KNN_CrossValidation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementing K-Nearest Neighbors algorithm including Cross-Validation\n",
    "## Trail-Test-Validate using Boston dataset\n",
    "\n",
    "##### I implement K-Nearest Neighbors algorithm and cross-validation procedure from scratch. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\nissi\\Anaconda3\\lib\\site-packages\\sklearn\\cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "import IPython\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "import sklearn\n",
    "from sklearn.cross_validation import train_test_split\n",
    "import math as m\n",
    "import operator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ---\n",
    "\n",
    "## Introduction\n",
    "\n",
    "For this project, I will be using the Boston Housing Prices Data Set.  This used to be housed by [UCI Machine Learning Repository](http://archive.ics.uci.edu/ml/datasets/Housing), but it is not housed there any more. You can read about it at [Kaggle](https://www.kaggle.com/vikrishnan/boston-house-prices) and at the [University of Toronto](https://www.cs.toronto.edu/~delve/data/boston/bostonDetail.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Load the Boston dataset\n",
    "from sklearn.datasets import load_boston\n",
    "bdata = load_boston()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following commands will provide some basic information about the shape of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dict_keys(['data', 'target', 'feature_names', 'DESCR'])\n",
      "['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO'\n",
      " 'B' 'LSTAT']\n",
      "(506, 13)\n",
      "(506,)\n"
     ]
    }
   ],
   "source": [
    "print(bdata.keys())\n",
    "print(bdata.feature_names)\n",
    "print(bdata.data.shape)\n",
    "print(bdata.target.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Boston House Prices dataset\n",
      "===========================\n",
      "\n",
      "Notes\n",
      "------\n",
      "Data Set Characteristics:  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive\n",
      "    \n",
      "    :Median Value (attribute 14) is usually the target\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "http://archive.ics.uci.edu/ml/datasets/Housing\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      "**References**\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "   - many more! (see http://archive.ics.uci.edu/ml/datasets/Housing)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# A lengthy description of the dataset\n",
    "print(bdata.DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "##Part 1: Descriptive analysis\n",
    "\n",
    "Before beginning the \"real\" work, let's dig into the data a bit do see what we're dealing with.\n",
    "\n",
    "###1.1: Histogram of housing prices\n",
    "\n",
    "Let's try a basic histogram of median housing prices (the \"target\" variable) for the dataset.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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ZxYckOWu1fQEAAFifveZxkqp6bZLDk9y0qr6c5Jgkh1fVIUk6ydlJfmsetQAA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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c310668438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# prepare your jupyter notebook to work with matplotlib and import the library to something convenient\n",
    "%matplotlib inline  \n",
    "import matplotlib.pyplot as plt  \n",
    "\n",
    "# Plot the histogram and set a bin size\n",
    "plt.figure(figsize=(15,7))\n",
    "plt.hist(bdata.target, bins = np.arange(min(bdata.target), max(bdata.target) + 1, 1), color=\"green\")\n",
    "\n",
    "#Set the axes labels and title\n",
    "plt.xlabel(\"Median Housing Prices x 1000 (USD)\", fontsize = 12)\n",
    "plt.ylabel(\"Frequency\", fontsize = 12)\n",
    "plt.title(\"Histogram of Median Housing Prices\", fontsize = 15)\n",
    "\n",
    "# Get rid of top and right axes\n",
    "ax = plt.axes()\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.spines['top'].set_visible(False)\n",
    "\n",
    "# Show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Median house prices are centered around 20k USD and lower. \n",
    "Comparatively, there are less median house prices between 30k USD and 45k USD."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###1.2: Scatter plot of housing prices and crime\n",
    "\n",
    "Let's use matplotlib to create a scatter plot that shows the relationship between the median value of the home (y-axis) and the per-capita crime rate (x-axis).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Create a dataframe of the data and median home values\n",
    "bdata_df = pd.DataFrame(bdata.data, columns=bdata.feature_names)\n",
    "bdata_df['TARGET'] = bdata.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VdRvZ1AqVDiQbu9isPfaXt3Y8igatBHXcXOec7iILaIrMY1h5HS8n+/BUUmrdbHQ/LCcL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\nL860FpQmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c31069c278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Make a scatter plot of variables and their values\n",
    "plt.figure(figsize=(15,7))\n",
