4.- K - Nearest Neighbors.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-Nearest Neighbors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The nearest neighbors algorithm is part of a family of algorithms that are known as lazy learners. These types of learners do not\n",
    "build a model, which means they do not really do any learning.\n",
    "Instead, they simply refer to the training data during the prediction\n",
    "phase in order to assign labels to unlabeled data. Lazy learners are\n",
    "also referred to as instance-based learners or rote learners due to \n",
    "their heavy reliance on the training set. Despite the simplicity of\n",
    "lazy learners, such as the k-nearest neighbors approach, they are\n",
    "powerful in dealing with difficult-to-understand data that have a\n",
    "large number of features with a large number of instances of fairly\n",
    "similar class. \n",
    "\n",
    "The k-nearest neighbors method is premised on the basic idea that things that are similar\n",
    "are likely to have properties that are similar. Therefore, to assign a class to new data,\n",
    "we first find k instances of existing data that are as similar as possible (nearest neighbors)\n",
    "to the new data. Then, we use the labels of those nearest neighbors to predict the\n",
    "label of the new data.\n",
    "\n",
    "## Dataset Heart Desease\n",
    "\n",
    "As we explore the nearest neighbors algorithm in this chapter, we will use a dataset\n",
    "containing information about patients with and without heart disease. This dataset was\n",
    "initially gathered for use by researchers at four medical institutions in the United States,\n",
    "Switzerland, and Hungary and is made available to the data science community through\n",
    "the University of California at Irvine’s Machine Learning Repository\n",
    "\n",
    "The dataset includes a variety of medical data for our analysis:\n",
    "- $age$ is the age, in years, of the patient.\n",
    "- $sex$ is the biological sex of the patient.\n",
    "- $painType$ describes the type of chest pain, if any, reported by the patient. The\n",
    "options for this variable are: Typical angina, Atypical angina, Nonanginal pain, and  Asymptomatic (no pain).\n",
    "- $restingBP$ is the patient’s systolic blood pressure at rest, measured in millimeters\n",
    "of mercury.\n",
    "- $cholesterol$ is the patient’s total cholesterol, measured in milligrams per liter.\n",
    "- $highBloodSugar$ is a logical value indicating whether the patient has a fasting\n",
    "blood sugar reading greater than 120 milligrams per deciliter.\n",
    "- $restingECG$ is a categorical variable providing an interpretation of the patient’s\n",
    "resting electrocardiographic results. The possible values are: Normal, Hypertrophy, WaveAbnormality.\n",
    "- $exerciseAngina$ is a logical value indicating whether the patient experiences\n",
    "exercise-induced angina.\n",
    "- $STdepression$ is a numeric evaluation of the patient’s degree of ST depression,\n",
    "an electrocardiogram finding related to heart disease.\n",
    "- $STslope$ is a categorical value describing the slope of the patient’s ST segment on\n",
    "an electrocardiogram. It may have these values: Downsloping, Flat, Upsloping.\n",
    "- $coloredVessels$ is the number of major vessels that appear colored when subjected\n",
    "to fluoroscopy. This value ranges from 0 to 3.\n",
    "- $defectType$ is a categorical value describing a defect identified in the patient’s\n",
    "heart. It may have these values: Normal, ReversibleDefect, FixedDefect.\n",
