diff --git a/labs/2019/lab7_clustering_sol.ipynb b/labs/2019/lab7_clustering_sol.ipynb
new file mode 100644
index 0000000..61fafbe
--- /dev/null
+++ b/labs/2019/lab7_clustering_sol.ipynb
@@ -0,0 +1,992 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Lab 7: Clustering\n",
+    "In this lab we'll try to get a better sense of all the clustering algorithms discussed in class. One of the many reasons to cluster is that it can help us better understand our data beyond looking at dsitributions of individual variables. To that end, we'll also get some more practice with data visualization techniques that may be helpful for your projects and future data analysis.\n",
+    "\n",
+    "Before we jump into using real data, we'll use a toy dataset."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import seaborn as sns\n",
+    "import pandas as pd\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We'll begin by messing around the Iris dataset, which is a fairly easy, small 3-way classification dataset. The dataset consists of 150 irises that each fall into one of 3 classes(Setosa, Versicolour, and Virginica). Each iris comes with 4 features: sepal length, sepal width, petal length, and petal width."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 155,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
+      "['setosa' 'versicolor' 'virginica']\n"
+     ]
+    }
+   ],
+   "source": [
+    "from sklearn.datasets import load_iris\n",
+    "data = load_iris()\n",
+    "# x is a n*4 matrix\n",
+    "x = data.data\n",
+    "# y is a size-n vector\n",
+    "y = data.target\n",
+    "print(data.feature_names)\n",
+    "print(data.target_names)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 156,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['target_names', 'data', 'target', 'DESCR', 'feature_names']"
+      ]
+     },
+     "execution_count": 156,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "data.keys()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 157,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "there are 150 samples\n",
+      "(array([[ 5.1,  3.5,  1.4,  0.2],\n",
+      "       [ 4.9,  3. ,  1.4,  0.2],\n",
+      "       [ 4.7,  3.2,  1.3,  0.2],\n",
+      "       [ 4.6,  3.1,  1.5,  0.2],\n",
+      "       [ 5. ,  3.6,  1.4,  0.2],\n",
+      "       [ 5.4,  3.9,  1.7,  0.4],\n",
+      "       [ 4.6,  3.4,  1.4,  0.3],\n",
+      "       [ 5. ,  3.4,  1.5,  0.2],\n",
+      "       [ 4.4,  2.9,  1.4,  0.2],\n",
+      "       [ 4.9,  3.1,  1.5,  0.1]]), array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
+      "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
+      "       0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
+      "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
+      "       1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
+      "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
+      "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]))\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(\"there are {} samples\".format(len(x)))\n",
+    "print(x[:10],y)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "To get a better sense of the distributions of the data. Let's first plot histograms of each of the four features:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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FrJacsHqymnO8VktOWD1Zx5FzlCmXm4CD+x4/FLhllDCSpKUbpdD/CzgsyfcmuRdwEnDR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\nhS5JjbDQJakRFrokNeL/AV3iFlq94rNyAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4ce833a90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4ce833f10>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c7c44fd0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c7be61d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# YOUR CODE HERE\n",
+    "for i,feature in enumerate(data.feature_names):\n",
+    "    plt.hist(x[:,i])\n",
+    "    plt.title(feature)\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "From the names of the features, it probably makes most sense to scatter the sepal length vs the sepal width and the petal length vs petal width. Use plt.scatter to visualize "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Make a dataframe out of the data to make it easier to do filtering/grouping operations later\n",
+    "col_names = ['sep_len', 'sep_wid', 'pet_len', 'pet_wid']\n",
+    "df = pd.DataFrame(data.data)\n",
+    "df.rename(columns=lambda x: col_names[x], inplace=True)\n",
+    "df['target'] = data.target"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5,1,u'sepal length vs sepal width')"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c7ba4950>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Scatter the sep_len vs sep_wid\n",