    "plt.scatter(x=bdata_df.CRIM, y=bdata_df.TARGET)\n",
    "\n",
    "#Set the axes labels and title\n",
    "plt.xlabel(\"Per-capita Crime Rate\", fontsize = 12)\n",
    "plt.ylabel(\"Median Housing Prices x 1000 (USD)\", fontsize = 12)\n",
    "plt.title(\"Scatter Plot of Per-capita Crime Rate vs. Median Housing Prices\", fontsize = 15)\n",
    "\n",
    "# Get rid of top and right axes\n",
    "ax = plt.axes()\n",
    "ax.spines['right'].set_visible(False)\n",
    "ax.spines['top'].set_visible(False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Per capita crime rate and median house prices don't seem to have a significant association."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###1.3 Correlation Matrix\n",
    "\n",
    "Let's see the correlation amongst all the features of the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pIyIiOqRgU4ukacDxVD9X7wSukDTH9g1tl15qe/dx3jtqnX7rHYG/2v7awAHb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\nlUqJ3WMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c30fe4bc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# correlation matrix\n",
    "fig = plt.figure(figsize=(15,7))\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "#Set color scale with two extreme colors for correlation plot\n",
    "colormap = plt.get_cmap('bwr')\n",
    "\n",
    "#Create a correlation matrix\n",
    "cax = ax.matshow(bdata_df.corr(), vmin=-1, vmax=1,\n",
    "                 interpolation='none', cmap = colormap)\n",
    "\n",
    "# Draw a colorbar\n",
    "fig.colorbar(cax)\n",
    "# Set the column names to include\n",
    "ticks = np.arange(0,bdata_df.shape[1],1)\n",
    "ax.set_xticks(ticks)\n",
    "ax.set_yticks(ticks)\n",
    "\n",
    "# Set tick names on x and y axes\n",
    "names = list(bdata_df)\n",
    "ax.set_xticklabels(names, rotation = 'vertical')\n",
    "ax.set_yticklabels(names)\n",
    "\n",
    "ax.set_xlabel(\"Correlation matrix among variables in Boston Housing dataset\",\n",
    "              labelpad = 20, fontsize = 12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Correlation matrix shows a high negative correlation between DIS and other variables like INDUS, NOX, AGE and LSTAT.\n",
    "# Variable CHAS is not strongly correlated with any other variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "##Part 2: Experimental Setup\n",
    "\n",
    "The goal of the next few sections is to design an experiment to predict the median home value for an instance in the data.\n",
    "\n",
    "###2.1 Let's begin by writing a function to compute the Root Mean Squared Error for a list of numbers\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Function\n",
    "--------\n",
    "compute_rmse\n",
    "\n",
    "Given two arrays, one of actual values and one of predicted values,\n",
    "compute the Roote Mean Squared Error\n",
    "\n",
    "Parameters\n",
    "----------\n",
    "predictions : array\n",
    "    Array of numerical values corresponding to predictions\n",
    "    for each of the N observations\n",
    "\n",
    "yvalues : array\n",
    "    Array of numerical values corresponding to the actual\n",
    "    values for each of the N observations\n",
    "\n",
    "Returns\n",
    "-------\n",
    "rmse : int\n",
    "    Root Mean Squared Error of the prediction\n",
    "\n",
    "Example\n",
    "-------\n",
    ">>> print compute_rmse((2,2,3),(0,2,6)\n",
    "2.16\n",
    "\"\"\"\n",
    "def compute_rmse(predictions, yvalues):\n",
    "    #print((predictions - yvalues)**2)\n",
    "    rmse = np.sqrt(((predictions - yvalues) ** 2).mean())\n",
    "    return float(rmse)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0816659994661326"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example\n",
    "compute_rmse(np.array([2,2,3]),np.array([0,2,6]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###2.2 Divide the data into training and testing datasets\n",
    "\n",
    "We will randomly select 66% of the data and put this in a training dataset (\"bdata_train\"), and place the remaining 34% in a testing dataset (\"bdata_test\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((506, 14), (333, 14), (173, 14))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(seed=13579)\n",
    "\n",
    "# Use Scikit-learn function to split data\n",
    "bdata_train, bdata_test = train_test_split(bdata_df, train_size=0.66)\n",
    "\n",
    "# Let's see if the split is proper\n",
    "bdata_df.shape, bdata_train.shape, bdata_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###2.3 For starters, let's use a very bad baseline for prediction, and compute RMSE\n",
    "\n",
    "Creating a model that predicts, for every observation x_i, that the median home value is the average (mean) of the median values for all instances in the training set. Compute the RMSE on the training set.  Now compute the RMSE on the test data set (but use the model we trained on the training set!).  \n",
    "What to watch for: How does RMSE compare for training vs. testing datasets?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create a baseline model for predicting median home\n",
    "# value as average of median home values in training dataset\n",