    "- $heartDisease$ is the variable we are trying to predict. It is a logical value that is\n",
    "TRUE if the patient suffers from heart disease and FALSE if he or she does not.\n",
    "\n",
    "\n",
    "## k-Nearest Neighbors\n",
    "The k-nearest neighbors method is premised on the basic idea that things that are similar\n",
    "are likely to have properties that are similar. Therefore, to assign a class to new data,\n",
    "we first find k instances of existing data that are as similar as possible (nearest neighbors)\n",
    "to the new data. Then, we use the labels of those nearest neighbors to predict the\n",
    "label of the new data.\n",
    "\n",
    "To illustrate how k-NN works, let’s attempt to deal with the problem we introduced\n",
    "in the previous section. Our goal is to use the existing set of patient records to predict\n",
    "whether a new patient is likely to suffer from heart disease or not. To keep things simple,\n",
    "let’s limit our analysis to only two of the predictor variables in our dataset: age and cholesterol. Our class variable is heartDisease.\n",
    "\n",
    "Now, consider a hypothetical 45-year-old new patient with a cholesterol level of 225.\n",
    "Based on their cholesterol level and age alone, how could we determine whether they\n",
    "suffer from heart disease or not? Using the k-nearest neighbors approach, the first thing\n",
    "we do is find the k most similar patients to our new patient in our dataset. These are the\n",
    "nearest neighbors to our new patient. Then, we assign the label of the most common\n",
    "class among the neighbors to our new patient. To illustrate this approach, we add a new\n",
    "data point to our previous scatterplot that represents the new patient.\n",
    "\n",
    "![title](images/ima1.png)\n",
    "\n",
    "If k is set to 1, we identify the one existing data point that is closest to our new data\n",
    "point. By visual inspection, we can see that this is either patient 11 or patient 9. Let’s\n",
    "assume that it is patient 9. This patient does not suffer from heart disease. Therefore, we\n",
    "will classify our new patient as also not suffering from heart disease. However, if k were\n",
    "set to 3, the three nearest neighbors to our new patient are patients 9, 11, and 5. Since\n",
    "the most common class among these three patients is TRUE for heart disease, then we\n",
    "would classify our new patient as suffering from heart disease as well.\n",
    "\n",
    "To quantify the distance between two points, the k-nearest neighbors\n",
    "algorithm uses a distance function that works for data with more than two dimensions.\n",
    "This measure is known as Euclidean distance.\n",
    "\n",
    "Euclidean distance is the straight-line distance between the coordinates of two points\n",
    "in multidimensional space. Mathematically, we define the Euclidean distance between\n",
    "two points p and q as follows:\n",
    "\n",
    "$$ dist(p,q) = \\sqrt{(p_1 - q_1)^2 + (p_2 - q_2)^2 + .... + (p_n - q_n)^2}$$\n",
    "\n",
    "\n",
    "## References:\n",
    "\n",
    "\n",
    "-- Practical Machine Learning in R, First Edition. Fred Nwanganga and Mike Chapple."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pros\n",
    "-  Very simple.\n",
    "- Training is trivial.\n",
    "- Works with any number of classes.\n",
    "- Easy to add more data.\n",
    "- Few parametres: K, distance mretic.\n",
    "\n",
    "## Cons\n",
    "- High prediction cost\n",
    "- Not good for high dimensional data.\n",
