                                                  1.978000                                   \n",
       "Afghanistan                                             31.577999                                   \n",
       "Albania                                                 28.076000                                   \n",
       "American Samoa                                                NaN                                   \n",
       "Andorra                                                       NaN                                   \n",
       "\n",
       "                Cost of business start-up procedures (% of GNI per capita)  \\\n",
       "country                                                                      \n",
       "Algeria                                                       0.0            \n",
       "Afghanistan                                                   0.0            \n",
       "Albania                                                       0.0            \n",
       "American Samoa                                                NaN            \n",
       "Andorra                                                       NaN            \n",
       "\n",
       "                Cost of business start-up procedures, female (% of GNI per capita)  \\\n",
       "country                                                                              \n",
       "Algeria                                                      11.8                    \n",
       "Afghanistan                                                   6.4                    \n",
       "Albania                                                      11.3                    \n",
       "American Samoa                                                NaN                    \n",
       "Andorra                                                       NaN                    \n",
       "\n",
       "                ...  \\\n",
       "country         ...   \n",
       "Algeria         ...   \n",
       "Afghanistan     ...   \n",
       "Albania         ...   \n",
       "American Samoa  ...   \n",
       "Andorra         ...   \n",
       "\n",
       "                Unemployment, youth total (% of total labor force ages 15-24) (modeled ILO estimate)  \\\n",
       "country                                                                                                \n",
       "Algeria                                                 29.952999                                      \n",
       "Afghanistan                                              2.639000                                      \n",
       "Albania                                                 30.979000                                      \n",
       "American Samoa                                                NaN                                      \n",
       "Andorra                                                       NaN                                      \n",
       "\n",
       "                Urban population  Urban population (% of total population)  \\\n",
       "country                                                                      \n",
       "Algeria               30670086.0                                    72.629   \n",
       "Afghanistan            9477100.0                                    25.495   \n",
       "Albania                1728969.0                                    60.319   \n",
       "American Samoa           48339.0                                    87.153   \n",
       "Andorra                  67813.0                                    88.062   \n",
       "\n",
       "                Urban population growth (annual %)  \\\n",
       "country                                              \n",
       "Algeria                                   2.804996   \n",
       "Afghanistan                               3.350383   \n",
       "Albania                                   1.317162   \n",
       "American Samoa                           -0.299516   \n",
       "Andorra                                  -0.092859   \n",
       "\n",
       "                Vulnerable employment, female (% of female employment) (modeled ILO estimate)  \\\n",
       "country                                                                                         \n",
       "Algeria                                                 24.337001                               \n",
       "Afghanistan                                             95.573997                               \n",
       "Albania                                                 54.663000                               \n",