    "def mean_model(m_df):\n",
    "    pred_medv = bdata_train.TARGET.mean()\n",
    "    print(\"Predicted value of median home values is: \", pred_medv)\n",
    "    predictions = np.full(len(m_df), pred_medv)\n",
    "    return predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted value of median home values is:  23.066366366366367\n"
     ]
    }
   ],
   "source": [
    "# Train the above model using training data\n",
    "bdata_train_mean_model_pred = mean_model(bdata_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.430689678794845"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the rmse using predictions of baseline model\n",
    "# and actual values in training dataset\n",
    "compute_rmse(bdata_train_mean_model_pred, bdata_train.TARGET)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted value of median home values is:  23.066366366366367\n"
     ]
    }
   ],
   "source": [
    "# Get the predicted median home values for test dataset\n",
    "bdata_test_mean_model_pred = mean_model(bdata_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.749574189135286"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the rmse using predictions of \n",
    "# baseline model and actual values in test dataset\n",
    "compute_rmse(bdata_test_mean_model_pred, bdata_test.TARGET)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMSE values for both training and test datasets are very close such that the difference between them is not significant. Since the predicted median home values are just average of median home values in training dataset, both RMSEs would be almost equal. Also, the model is not a good one as expected, since RMSE value is higher than KNN model implemented below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "##Part 3: Nearest Neighbors\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###3.1 Nearest Neighbors: Distance function\n",
    "Let's try and build a machine learning algorithm to beat the \"Average Value\" baseline that we computed above.  Soon I will implement the Nearest Neighbor algorithm, but first we need to create a distance metric to measure the distance (and similarity) between two instances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Function\n",
    "--------\n",
    "distance\n",
    "\n",
    "Given two instances and a value for L, \n",
    "return the L-Norm distance between them\n",
    "\n",
    "Parameters\n",
    "----------\n",
    "x1, x2 : array\n",
    "    Array of numerical values corresponding to \n",
    "    predictions for each of the N observations\n",
    "\n",
    "L: int\n",
    "    Value of L to use in computing distances\n",
    "\n",
    "Returns\n",
    "-------\n",
    "dist : int\n",
    "    The L-norm distance between instances\n",
    "\n",
    "Example\n",
    "-------\n",
    ">>> print distance((3,4),(6,8),2)\n",
    "7\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "def distance(x1, x2, L):\n",
    "    # if arrays are not of equal length,\n",
    "    # ignore the extra elements in larger array\n",
    "    if len(x1) != len(x2):\n",
    "        if len(x1) < len(x2):\n",
    "            x2 = x2[:len(x1)]\n",
    "        else:\n",
    "            x1 = x1[:len(x2)]\n",
    "    \n",
    "    # Initialize sum variable with 0\n",
    "    sum=0\n",
    "    \n",
    "    # Find the power sum of corresponding elements\n",
    "    for i in range(0,len(x1)):\n",
    "        sum += ((x1[i]-x2[i])**L)\n",
    "    \n",
    "    # Take L'th root of sum\n",
    "    dist = (sum)**(1/float(L))\n",
    "    \n",
    "    return float(dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 1 - Euclidean distance in 2D\n",
    "distance((3,4), (6,8), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.23906857562847"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example 2\n",
    "distance((5,4,7), (1,8,15), 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's create a function to make a scatterplot using two arrays: predicted and observed value of response variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Function\n",
    "--------\n",
    "plot_obs_pred\n",
    "\n",
    "Plot a scatter plot using two arrays\n",
    "\n",
    "Parameters\n",
    "----------\n",
    "array1, array2 : arrays\n",
    "    Arrays of equal length of numerical values\n",
    "\n",
    "\n",
    "Returns\n",
    "-------\n",
    "N/A\n",
    "\n",
    "Example\n",
    "-------\n",
    ">>> plot_obs_pred(test_data[:,(test_data.shape[1]-1)],\n",
    "        np.asarray(medv_pred))\n",
    "\"\"\"\n",
    "\n",
    "def plot_obs_pred(array1, array2):\n",
    "    \n",
    "    # Plot a scatter plot of arrays\n",
    "    plt.figure(figsize=(15,7))\n",
    "    plt.scatter(array1, array2, color =\"green\")\n",
    "    plt.xlabel(\"Observed Values\", fontsize=12)\n",
    "    plt.ylabel(\"Predicted Values\", fontsize=12)\n",
    "    plt.title(\"Observed vs Predicted Values (X1000 USD)\", fontsize=15)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###3.2 Basic Nearest Neighbor algorithm\n",
    "\n",