+    "# YOUR CODE HERE\n",
+    "# This is what the scatter plot should look like:\n",
+    "plt.scatter(df.sep_len, df.sep_wid)\n",
+    "plt.title(\"sepal length vs sepal width\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0.5,1,u'petal length vs petal width')"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c7bcdfd0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Scatter the pet_len vs pet_wid\n",
+    "# YOUR CODE HERE\n",
+    "# This is what the scatter plot should look like:\n",
+    "plt.scatter(df.pet_len, df.pet_wid)\n",
+    "plt.title(\"petal length vs petal width\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "It may be hard to see anything interesting from just monochromatic scatter plots. Let's color in the datapoints according to their class. Hint: try grouping by the target value and then do plt.scatter on each group with different colors."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "# Write a function to plot a scatter plot of two columns of a dataframe that color points\n",
+    "# according to their class.\n",
+    "# YOUR CODE HERE\n",
+    "\n",
+    "groups = df.groupby('target')\n",
+    "\n",
+    "# Plot\n",
+    "fig, ax = plt.subplots()\n",
+    "for name_idx, group in groups:\n",
+    "    ax.scatter(group.sep_len, group.sep_wid, label=data.target_names[name_idx])\n",
+    "ax.legend()\n",
+    "plt.title(\"sepal length vs sepal width\")\n",
+    "plt.show()\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "for name_idx, group in groups:\n",
+    "    ax.scatter(group.pet_len, group.pet_wid, label=data.target_names[name_idx])\n",
+    "ax.legend()\n",
+    "plt.title(\"petal length vs petal width\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "metadata": {
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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pS5+n/vgmN7FL7rnWf/t5fT76nFsdexYC6NeeD1518PnoBx9IX/o89cc3uYnd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\nE0OW3I0xJob+P42ZxdutB+ibAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c59211d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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ly5fzne98h29+85vMmTOHGTNmcPvtt1NeXo6ZMXr0aP793/+dUaNGMXToUIYPH84777zD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\nrkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c5921e90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# This is what the output should look like:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "From the plots, its clear that we can easily cluster the data into 3 clusters. Let's see if KMeans and Meanshift can recover these clusters."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## KMeans\n",
+    "Now that we have a good sense of what the Iris dataset looks like, we'll try running a few clustering algorithms on the data starting with KMeans.\n",
+    "Ref: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html\n",
+    "\n",
+    "Run KMeans with n_clusters = 2, 3, 4 plot a color coded(according to the cluster value) scatter plot for petal length vs petal width(or any two features of your choice). You should be able to modify the function you wrote above to color the datapoints according to its cluster value."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 92,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "from sklearn.cluster import KMeans, MeanShift, DBSCAN\n",
+    "X = df[['pet_len','pet_wid']]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 78,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+CMD6zds4+5p7ANzgzax0vFsmp/NX3/98Yx+ybfsg56++v6CKzMwac3PPacPm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\nrkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c5a00450>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c5c18050>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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iVMvcA4wHBgNvAdcADQDufquZXQL8I7AZ2Ahc7u5Pd7VjVcuIiBSvZHXu7n5O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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c5c180d0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "pd.options.mode.chained_assignment = None\n",
+    "\n",
+    "for n_clusters in [2,3,4]:\n",
+    "    kmeans = KMeans(n_clusters=n_clusters).fit(X)\n",
+    "    X['pred_label'] = pd.Series(kmeans.labels_)\n",
+    "\n",
+    "    groups = X.groupby('pred_label')\n",
+    "\n",
+    "    # Plot\n",
+    "    fig, ax = plt.subplots()\n",
+    "    for pred_class, group in groups:\n",
+    "        ax.scatter(group.pet_len, group.pet_wid, label=pred_class)\n",
+    "    ax.legend()\n",
+    "    plt.title(\"sepal length vs sepal width with {} classes\".format(n_clusters))\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## MeanShift\n",