       "American Samoa                                                NaN                               \n",
       "Andorra                                                       NaN                               \n",
       "\n",
       "                Vulnerable employment, male (% of male employment) (modeled ILO estimate)  \\\n",
       "country                                                                                     \n",
       "Algeria                                                 27.227001                           \n",
       "Afghanistan                                             85.993001                           \n",
       "Albania                                                 54.994001                           \n",
       "American Samoa                                                NaN                           \n",
       "Andorra                                                       NaN                           \n",
       "\n",
       "                Vulnerable employment, total (% of total employment) (modeled ILO estimate)  \\\n",
       "country                                                                                       \n",
       "Algeria                                                 26.762000                             \n",
       "Afghanistan                                             89.378998                             \n",
       "Albania                                                 54.854000                             \n",
       "American Samoa                                                NaN                             \n",
       "Andorra                                                       NaN                             \n",
       "\n",
       "                Wage and salaried workers, female (% of female employment) (modeled ILO estimate)  \\\n",
       "country                                                                                             \n",
       "Algeria                                                 73.734001                                   \n",
       "Afghanistan                                              4.282000                                   \n",
       "Albania                                                 44.320999                                   \n",
       "American Samoa                                                NaN                                   \n",
       "Andorra                                                       NaN                                   \n",
       "\n",
       "                Wage and salaried workers, male (% of male employment) (modeled ILO estimate)  \\\n",
       "country                                                                                         \n",
       "Algeria                                                 68.160004                               \n",
       "Afghanistan                                             13.292000                               \n",
       "Albania                                                 41.542999                               \n",
       "American Samoa                                                NaN                               \n",
       "Andorra                                                       NaN                               \n",
       "\n",
       "                Wage and salaried workers, total (% of total employment) (modeled ILO estimate)  \n",
       "country                                                                                          \n",
       "Algeria                                                 69.056000                                \n",
       "Afghanistan                                             10.108000                                \n",
       "Albania                                                 42.720001                                \n",
       "American Samoa                                                NaN                                \n",
       "Andorra                                                       NaN                                \n",
       "\n",
       "[5 rows x 209 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "world_bank_data = pd.read_csv(\"world_bank_data.csv\", index_col = 'country')\n",