    "Let's start the fun now.  Here, I implement a basic nearest neighbor algorithm from scratch. Starting with a simple model that will use two input features (CRIM and RM) and a single output (MEDV).  In other words, I am modelling the relationship between median home value and crime rates and house size.\n",
    "\n",
    "Use the training data (bdata_train) to \"fit\" the model, although as we know, with Nearest Neighbors there is no real training, we just need to keep your training data in memory.  Bellow is a function that predicts, for each instance in the testing data (bdata_test), the median home value using the nearest neighbor algorithm.  Since this is a small dataset, we can simply compare our test instance to every instance in the training set, and return the MEDV value of the closest training instance.  We also have the function take L as an input, where L is passed to the distance function.\n",
    "\n",
    "Furthermore we compute the RMSE for the Nearest Neighbor predictions on the test set, using the Euclidean distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Function\n",
    "--------\n",
    "nneighbor\n",
    "\n",
    "Given training and test data and a value for L,\n",
    "return the predicted median home values\n",
    "\n",
    "Parameters\n",
    "----------\n",
    "training data, test data : array\n",
    "    Array of numerical values corresponding to (N-1)\n",
    "    features and 1 result variable\n",
    "    for both training and test datasets\n",
    "\n",
    "L: int\n",
    "    Value of L to use in computing distances\n",
    "\n",
    "Returns\n",
    "-------\n",
    "medv_pred : array\n",
    "    Array of predicted values for median home prices\n",
    "rmase_nn : float\n",
    "    Value for RMSE between observed and \n",
    "    predicted values for test data\n",
    "\n",
    "Example\n",
    "-------\n",
    ">>> nneighbor(test_data,train_data,2)\n",
    "[20.300000000000001,\n",
    " 25.300000000000001,\n",
    " 14.4,\n",
    " 10.4,\n",
    " 48.299999999999997,\n",
    " 22.0,\n",
    " 23.800000000000001,\n",
    " .....\n",
    " .....\n",
    " ]\n",
    " \n",
    "6.618692249008643\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "import time\n",
    "def nneighbor(train_data, test_data, L):\n",
    "    \n",
    "    # Begin the timer\n",
    "    start_time = time.time()\n",
    "    \n",
    "    # Declare an array to store median home \n",
    "    # value for all instances in test dataset\n",
    "    medv_pred = []\n",
    "    \n",
    "    #########test_first = bdata_test.head(1)\n",
    "    \n",
    "    # Loop through all instances in test dataset\n",
    "    for test_inst in test_data:\n",
    "        \n",
    "        # Declare a variable to store smallest distance,\n",
    "        # thus initialize to infinity\n",
    "        min_dist = np.Inf\n",
    "           \n",
    "        # Loop through entire training dataset for each of the test instances\n",
    "        for train_inst in train_data:\n",
    "            \n",
    "            # Get Euclidean distance between test and training instance\n",
    "            dist = distance(test_inst[:-1], train_inst[:-1], L)\n",
    "            \n",
    "            # Check if current distance is minimum between test instance\n",
    "            # and training instance. If yes, store it as new minimum distance\n",
    "            # and corresponding median home value as the prediction\n",
    "            if dist < min_dist:\n",
    "                min_dist = dist\n",
    "                pred_value = train_inst[-1]\n",
    "        \n",
    "        # Append predicted median home value\n",
    "        medv_pred.append(pred_value)\n",
    "    \n",
    "    # Stop the timer and print the time taken\n",
    "    print(\"Time taken: \" + str(round(time.time() - start_time,2)) + \" seconds\")\n",
    "    \n",
    "    # Compute RMSE for predicted and test values\n",
    "    rmase_nn = compute_rmse(np.asarray(medv_pred),\n",
    "                            test_data[:,(test_data.shape[1]-1)])\n",
    "    \n",
    "    return medv_pred, rmase_nn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 0.23 seconds\n",
      "Root Mean Square Error for the basic KNN model: 6.681010099809551\n"
     ]
    },
    {
     "data": {
      "image/png": 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BYxUUpXhHjNA/Lulfwp8v144nc/ebw2qFOyyYcPrLCrrYP1jSce7+7HDVt0q6yMzerSDh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\nGsec4h7FRpEdAOg/cQu0rE4jGADlML1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c30fe205c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Without normalization\n",
    "train_data = bdata_train[['CRIM','RM','TARGET']].values\n",
    "test_data = bdata_test[['CRIM','RM','TARGET']].values\n",
    "\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,2)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###3.3 Results and Normalization\n",
    "\n",
    "We did not really normalized our features - a big no-no with Nearest Neighbor algorithms.  Let's write a generic normalization function that takes as input an array of values for a given feature, and returns the normalized array (subtract the mean and divide by the standard deviation).\n",
    "\n",