+    "Use MeanShift to cluster the data points. Remember that the bandwidth parameter of MeanShift determines how much to weigh the neighbors of each point when cluster centroids are recomputed. Vary the bandwidth parameter from very low to very high and see how the clustering changes. As with KMeans, plot a color coded scatter plot."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 98,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4bcdeb710>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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5YpDGvPyeZ3h5/SZGjxjMl4/bf/vwJKZNm8a0adMSL0ckjZLmzeOYs2QONz9z8/bn23zb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\nLiKSQ/8f9BvFtUvlTB8AAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c59d8f10>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7fd4c58ffb90>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "for bandwidth in [0.4,0.6,1.2]:\n",
+    "    X = df[['pet_len','pet_wid']]\n",
+    "    meanshift = MeanShift(bandwidth=bandwidth).fit(X)\n",
+    "    X['pred_label'] = pd.Series(meanshift.labels_)\n",
+    "\n",
+    "    groups = X.groupby('pred_label')\n",
+    "\n",
+    "    # Plot\n",
+    "    fig, ax = plt.subplots()\n",
+    "    for pred_class, group in groups:\n",
+    "        ax.scatter(group.pet_len, group.pet_wid, label=pred_class)\n",
+    "    ax.legend()\n",
+    "    plt.title(\"sepal length vs sepal width with bandwidth {}\".format(bandwidth))\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### DBSCAN\n",
+    "The last clustering algorithm we'll explore in today's lab is dbscan.\n",
+    "Ref: http://scikit-learn.org/stable/modules/generated/sklearn.cluster.dbscan.html\n",
+    "dbscan has many parameters that you can set but we will mostly be concerned with:\n",
+    "- eps: max distance \n",
+    "- min_samples: minimum number of points within a neighborhood of a point for it to be considered a \"core\" point\n",
+    "\n",
+    "Run DBScan with varying epsilon and min_sample values to get a sense of how they affect the resulting clusters. First fix the min_sample values and vary epsilon to see how epsilon affects the clustering. Then use the epsilon that gave the \"best\" results and vary the min_sample values. Plot the color coded scatter plots as we did for KMeans and MeanShift. How do the clusters look as eps and min_samples are varied?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Applying Clustering to Real Data\n",
+    "The Iris dataset is a super simple dataset but served us well in better understanding kmeans, meanshift and dbscan. Let's now apply these clustering techniques to real data. For this we'll use the credit-loan dataset from assignment 2."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "PersonID                                41016\n",
+      "SeriousDlqin2yrs                        41016\n",
+      "RevolvingUtilizationOfUnsecuredLines    41016\n",
+      "age                                     41016\n",
+      "zipcode                                 41016\n",
+      "NumberOfTime30-59DaysPastDueNotWorse    41016\n",
+      "DebtRatio                               41016\n",
+      "MonthlyIncome                           33042\n",
+      "NumberOfOpenCreditLinesAndLoans         41016\n",
+      "NumberOfTimes90DaysLate                 41016\n",
+      "NumberRealEstateLoansOrLines            41016\n",
+      "NumberOfTime60-89DaysPastDueNotWorse    41016\n",
+      "NumberOfDependents                      39979\n",
+      "dtype: int64\n"
+     ]
+    }
+   ],
+   "source": [
+    "loan_df = pd.read_csv('../data/credit-data.csv')\n",
+    "print(loan_df.count())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Prepping the Data\n",
+    "Before we do any sort of clustering, we need to prep the data a bit. Use the functions you'e written for your ML pipeline to clean the data, deal with missing values. We'll also get rid of the categorical features(PersonID and zipcode) - why shouldn't we include these two features when clustering on this data?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "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>RevolvingUtilizationOfUnsecuredLines</th>\n",
+       "      <th>age</th>\n",
+       "      <th>NumberOfTime30-59DaysPastDueNotWorse</th>\n",
+       "      <th>DebtRatio</th>\n",
+       "      <th>NumberOfOpenCreditLinesAndLoans</th>\n",
+       "      <th>NumberOfTimes90DaysLate</th>\n",
+       "      <th>NumberRealEstateLoansOrLines</th>\n",
+       "      <th>NumberOfTime60-89DaysPastDueNotWorse</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>55</td>\n",
+       "      <td>0</td>\n",
+       "      <td>505.000000</td>\n",
+       "      <td>2</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0.547745</td>\n",