    "world_bank_data.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are some missing values. For the sake of convenience and of keeping the lab short, we will fill them all with zeros. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "world_bank_data = world_bank_data.fillna(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "Like with PCA, it sometimes makes sense to center and scale our data so that features with higher variance don't dominate the analysis. For example, without standardization, statistics like population will completely dominate features like \"percent of total population that live in urban areas.\" This is because the range of populations is on the order of billions, whereas percentages are always between 0 and 100. The ultimate effect is that many of our columns are not really considered by our clustering algorithm.\n",
    "\n",
    "Below, fit a `cluster.KMeans` object called `kmeans_q4` with four clusters and a `random_state` parameter of 42.\n",
    "\n",
    "Make sure you should use a centered and scaled version of the world bank data. By centered and scaled we mean that the mean in each column should be zero and the variance should be 1.\n",
    "\n",
    "<!--\n",
    "BEGIN QUESTION\n",
    "name: q4\n",
    "-->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "world_bank_data = (world_bank_data - world_bank_data.mean(axis=0)) / world_bank_data.std(axis=0)\n",
    "kmeans_q4 = cluster.KMeans(n_clusters = 4, \n",
    "                           random_state = 42).fit(world_bank_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<p><strong><pre style='display: inline;'>q4</pre></strong> passed!</p>"
      ],
      "text/plain": [
       "q4 results: All test cases passed!"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grader.check(\"q4\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at these new clusters, we see that they seem to correspond to:\n",
    "\n",
    "0: Very small countries.\n",
    "\n",
    "1: Developed countries.\n",
    "\n",
    "2: Less developed countries.\n",
    "\n",
    "3: Huge countries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "labeled_world_bank_data_q4 = pd.Series(kmeans_q4.labels_, \n",
    "                                       name = \"cluster\", \n",
    "                                       index  = world_bank_data.index).to_frame()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['American Samoa',\n",
       " 'Andorra',\n",
       " 'Aruba',\n",
       " 'Bermuda',\n",
       " 'British Virgin Islands',\n",
       " 'Cayman Islands',\n",
       " 'Curacao',\n",
       " 'Dominica',\n",
       " 'Faroe Islands',\n",
       " 'Gibraltar',\n",
       " 'Greenland',\n",
       " 'Isle of Man',\n",
       " 'Kosovo',\n",
       " 'Liechtenstein',\n",
       " 'Marshall Islands',\n",
       " 'Monaco',\n",
       " 'Nauru',\n",
       " 'Northern Mariana Islands',\n",
       " 'Palau',\n",
       " 'San Marino',\n",
       " 'Sint Maarten (Dutch part)',\n",
       " 'St. Kitts and Nevis',\n",
       " 'St. Martin (French part)',\n",
       " 'Turks and Caicos Islands',\n",
       " 'Tuvalu']"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(labeled_world_bank_data_q4.query('cluster == 0').index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Albania',\n",
       " 'Antigua and Barbuda',\n",
       " 'Argentina',\n",
       " 'Armenia',\n",
       " 'Australia',\n",
       " 'Austria',\n",
       " 'Azerbaijan',\n",
       " 'Bahamas, The',\n",
       " 'Bahrain',\n",
       " 'Barbados',\n",
       " 'Belarus',\n",
       " 'Belgium',\n",
       " 'Bosnia and Herzegovina',\n",
       " 'Brazil',\n",
       " 'Brunei Darussalam',\n",
       " 'Bulgaria',\n",
       " 'Canada',\n",
       " 'Channel Islands',\n",
       " 'Chile',\n",
       " 'Colombia',\n",
       " 'Costa Rica',\n",
       " 'Croatia',\n",
       " 'Cuba',\n",
       " 'Cyprus',\n",
       " 'Czech Republic',\n",
       " 'Denmark',\n",
       " 'Dominican Republic',\n",
       " 'El Salvador',\n",
       " 'Estonia',\n",
       " 'Finland',\n",
       " 'France',\n",
       " 'French Polynesia',\n",
       " 'Georgia',\n",
       " 'Germany',\n",
       " 'Greece',\n",
       " 'Grenada',\n",
       " 'Guam',\n",
       " 'Hong Kong SAR, China',\n",
       " 'Hungary',\n",
       " 'Iceland',\n",
       " 'Iran, Islamic Rep.',\n",
       " 'Ireland',\n",
       " 'Israel',\n",
       " 'Italy',\n",
       " 'Jamaica',\n",
       " 'Japan',\n",
       " 'Jordan',\n",
       " 'Kazakhstan',\n",
       " 'Korea, Rep.',\n",
       " 'Kuwait',\n",
       " 'Latvia',\n",
       " 'Lebanon',\n",
       " 'Libya',\n",
       " 'Lithuania',\n",
       " 'Luxembourg',\n",
       " 'Macao SAR, China',\n",
       " 'Malaysia',\n",
       " 'Maldives',\n",
       " 'Malta',\n",
       " 'Mauritius',\n",
       " 'Mexico',\n",
       " 'Moldova',\n",
       " 'Montenegro',\n",
       " 'Netherlands',\n",
       " 'New Caledonia',\n",
       " 'New Zealand',\n",