    "Then we re-run the Nearest Neighbor algorithm on the normalized dataset (still just using CRIM and RM as input), and compare the RMSE from this method with your previous RMSE evaluations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Function to normalize each column of input array\n",
    "# using the column's mean and standard deviation\n",
    "\"\"\"\n",
    "Function\n",
    "--------\n",
    "normalize\n",
    "\n",
    " Takes as input an array of values for a given feature,\n",
    " and returns the normalized array \n",
    " (subtract the mean and divide by the standard deviation).\n",
    "\n",
    "Parameters\n",
    "----------\n",
    "data : array\n",
    "    Array of numerical values\n",
    "\n",
    "Returns\n",
    "-------\n",
    "data : array\n",
    "    normalized array\n",
    "\n",
    "Example\n",
    "-------\n",
    ">>> normalize(bdata_train[['ZN','AGE','TARGET']].values)\n",
    "array([[ -3.81161053e-01,  -8.13382747e-01,   1.87000000e+01],\n",
    "       [ -3.80561354e-01,  -2.43503114e-01,   2.33000000e+01],\n",
    "       [ -2.66918872e-01,  -1.84170516e+00,   1.53000000e+01],\n",
    "       .....\n",
    "       .....\n",
    "       ]\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "def normalize(data):\n",
    "    # For each column, normalize each value\n",
    "    for k in range(0,data.shape[1]-1):\n",
    "        data[:,k] = (data[:,k]-data[:,k].mean())/(data[:,k].std())\n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 0.24 seconds\n",
      "Root Mean Square Error for the basic KNN model: 6.800973238751911\n"
     ]
    },
    {
     "data": {
      "image/png": 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pMFHQ/LZ5laZKSYcWK5LeaLhOADoxd086hq5MT0/74uJi0mEAAIABqixVNLcw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\nkjRChj1JkiRJGiHDniRJkiSN0L8Bym1v0UzpcbIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c30fe6f898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# With normalization\n",
    "train_data = normalize(bdata_train[['CRIM','RM','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['CRIM','RM','TARGET']].values)\n",
    "\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,2)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###3.4 Optimization\n",
    "\n",
    "A lot of the decisions we've made so far have been arbitrary.  Let's try to increase the performance of our nearest neighbor algorithm by adding features that we think might be relevant, and by using different values of L in the distance function. Let's also try a few different combinations of features and L!\n",
    "\n",
    "What to look out for: What combination of features and distance function provide the lowest RMSE?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 1 using ZN, AGE and L=2\n",
      "Time taken: 0.23 seconds\n",
      "Root Mean Square Error for the basic KNN model: 10.254298407894627\n"
     ]
    },
    {
     "data": {
      "image/png": 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pkk6S9ExJL4ojKABoVTePiygOFzW1aUpDA0MymYYGhjS1aSqxbpCtJGa91rsi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\nIWm5pPsl7d3o54uSFtV9f5d0SG3fSNI5khZIWip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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c31056f5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 2 using NOX, LSTAT and L=2\n",
      "Time taken: 0.29 seconds\n",
      "Root Mean Square Error for the basic KNN model: 5.990623694936551\n"
     ]
    },
    {
     "data": {
      "image/png": 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gh0j2AAAAACCHIiV7ZrbezI4I/+41s7PNbJOZkSwCAAAAQAZFTda+IOm48O9x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\nSrIXERERERHRhZLsRUREREREdKH/AG8fPE/nmrzjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c310580ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 3 using CRIM, RM, NOX, LSTAT and L=2\n",
      "Time taken: 0.47 seconds\n",
      "Root Mean Square Error for the basic KNN model: 4.129192561975384\n"
     ]
    },
    {
     "data": {
      "image/png": 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AaTCyfqQrkrtSSY9XbOT4SccMAFnAmD0AADIu6fGKjRw/6ZgBIAtI9gAAyLik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\nD6W9330AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c30fd04c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 4 using 'CRIM','RM','NOX','CHAS','LSTAT' and L=2\n",
      "Time taken: 0.53 seconds\n",
      "Root Mean Square Error for the basic KNN model: 4.084285406682177\n"
     ]
    },
    {
     "data": {
      "image/png": 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BUYqPRAj9S5L+Ifz6Tvl4Mne/K6xWeK4FE05/R0EX+8dLeo67vzjc9IOSLjKz8xQkvM/W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\n0YWS7EVERERERHShJHsRERERERFd6D8ixRWLDWoOOgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c310760d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 5 using 'CRIM','RM','NOX','RAD','LSTAT' and L=2\n",
      "Time taken: 0.52 seconds\n",
      "Root Mean Square Error for the basic KNN model: 4.014280865491604\n"
     ]
    },
    {
     "data": {