+       "      <td>71</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0.459565</td>\n",
+       "      <td>7</td>\n",
+       "      <td>0</td>\n",
+       "      <td>2</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>0.044280</td>\n",
+       "      <td>51</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0.014520</td>\n",
+       "      <td>5</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>0.914249</td>\n",
+       "      <td>55</td>\n",
+       "      <td>4</td>\n",
+       "      <td>0.794875</td>\n",
+       "      <td>12</td>\n",
+       "      <td>0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>0.026599</td>\n",
+       "      <td>45</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0.049966</td>\n",
+       "      <td>4</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   RevolvingUtilizationOfUnsecuredLines  age  \\\n",
+       "0                              1.000000   55   \n",
+       "1                              0.547745   71   \n",
+       "2                              0.044280   51   \n",
+       "3                              0.914249   55   \n",
+       "4                              0.026599   45   \n",
+       "\n",
+       "   NumberOfTime30-59DaysPastDueNotWorse   DebtRatio  \\\n",
+       "0                                     0  505.000000   \n",
+       "1                                     0    0.459565   \n",
+       "2                                     0    0.014520   \n",
+       "3                                     4    0.794875   \n",
+       "4                                     0    0.049966   \n",
+       "\n",
+       "   NumberOfOpenCreditLinesAndLoans  NumberOfTimes90DaysLate  \\\n",
+       "0                                2                        0   \n",
+       "1                                7                        0   \n",
+       "2                                5                        0   \n",
+       "3                               12                        0   \n",
+       "4                                4                        0   \n",
+       "\n",
+       "   NumberRealEstateLoansOrLines  NumberOfTime60-89DaysPastDueNotWorse  \n",
+       "0                             0                                     0  \n",
+       "1                             2                                     0  \n",
+       "2                             0                                     0  \n",
+       "3                             3                                     0  \n",
+       "4                             0                                     0  "
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Do any necessary preprocessing: fill nans, drop rows if needed, etc\n",
+    "# For simplicity, simply drop PersonID, zipcode, MonthlyIncome and NumberOfDependents. \n",
+    "# also remember to drop the label SeriousDlqin2yrs \n",
+    "df = loan_df.drop(['PersonID', 'zipcode', 'MonthlyIncome','NumberOfDependents', 'SeriousDlqin2yrs'], axis=1)\n",
+    "df.dropna()\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "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>0</th>\n",
+       "      <th>1</th>\n",
+       "      <th>2</th>\n",
+       "      <th>3</th>\n",
+       "      <th>4</th>\n",
+       "      <th>5</th>\n",
+       "      <th>6</th>\n",
+       "      <th>7</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>0.000045</td>\n",
+       "      <td>0.386364</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>4.724704e-03</td>\n",
+       "      <td>0.035714</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.00000</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>0.000025</td>\n",
+       "      <td>0.568182</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>4.299618e-06</td>\n",
+       "      <td>0.125000</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.06250</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>0.000002</td>\n",
+       "      <td>0.340909</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>1.358502e-07</td>\n",
+       "      <td>0.089286</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.00000</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>0.000042</td>\n",
+       "      <td>0.386364</td>\n",
+       "      <td>0.040816</td>\n",
+       "      <td>7.436728e-06</td>\n",
+       "      <td>0.214286</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.09375</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>0.000001</td>\n",
+       "      <td>0.272727</td>\n",
+       "      <td>0.000000</td>\n",
+       "      <td>4.674778e-07</td>\n",
+       "      <td>0.071429</td>\n",
+       "      <td>0.0</td>\n",
+       "      <td>0.00000</td>\n",
+       "      <td>0.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "          0         1         2             3         4    5        6    7\n",