       " 'North Macedonia',\n",
       " 'Norway',\n",
       " 'Oman',\n",
       " 'Panama',\n",
       " 'Poland',\n",
       " 'Portugal',\n",
       " 'Puerto Rico',\n",
       " 'Qatar',\n",
       " 'Romania',\n",
       " 'Russian Federation',\n",
       " 'Saudi Arabia',\n",
       " 'Serbia',\n",
       " 'Seychelles',\n",
       " 'Singapore',\n",
       " 'Slovak Republic',\n",
       " 'Slovenia',\n",
       " 'South Africa',\n",
       " 'Spain',\n",
       " 'Sri Lanka',\n",
       " 'St. Lucia',\n",
       " 'St. Vincent and the Grenadines',\n",
       " 'Suriname',\n",
       " 'Sweden',\n",
       " 'Switzerland',\n",
       " 'Thailand',\n",
       " 'Trinidad and Tobago',\n",
       " 'Tunisia',\n",
       " 'Turkey',\n",
       " 'Ukraine',\n",
       " 'United Arab Emirates',\n",
       " 'United Kingdom',\n",
       " 'Uruguay',\n",
       " 'Virgin Islands (U.S.)']"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(labeled_world_bank_data_q4.query('cluster == 1').index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Algeria',\n",
       " 'Afghanistan',\n",
       " 'Angola',\n",
       " 'Bangladesh',\n",
       " 'Belize',\n",
       " 'Benin',\n",
       " 'Bhutan',\n",
       " 'Bolivia',\n",
       " 'Botswana',\n",
       " 'Burkina Faso',\n",
       " 'Burundi',\n",
       " 'Cabo Verde',\n",
       " 'Cambodia',\n",
       " 'Cameroon',\n",
       " 'Central African Republic',\n",
       " 'Chad',\n",
       " 'Comoros',\n",
       " 'Congo, Dem. Rep.',\n",
       " 'Congo, Rep.',\n",
       " \"Cote d'Ivoire\",\n",
       " 'Djibouti',\n",
       " 'Ecuador',\n",
       " 'Egypt, Arab Rep.',\n",
       " 'Equatorial Guinea',\n",
       " 'Eritrea',\n",
       " 'Eswatini',\n",
       " 'Ethiopia',\n",
       " 'Fiji',\n",
       " 'Gabon',\n",
       " 'Gambia, The',\n",
       " 'Ghana',\n",
       " 'Guatemala',\n",
       " 'Guinea',\n",
       " 'Guinea-Bissau',\n",
       " 'Guyana',\n",
       " 'Haiti',\n",
       " 'Honduras',\n",
       " 'Indonesia',\n",
       " 'Iraq',\n",
       " 'Kenya',\n",
       " 'Kiribati',\n",
       " 'Korea, Dem. People’s Rep.',\n",
       " 'Kyrgyz Republic',\n",
       " 'Lao PDR',\n",
       " 'Lesotho',\n",
       " 'Liberia',\n",
       " 'Madagascar',\n",
       " 'Malawi',\n",
       " 'Mali',\n",
       " 'Mauritania',\n",
       " 'Micronesia, Fed. Sts.',\n",
       " 'Mongolia',\n",
       " 'Morocco',\n",
       " 'Mozambique',\n",
       " 'Myanmar',\n",
       " 'Namibia',\n",
       " 'Nepal',\n",
       " 'Nicaragua',\n",
       " 'Niger',\n",
       " 'Nigeria',\n",
       " 'Pakistan',\n",
       " 'Papua New Guinea',\n",
       " 'Paraguay',\n",
       " 'Peru',\n",
       " 'Philippines',\n",
       " 'Rwanda',\n",
       " 'Samoa',\n",
       " 'Sao Tome and Principe',\n",
       " 'Senegal',\n",
       " 'Sierra Leone',\n",
       " 'Solomon Islands',\n",
       " 'Somalia',\n",
       " 'South Sudan',\n",
       " 'Sudan',\n",
       " 'Syrian Arab Republic',\n",
       " 'Tajikistan',\n",
       " 'Tanzania',\n",
       " 'Timor-Leste',\n",
       " 'Togo',\n",
       " 'Tonga',\n",
       " 'Turkmenistan',\n",
       " 'Uganda',\n",
       " 'Uzbekistan',\n",
       " 'Vanuatu',\n",
       " 'Venezuela, RB',\n",
       " 'Vietnam',\n",
       " 'West Bank and Gaza',\n",
       " 'Yemen, Rep.',\n",
       " 'Zambia',\n",
       " 'Zimbabwe']"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(labeled_world_bank_data_q4.query('cluster == 2').index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['China', 'India', 'United States']"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(labeled_world_bank_data_q4.query('cluster == 3').index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "---\n",
    "\n",
    "To double-check your work, the cell below will rerun all of the autograder tests."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "q1 results: All test cases passed!\n",
       "\n",
       "q2a results: All test cases passed!\n",
       "\n",
       "q2b results: All test cases passed!\n",
       "\n",
       "q3 results: All test cases passed!\n",
       "\n",
       "q4 results: All test cases passed!"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grader.check_all()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "source": [
    "## Submission\n",
    "\n",
    "Make sure you have run all cells in your notebook in order before running the cell below, so that all images/graphs appear in the output. The cell below will generate a zip file for you to submit. **Please save before exporting!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       ".output_subarea { /* HACK to make tooltips at edge show */\n",