      "image/png": 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Zgq6CJyooSvGOCKF/UtLbwsdXK8eTufstYbXC8yyYcPqrCrrY/5Gkk939L8NN3yzpIjO7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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3106b0eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 6 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=4\n",
      "Time taken: 0.49 seconds\n",
      "Root Mean Square Error for the basic KNN model: 4.116665691574307\n"
     ]
    },
    {
     "data": {
      "image/png": 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XwZMUFKV4R4TQPyXpbeHX1yvHk7n7TWG1wvMtmHD66wq62N9P0inu/tRw07dIusjMLlCQ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\ng3rCzUcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3104b5dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 7 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=2\n",
      "Time taken: 0.39 seconds\n",
      "Root Mean Square Error for the basic KNN model: 3.9949100563569018\n"
     ]
    },
    {
     "data": {
      "image/png": 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M9A3oyA1H6p7996zathfuY9+uvjVjFqWgxXPlvJUUIgKQJgq0AABQIUutNElL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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c30fd10dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model 8 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=8\n",
      "Time taken: 0.4 seconds\n",
      "Root Mean Square Error for the basic KNN model: 3.8597373297071993\n"
     ]
    },
    {
     "data": {
      "image/png": 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+2jEDQB4wZg8AgJxLe7xiM8dPO2YAyAOSPQAAci7tqpLNHD/tmAEgD0j2AADI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\nyV5EREREREQXSrIXERERERHRhf4DVT31SGiH59IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3104faef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use ZN and AGE as features\n",
    "train_data = normalize(bdata_train[['ZN','AGE','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['ZN','AGE','TARGET']].values)\n",
    "print(\"Model 1 using ZN, AGE and L=2\")\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,2)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))\n",
    "\n",
    "# Use NOX and LSTAT as features\n",
    "train_data = normalize(bdata_train[['NOX','LSTAT','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['NOX','LSTAT','TARGET']].values)\n",
    "print(\"Model 2 using NOX, LSTAT and L=2\")\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,2)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))\n",
    "\n",
    "# Model 3 using CRIM, RM, NOX, LSTAT and L=2\n",
    "train_data = normalize(bdata_train[['CRIM','RM','NOX','LSTAT','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['CRIM','RM','NOX','LSTAT','TARGET']].values)\n",
    "print(\"Model 3 using CRIM, RM, NOX, LSTAT and L=2\")\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,2)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))\n",
    "\n",
    "# Model 4 using 'CRIM','RM','NOX','CHAS','LSTAT' and L=2\n",
    "train_data = normalize(bdata_train[['CRIM','RM','NOX','CHAS','LSTAT','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['CRIM','RM','NOX','CHAS','LSTAT','TARGET']].values)\n",
    "print(\"Model 4 using 'CRIM','RM','NOX','CHAS','LSTAT' and L=2\")\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,2)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))\n",
    "\n",
    "# Model 5 using 'CRIM','RM','NOX','RAD','LSTAT','TARGET' and L=2\n",
    "train_data = normalize(bdata_train[['CRIM','RM','NOX','RAD','LSTAT','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['CRIM','RM','NOX','RAD','LSTAT','TARGET']].values)\n",
    "print(\"Model 5 using 'CRIM','RM','NOX','RAD','LSTAT' and L=2\")\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,2)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))\n",
    "\n",
    "# Model 8 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=4\n",
    "train_data = normalize(bdata_train[['CRIM','RM','NOX','CHAS','RAD','LSTAT','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['CRIM','RM','NOX','CHAS','RAD','LSTAT','TARGET']].values)\n",
    "print(\"Model 6 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=4\")\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,4)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))\n",
    "\n",
    "# Model 8 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=2\n",
    "train_data = normalize(bdata_train[['CRIM','RM','NOX','CHAS','RAD','LSTAT','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['CRIM','RM','NOX','CHAS','RAD','LSTAT','TARGET']].values)\n",
    "print(\"Model 7 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=2\")\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,2)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))\n",
    "\n",
    "# Model 8 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=8\n",
    "train_data = normalize(bdata_train[['CRIM','RM','NOX','CHAS','RAD','LSTAT','TARGET']].values)\n",
    "test_data = normalize(bdata_test[['CRIM','RM','NOX','CHAS','RAD','LSTAT','TARGET']].values)\n",
    "print(\"Model 8 using 'CRIM','RM','NOX','CHAS','RAD','LSTAT' and L=8\")\n",
    "medv_pred, rmase_nn = nneighbor(train_data,test_data,8)\n",
    "print('Root Mean Square Error for the basic KNN model:', rmase_nn)\n",