+       "0  0.000045  0.386364  0.000000  4.724704e-03  0.035714  0.0  0.00000  0.0\n",
+       "1  0.000025  0.568182  0.000000  4.299618e-06  0.125000  0.0  0.06250  0.0\n",
+       "2  0.000002  0.340909  0.000000  1.358502e-07  0.089286  0.0  0.00000  0.0\n",
+       "3  0.000042  0.386364  0.040816  7.436728e-06  0.214286  0.0  0.09375  0.0\n",
+       "4  0.000001  0.272727  0.000000  4.674778e-07  0.071429  0.0  0.00000  0.0"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Normalize the columns\n",
+    "from sklearn import preprocessing\n",
+    "\n",
+    "x = df.values #returns a numpy array\n",
+    "min_max_scaler = preprocessing.MinMaxScaler()\n",
+    "x_scaled = min_max_scaler.fit_transform(x)\n",
+    "df = pd.DataFrame(x_scaled)\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Now apply any of the three clustering algorithms from above on the data."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Do some clustering with kmeans/meanshift/dbscan\n",
+    "from sklearn.cluster import DBSCAN\n",
+    "dbscan = DBSCAN(eps=0.5, min_samples=10).fit(df)\n",
+    "pred_labels = pd.Series(dbscan.labels_)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Counter({0: 40902, 1: 114})"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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4c8FGJ0makxnDoaquGVCe9h/wqroZuHlAfQ+wZ0D9Bf7fZSlJ0knAT0hLkjoMB0lSh+Eg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\nSeowHCRJHYaDJKnDcJAkdRgOkqSO/wvWgzli3/owtAAAAABJRU5ErkJggg==\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f7b718d8350>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from collections import Counter\n",
+    "plt.hist(pred_labels)\n",
+    "Counter(pred_labels)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We'd like to visualize the clusters just as we did for the Iris Dataset, but we can't realy visualize 9 dimensions. So instead, we'll use PCA to project our data onto a 2-dimensional subspace and then plot our 2-d points. Before we do PCA, also make sure to normalize the columns!  If we don't normalize, a column like MonthlyIncome will completely drown out all the other columns which almost all have values in the range 0-10."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.collections.PathCollection at 0x7f7b71860990>"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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TYo1LKpSCQZqgACgodJl9MQV2qz6jFZ+twDCDpXm6r6cGsH7z7oon6vGJSdZv3j11vrww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\nKDCIiEiEAoOIiEQoMIiISMT/B2tuj5icjl95AAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f7b71894350>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from sklearn.decomposition import PCA\n",
+    "# Run PCA to get a 2-dimensional projection of the data\n",
+    "pca = PCA(n_components=2)\n",
+    "X=df\n",
+    "pca.fit(X)\n",
+    "projection = pca.transform(X)\n",
+    "plt.scatter(projection[:,0], projection[:,1])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(6620, 34396)\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.collections.PathCollection at 0x7f7b71945f50>"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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MMgRBanXOaCYREakyc0/sDqhrbW1t3tHRUetsiEitPLUOHrsRDu6EyXPghHPgue8PPT/r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\nFBhERCRGgUFERGL+f8vGU021/nXbAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7f7b71f9a690>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "dlq_filter = (loan_df.SeriousDlqin2yrs==1)\n",
+    "1.*sum(dlq_filter)/len(dlq_filter)\n",
+    "\n",
+    "dlq_group = projection[dlq_filter]\n",
+    "not_dlq_group = projection[~dlq_filter]\n",
+    "print(len(dlq_group),len(not_dlq_group))\n",
+    "plt.scatter(dlq_group[:,0], dlq_group[:,1])\n",
+    "plt.scatter(not_dlq_group[:,0], not_dlq_group[:,1])\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Scatter the 2-dimensional projected datapoints color coded by cluster value and then do the same plot except color coded by their SeriousDlqin2yrs value. Try to reuse some of the functions you've written for the previous part of of the lab.\n",
+    "\n",
+    "It can be hard to see any coherent pattern when there is so much data. Here are some ways around this:\n",
+    "- Plot a smaller subset of the data\n",
+    "- Plot different classes/clusters of the data separately(but using shared axes) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Food for thought\n",
+    "- Does it matter if you perform clustering and then PCA or PCA then clustering?\n",
+    "- How can we better select the parameters in our clustering algorithms? "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.14"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 1
+}