       "    overflow-x: visible\n",
       "}\n",
       ".ellipsis {\n",
       "    background-color:#eee;\n",
       "    color:#666;\n",
       "    border-radius:2px;\n",
       "    cursor:pointer;\n",
       "    padding: 0 5px;\n",
       "}\n",
       ".ellipsis:hover {\n",
       "    background-color:#e3e3e3;\n",
       "    color:#000;\n",
       "}\n",
       ".output_area pre.code-block, .jp-OutputArea pre.code-block {\n",
       "    padding:0.5em 0 0.5em 1em;\n",
       "    margin:0 0 0.25em 0;\n",
       "    border-radius:0.35em;\n",
       "    overflow:visible;\n",
       "    color:#999;\n",
       "    background-color:#f6f6f6;\n",
       "}\n",
       ".variable {\n",
       "    position:relative;\n",
       "    cursor:pointer;\n",
       "    border-bottom:1px solid #666;\n",
       "}\n",
       ".variable:before {\n",
       "  content: attr(data-tooltip); /* here's the magic */\n",
       "  position:absolute;\n",
       "  \n",
       "  /* horizontally center */\n",
       "  left:50%;\n",
       "  transform: translateX(-50%);\n",
       "  \n",
       "  /* move to top */\n",
       "  bottom: 100%;\n",
       "  margin-bottom: 5px; /* and add a small bottom margin */\n",
       "  \n",
       "  /* basic styles */\n",
       "  padding: 7px 10px;\n",
       "  border-radius:2px;\n",
       "  background:#000;\n",
       "  color: #fff;\n",
       "  text-align:center;\n",
       "  \n",
       "  width: max-content; \n",
       "  max-width: 200px;\n",
       "\n",
       "  display:none; /* hide by default */\n",
       "}\n",
       ".variable:hover:before {\n",
       "  display:block;\n",
       "}\n",
       ".variable:after {\n",
       "  content: \"\";\n",
       "  position:absolute;\n",
       "  \n",
       "  /* position tooltip correctly */\n",
       "  transform: translateX(-50%);\n",
       "  left:50%;\n",
       " \n",
       "  /* move to bottom */\n",
       "  bottom:100%;\n",
       "  margin-bottom:-10px;\n",
       " \n",
       "  /* the arrow */\n",
       "  border:10px solid #000;\n",
       "  border-color: black transparent transparent transparent;\n",
       "  \n",
       "  display:none;\n",
       "}\n",
       ".variable:hover {\n",
       "    color:#208FFB;\n",
       "    border-bottom:1px solid #208FFB;\n",
       "}\n",
       ".variable:hover:before, .variable:hover:after {\n",
       "  display:block;\n",
       "}\n",
       ".line {\n",
       "    padding:0;\n",
       "}\n",
       ".output_area .line.highlight, .jp-OutputArea-output .line.highlight {\n",
       "    color:#000;\n",
       "}\n",
       ".output_area pre.meta, .jp-OutputArea-output pre.meta {\n",
       "    padding:5px;\n",
       "    border-radius:2px;\n",
       "    margin:5px 0;\n",
       "}\n",
       ".output_area pre.meta:first-child, .jp-OutputArea-output pre.meta:first-child {\n",
       "    padding-top:0;\n",
       "    margin-top:0;\n",
       "}\n",
       ".lineno {\n",
       "    border-right:1px solid #999;\n",
       "    padding-right:5px;\n",
       "    color:#999;\n",
       "}\n",
       ".highlight .lineno {\n",
       "    color:#000;\n",
       "    border-right:1px solid #000;\n",
       "}\n",
       ".error-container {\n",
       "    padding:0.5em 1em;\n",
       "    border-left:3px solid #eee;\n",
       "}\n",
       ".error-container summary {\n",
       "    list-style: none;\n",
       "    margin-top:0.5em;\n",
       "}\n",
       ".output_area .error-summary, .jp-OutputArea-output .error-summary {\n",
       "    margin-top:1em;\n",
       "}\n",
       "</style>\n",
       "<div class='error-container'>\n",
       "<details><summary><span class=\"ellipsis\">&middot;&middot;&middot;</span></summary>\n",
       "<pre class='meta'><b><span style='color:#60C6C8'>run_code</span></b> in <span style='color:#00A250'>/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/IPython/core/interactiveshell.py</span></pre>\n",
       "<pre class='code-block'>\n",
       "<span class='line'>  <span class='lineno'>3455</span>              if <span class=\"variable\" data-tooltip=\"&lt;ExecutionResult object at 7fddedc142e0, execution_count=32 error_before_exec=None error_in_exec=Expected a notebook file named &#x27;lab14.ipynb&#x27; but no such file found info=&lt;ExecutionInfo object at 7fddedc14190, raw_cell=&quot;# Save your notebook first, then run this cell to ..&quot; store_history=True silent=False shell_futures=True&gt; result=None&gt;\">result</span> is not None:</span>\n",