    "# Plot the observed and predicted values on a scatter plot\n",
    "plot_obs_pred(test_data[:,(test_data.shape[1]-1)], np.asarray(medv_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model 8 which uses 'CRIM','RM','NOX','CHAS','RAD','LSTAT' features and L=8 gives best RMSE of 3.85. Increasing the number of dimensions (features) and increasing the value of L increases the time taken to run through the algorithm as expected. It is because more dimensions need more computations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.5 Cross-Validation\n",
    "\n",
    "The more we tinkered with your features and distance function, the higher the risk that you overfit your training data. To prevent this sort of overfitting, we need to use cross-validation.\n",
    "\n",
    "Let's use 10-fold cross-validation and see the average RMSE for Nearest Neighbors using Euclidean distance with CRIM and RM input features, as well as the total running time for the full run of 10 folds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Function\n",
    "--------\n",
    "cross_validation\n",
    "\n",
    " Takes as input a dataset, a value for L, a value for K,\n",
    " type of algorhtm (basicKNN or KNN), return the \n",
    " RMSE value and runtime for execution\n",
    "\n",
    "Parameters\n",
    "----------\n",
    "data : array\n",
    "    Array of numerical values\n",
    "\n",
    "Returns\n",
    "-------\n",
    "RMSE:\n",
    "    RMSE value\n",
    "runtime:\n",
    "    Time taken for execution\n",
    "\n",
    "Example\n",
    "-------\n",
    ">>> cross_validation(normalize(bdata_df[['CRIM','RM','TARGET']].values),2,3,\"basic_knn\")\n",
    "Total Time taken for cross-validation:  0.85  seconds\n",
    "Mean RMSE:  7.458960636085439\n",
    "\n",
    "\"\"\"\n",
    "def cross_validation(data,L,K,algorithm):\n",
    "    \n",
    "    np.random.seed(seed=13579)\n",
    "    np.random.shuffle(data)\n",
    "    total_rmse = 0\n",
    "    \n",
    "    # Begin the timer\n",
    "    start_time = time.time()\n",
    "    \n",
    "    # Loop through 10 times, selecting different test (1 part) \n",
    "    # and training (9 parts) datasets for each iteration\n",
    "    for i in range(10):\n",
    "        test_range = range(int((i/10.0)*data.shape[0]),\n",
    "                           int(((i+1)/10.0)*data.shape[0]))\n",
    "        test = data[test_range,:]\n",
    "        train = np.delete(data,test_range,0)\n",
    "        if algorithm.lower() == \"basic_knn\":\n",
    "            medv_pred, rmse = nneighbor(train,test,L)\n",
    "        if algorithm.lower() == \"knn\":\n",
    "            medv_pred, rmse, runtime = knn(train,test,L,K)\n",
    "            #print(\"Not implemented yet\")\n",
    "        \n",
    "        total_rmse += rmse\n",
    "    \n",
    "    # Stop the timer and calculate runtime\n",
    "    runtime = str(round(time.time() - start_time,2))\n",
    "    \n",
    "    # Get the avarage of RMSE total\n",
    "    mean_rmse = total_rmse/10\n",
    "    \n",
    "    return mean_rmse, runtime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 0.11 seconds\n",
      "Time taken: 0.09 seconds\n",
      "Time taken: 0.08 seconds\n",
      "Time taken: 0.09 seconds\n",
      "Time taken: 0.1 seconds\n",
      "Time taken: 0.08 seconds\n",
      "Time taken: 0.08 seconds\n",
      "Time taken: 0.1 seconds\n",
      "Time taken: 0.08 seconds\n",
      "Time taken: 0.08 seconds\n",
      "Total Time taken for cross-validation:  0.89  seconds\n",
      "Mean RMSE:  7.458960636085439\n"
     ]
    }
   ],
   "source": [
    "# Use 10-fold cross validation for CRIM and RM\n",
    "# features using the basic Nearest Neighbors model.\n",
    "mean_rmse, runtime = cross_validation(normalize(bdata_df[['CRIM','RM','TARGET']].values),\n",
    "                                      2,3,\"basic_knn\")\n",
    "# Stop the timer and print the time taken\n",
    "print(\"Total Time taken for cross-validation: \",runtime,\" seconds\")\n",
    "print(\"Mean RMSE: \", mean_rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Total time taken for above process is 0.95 seconds, which is more than the time taken without using cross-validation, since we are repeating the process 10 times."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###3.6 K-Nearest Neighbors Algorithm\n",
    "\n",
    "Finally, let us implement the K-Nearest Neighbors algorithm.  Using 10-fold cross validation, let's see the RMSE for K=3 and the running time of the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Function\n",
    "--------\n",
    "knn\n",
    "\n",
    " Takes as input training and test datasets,\n",
    " a value for L, a value for K,\n",
    " return the predicted median home values, RMSE and time taken.\n",
    "\n",
    "Parameters\n",
    "----------\n",
    "train_data : array\n",
    "    Array of numerical values\n",
    "test_data : array\n",
    "    Array of numerical values\n",
    "\n",
    "Returns\n",
    "-------\n",
    "med_pred : array\n",
    "    predictions of median home values\n",
    "rmse_knn:\n",
    "    RMSE value\n",
    "runtime:\n",
    "    time taken for execution\n",
    "\n",