       "<span class='line'>  <span class='lineno'>3456</span>                  <span class=\"variable\" data-tooltip=\"&lt;ExecutionResult object at 7fddedc142e0, execution_count=32 error_before_exec=None error_in_exec=Expected a notebook file named &#x27;lab14.ipynb&#x27; but no such file found info=&lt;ExecutionInfo object at 7fddedc14190, raw_cell=&quot;# Save your notebook first, then run this cell to ..&quot; store_history=True silent=False shell_futures=True&gt; result=None&gt;\">result</span>.error_in_exec = <span class=\"variable\" data-tooltip=\"ValueError(&quot;Expected a notebook file named &#x27;lab14.ipynb&#x27; but no such file found&quot;)\">value</span></span>\n",
       "<span class='line highlight'>&rightarrow; <span class='lineno'>3457</span>              <span class=\"variable\" data-tooltip=\"&lt;ipykernel.zmqshell.ZMQInteractiveShell object at 0x7fdde9b05340&gt;\">self</span>.CustomTB(<span class=\"variable\" data-tooltip=\"&lt;class &#x27;ValueError&#x27;&gt;\">etype</span>, <span class=\"variable\" data-tooltip=\"ValueError(&quot;Expected a notebook file named &#x27;lab14.ipynb&#x27; but no such file found&quot;)\">value</span>, <span class=\"variable\" data-tooltip=\"&lt;traceback object at 0x7fddedac55c0&gt;\">tb</span>)</span>\n",
       "<span class='line'>  <span class='lineno'>3458</span>          except:</span>\n",
       "<span class='line'>  <span class='lineno'>3459</span>              if <span class=\"variable\" data-tooltip=\"&lt;ExecutionResult object at 7fddedc142e0, execution_count=32 error_before_exec=None error_in_exec=Expected a notebook file named &#x27;lab14.ipynb&#x27; but no such file found info=&lt;ExecutionInfo object at 7fddedc14190, raw_cell=&quot;# Save your notebook first, then run this cell to ..&quot; store_history=True silent=False shell_futures=True&gt; result=None&gt;\">result</span> is not None:</span>\n",
       "</pre>\n",
       "</details>\n",
       "<pre class='meta'><span style='color:#00A250'>/var/folders/3_/jrt9zgs55sdd91gbzjynsk880000gn/T/ipykernel_73887/209285916.py</span></pre>\n",
       "<pre class='code-block'>\n",
       "<span class='line'>  <span class='lineno'>1</span>  # Save your notebook first, then run this cell to export your submission.</span>\n",
       "<span class='line highlight'>&rightarrow; <span class='lineno'>2</span>  <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">grader</span>.export(<span class=\"variable\" data-tooltip=\"&lt;module &#x27;pandas&#x27; from &#x27;/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/pandas/__init__.py&#x27;&gt;\">pd</span>f=False)</span>\n",
       "</pre>\n",
       "<details><summary><span class=\"ellipsis\">&middot;&middot;&middot;</span></summary>\n",
       "<pre class='meta'><b><span style='color:#60C6C8'>colab_only_method</span></b> in <span style='color:#00A250'>/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/otter/check/utils.py</span></pre>\n",
       "<pre class='code-block'>\n",
       "<span class='line'>  <span class='lineno'>95</span>          i<span class=\"variable\" data-tooltip=\"&lt;function logs_event.&lt;locals&gt;.event_logger.&lt;locals&gt;.run_function at 0x7fddeba15430&gt;\">f</span> <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>._colab:</span>\n",
       "<span class='line'>  <span class='lineno'>96</span>              raise RuntimeError(\"This method is not compatible with Google Colab\")</span>\n",
       "<span class='line highlight'>&rightarrow; <span class='lineno'>97</span>          return <span class=\"variable\" data-tooltip=\"&lt;function logs_event.&lt;locals&gt;.event_logger.&lt;locals&gt;.run_function at 0x7fddeba15430&gt;\">f</span>(<span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>, *<span class=\"variable\" data-tooltip=\"()\">args</span>, **kw<span class=\"variable\" data-tooltip=\"()\">args</span>)</span>\n",
       "<span class='line'>  <span class='lineno'>98</span>      return colab_only_method</span>\n",
       "<span class='line'>  <span class='lineno'>99</span>  </span>\n",
       "</pre>\n",
       "<pre class='meta'><b><span style='color:#60C6C8'>run_function</span></b> in <span style='color:#00A250'>/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/otter/check/utils.py</span></pre>\n",
       "<pre class='code-block'>\n",
       "<span class='line'>  <span class='lineno'>129</span>                  except Exception as e:</span>\n",
       "<span class='line'>  <span class='lineno'>130</span>                      <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>._log_event(<span class=\"variable\" data-tooltip=\"&lt;EventType.END_EXPORT: 6&gt;\">event_type</span>, success=False, error=e)</span>\n",
       "<span class='line highlight'>&rightarrow; <span class='lineno'>131</span>                      raise e</span>\n",
       "<span class='line'>  <span class='lineno'>132</span>                  else:</span>\n",
       "<span class='line'>  <span class='lineno'>133</span>                      <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>._log_event(<span class=\"variable\" data-tooltip=\"&lt;EventType.END_EXPORT: 6&gt;\">event_type</span>, results=results, question=question, shelve_env=shelve_env)</span>\n",
       "</pre>\n",
       "<pre class='meta'><b><span style='color:#60C6C8'>run_function</span></b> in <span style='color:#00A250'>/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/otter/check/utils.py</span></pre>\n",
       "<pre class='code-block'>\n",
       "<span class='line'>  <span class='lineno'>129</span>                  except Exception as e:</span>\n",
       "<span class='line'>  <span class='lineno'>130</span>                      <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>._log_event(<span class=\"variable\" data-tooltip=\"&lt;EventType.END_EXPORT: 6&gt;\">event_type</span>, success=False, error=e)</span>\n",
       "<span class='line highlight'>&rightarrow; <span class='lineno'>131</span>                      raise e</span>\n",
       "<span class='line'>  <span class='lineno'>132</span>                  else:</span>\n",
       "<span class='line'>  <span class='lineno'>133</span>                      <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>._log_event(<span class=\"variable\" data-tooltip=\"&lt;EventType.END_EXPORT: 6&gt;\">event_type</span>, results=results, question=question, shelve_env=shelve_env)</span>\n",
       "</pre>\n",
       "<pre class='meta'><b><span style='color:#60C6C8'>export</span></b> in <span style='color:#00A250'>/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/otter/check/notebook.py</span></pre>\n",
       "<pre class='code-block'>\n",
       "<span class='line'>  <span class='lineno'>290</span>          <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>._log_event(EventType.BEGIN_EXPORT)</span>\n",
       "<span class='line'>  <span class='lineno'>291</span>  </span>\n",
       "<span class='line highlight'>&rightarrow; <span class='lineno'>292</span>          <span class=\"variable\" data-tooltip=\"None\">nb_path</span> = <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>._resolve_<span class=\"variable\" data-tooltip=\"None\">nb_path</span>(<span class=\"variable\" data-tooltip=\"None\">nb_path</span>)</span>\n",
       "<span class='line'>  <span class='lineno'>293</span>  </span>\n",
       "<span class='line'>  <span class='lineno'>294</span>          if <span class=\"variable\" data-tooltip=\"False\">force_save</span>:</span>\n",
       "</pre>\n",
       "</details>\n",
       "<pre class='meta'><b><span style='color:#60C6C8'>_resolve_nb_path</span></b> in <span style='color:#00A250'>/usr/local/Caskroom/miniconda/base/envs/mixed/lib/python3.9/site-packages/otter/check/notebook.py</span></pre>\n",
       "<pre class='code-block'>\n",
       "<span class='line'>  <span class='lineno'>132</span>              <span class=\"variable\" data-tooltip=\"&#x27;lab14.ipynb&#x27;\">nb_path</span> = <span class=\"variable\" data-tooltip=\"&lt;otter.check.notebook.Notebook object at 0x7fdde9b494c0&gt;\">self</span>._notebook</span>\n",
       "<span class='line'>  <span class='lineno'>133</span>              if not os.path.isfile(<span class=\"variable\" data-tooltip=\"&#x27;lab14.ipynb&#x27;\">nb_path</span>):</span>\n",
       "<span class='line highlight'>&rightarrow; <span class='lineno'>134</span>                  raise ValueError(f\"Expected a notebook file named '{<span class=\"variable\" data-tooltip=\"&#x27;lab14.ipynb&#x27;\">nb_path</span>}' but no such file found\")</span>\n",
       "<span class='line'>  <span class='lineno'>135</span>  </span>\n",
       "<span class='line'>  <span class='lineno'>136</span>          elif <span class=\"variable\" data-tooltip=\"&#x27;lab14.ipynb&#x27;\">nb_path</span> is None and glob(\"*.ipynb\"):</span>\n",
       "</pre>\n",
       "<pre class='error-summary'><span style='color:#E75C58'>ValueError</span>: Expected a notebook file named 'lab14.ipynb' but no such file found</pre>\n",
       "</div>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Save your notebook first, then run this cell to export your submission.\n",
    "grader.export(pdf=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Create Assignment",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}