    "Example\n",
    "-------\n",
    ">>> knn(train,test,L,K)\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "def knn(train_data, test_data, L, K):\n",
    "    \n",
    "    # Begin the timer\n",
    "    stime = time.time()\n",
    "    medv_pred = []\n",
    "    \n",
    "    # Loop for each instance in test data\n",
    "    for test_inst in test_data:\n",
    "            neighbors = []\n",
    "            # Loop for each instance in training data\n",
    "            for train_inst in train_data:\n",
    "                # Get Eucledian distance\n",
    "                dist = distance(train_inst[:-1],test_inst[:-1],L)\n",
    "                # Append median home value and distance to list\n",
    "                neighbors.append((train_inst[train_inst.shape[0]-1], dist))\n",
    "            # Sort based on distance in ascending order\n",
    "            neighbors.sort(key = operator.itemgetter(1),reverse = False)\n",
    "            # Take average of median house values based on K\n",
    "            medv_pred.append(np.mean(neighbors[0:K],axis = 0))\n",
    "    medv_pred = np.array(medv_pred)\n",
    "    runtime = np.round(time.time()-stime,2)\n",
    "    \n",
    "    # Get RMSE\n",
    "    rmse_knn = compute_rmse(test_data[:,(test_data.shape[1]-1)],medv_pred[:,0])\n",
    "    \n",
    "    return medv_pred, rmse_knn, runtime\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 1.0 seconds\n",
      "RMSE using 10-fold cross-validation for K=3: 5.563119270931979\n"
     ]
    }
   ],
   "source": [
    "# Use KNN with K=3 and cross validation for predicting median home values using CRIM and RM featues.\n",
    "\n",
    "mean_rmse, runtime = cross_validation(normalize(bdata_df[['CRIM','RM','TARGET']].values),2,3,\"knn\")\n",
    "print(\"Time taken:\", runtime, \"seconds\")\n",
    "print(\"RMSE using 10-fold cross-validation for K=3:\", mean_rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###3.7 Using cross validation to find K\n",
    "\n",
    "What is the best choice of K?  Let's compute the RMSE for values of K between 1 and 25 using 10-fold cross-validation. Let us use the following features in your model: CRIM, ZN, RM, AGE, DIS, TAX."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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DQWyrK5UUpNNsrKph9sqtTBhYyPB+PTv0AR55qWhnXXCp6KsnjCFfl4qkg/SX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\npIWSgoiItPj/bFpqP42qlmwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c31001b470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Declare a list to store RMSE values and corresponding K value\n",
    "rmse_k = []\n",
    "# K starts from 1\n",
    "k = 1\n",
    "\n",
    "# For each value of K, perform cross-validation \n",
    "# on 6 features to predict median house values\n",
    "# using KNN and L = 2 \n",
    "for i in range(1,26):\n",
    "    mean_rmse, runtime = cross_validation(normalize(\n",
    "        bdata_df[['CRIM','ZN','RM','AGE','DIS','TAX','TARGET']].values)\n",
    "                                          ,2,i,'knn')\n",
    "    rmse_k.append((k,mean_rmse))\n",
    "    k += 1   \n",
    "# Make an array from the list of tuples\n",
    "rmse_k = np.asarray(rmse_k)\n",
    "\n",
    "# Plot RMSE values and corresponding K values\n",
    "plt.xticks(np.arange(min(rmse_k[:,0]), max(rmse_k[:,0])+1, 1.0))\n",
    "plt.plot(rmse_k[:,0],rmse_k[:,1])\n",
    "plt.xlabel(\"K Values\")\n",
    "plt.ylabel(\"RMSE Values\")\n",
    "plt.title(\"RMSE vs K values for L=2\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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FNCmoar57XyAi04ExwF5JQUQOBp4ATnKvC+1vPVNw9jeQm5vr/8DuRpblSbVr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\nqWNJwRhjTB1LCsYYY+r8Pw05IRZJbYOFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3104ef8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Declare a list to store RMSE values and corresponding K value\n",
    "rmse_k = []\n",
    "# K starts from 1\n",
    "k = 1\n",
    "\n",
    "# For each value of K, perform cross-validation \n",
    "# on 6 features to predict median house values\n",
    "# using KNN and L = 6\n",
    "for i in range(1,26):\n",
    "    mean_rmse, runtime = cross_validation(normalize(\n",
    "        bdata_df[['CRIM','ZN','RM','AGE','DIS','TAX','TARGET']].values),\n",
    "                                          6,i,'knn')\n",
    "    rmse_k.append((k,mean_rmse))\n",
    "    k += 1   \n",
    "# Make an array from the list of tuples\n",
    "rmse_k = np.asarray(rmse_k)\n",
    "\n",
    "# Plot RMSE values and corresponding K values\n",
    "plt.xticks(np.arange(min(rmse_k[:,0]), max(rmse_k[:,0])+1, 1.0))\n",
    "plt.plot(rmse_k[:,0],rmse_k[:,1])\n",
    "plt.xlabel(\"K Values\")\n",
    "plt.ylabel(\"RMSE Values\")\n",
    "plt.title(\"RMSE vs K values for L=6\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the graph, RMSE value decreases and K increases at first and then goes on increasing. Also, choosing a higher K value means more calculations, so K should be chosen reasonably. I found K=4 to be ideal since it has the lowest RMSE value. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}