    "- Categorical Feature don't work well.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical example with R"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install.packages(\"caTools\")\n",
    "library(\"ISLR\")\n",
    "library(\"caTools\")\n",
    "library(\"dplyr\")\n",
    "library(\"class\") # knn\n",
    "library(\"ggplot2\")\n",
    "options(repr.plot.width = 16, repr.plot.height = 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'data.frame':\t5822 obs. of  86 variables:\n",
      " $ MOSTYPE : num  33 37 37 9 40 23 39 33 33 11 ...\n",
      " $ MAANTHUI: num  1 1 1 1 1 1 2 1 1 2 ...\n",
      " $ MGEMOMV : num  3 2 2 3 4 2 3 2 2 3 ...\n",
      " $ MGEMLEEF: num  2 2 2 3 2 1 2 3 4 3 ...\n",
      " $ MOSHOOFD: num  8 8 8 3 10 5 9 8 8 3 ...\n",
      " $ MGODRK  : num  0 1 0 2 1 0 2 0 0 3 ...\n",
      " $ MGODPR  : num  5 4 4 3 4 5 2 7 1 5 ...\n",
      " $ MGODOV  : num  1 1 2 2 1 0 0 0 3 0 ...\n",
      " $ MGODGE  : num  3 4 4 4 4 5 5 2 6 2 ...\n",
      " $ MRELGE  : num  7 6 3 5 7 0 7 7 6 7 ...\n",
      " $ MRELSA  : num  0 2 2 2 1 6 2 2 0 0 ...\n",
      " $ MRELOV  : num  2 2 4 2 2 3 0 0 3 2 ...\n",
      " $ MFALLEEN: num  1 0 4 2 2 3 0 0 3 2 ...\n",
      " $ MFGEKIND: num  2 4 4 3 4 5 3 5 3 2 ...\n",
      " $ MFWEKIND: num  6 5 2 4 4 2 6 4 3 6 ...\n",
      " $ MOPLHOOG: num  1 0 0 3 5 0 0 0 0 0 ...\n",
      " $ MOPLMIDD: num  2 5 5 4 4 5 4 3 1 4 ...\n",
      " $ MOPLLAAG: num  7 4 4 2 0 4 5 6 8 5 ...\n",
      " $ MBERHOOG: num  1 0 0 4 0 2 0 2 1 2 ...\n",
      " $ MBERZELF: num  0 0 0 0 5 0 0 0 1 0 ...\n",
      " $ MBERBOER: num  1 0 0 0 4 0 0 0 0 0 ...\n",
      " $ MBERMIDD: num  2 5 7 3 0 4 4 2 1 3 ...\n",
      " $ MBERARBG: num  5 0 0 1 0 2 1 5 8 3 ...\n",
      " $ MBERARBO: num  2 4 2 2 0 2 5 2 1 3 ...\n",
      " $ MSKA    : num  1 0 0 3 9 2 0 2 1 1 ...\n",
      " $ MSKB1   : num  1 2 5 2 0 2 1 1 1 2 ...\n",
      " $ MSKB2   : num  2 3 0 1 0 2 4 2 0 1 ...\n",
      " $ MSKC    : num  6 5 4 4 0 4 5 5 8 4 ...\n",
      " $ MSKD    : num  1 0 0 0 0 2 0 2 1 2 ...\n",
      " $ MHHUUR  : num  1 2 7 5 4 9 6 0 9 0 ...\n",
      " $ MHKOOP  : num  8 7 2 4 5 0 3 9 0 9 ...\n",
      " $ MAUT1   : num  8 7 7 9 6 5 8 4 5 6 ...\n",
      " $ MAUT2   : num  0 1 0 0 2 3 0 4 2 1 ...\n",
      " $ MAUT0   : num  1 2 2 0 1 3 1 2 3 2 ...\n",
      " $ MZFONDS : num  8 6 9 7 5 9 9 6 7 6 ...\n",
      " $ MZPART  : num  1 3 0 2 4 0 0 3 2 3 ...\n",
      " $ MINKM30 : num  0 2 4 1 0 5 4 2 7 2 ...\n",
      " $ MINK3045: num  4 0 5 5 0 2 3 5 2 3 ...\n",
      " $ MINK4575: num  5 5 0 3 9 3 3 3 1 3 ...\n",
      " $ MINK7512: num  0 2 0 0 0 0 0 0 0 1 ...\n",
      " $ MINK123M: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ MINKGEM : num  4 5 3 4 6 3 3 3 2 4 ...\n",
      " $ MKOOPKLA: num  3 4 4 4 3 3 5 3 3 7 ...\n",
      " $ PWAPART : num  0 2 2 0 0 0 0 0 0 2 ...\n",
      " $ PWABEDR : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PWALAND : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PPERSAUT: num  6 0 6 6 0 6 6 0 5 0 ...\n",
      " $ PBESAUT : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PMOTSCO : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PVRAAUT : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PAANHANG: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PTRACTOR: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PWERKT  : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PBROM   : num  0 0 0 0 0 0 0 3 0 0 ...\n",
      " $ PLEVEN  : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PPERSONG: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PGEZONG : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PWAOREG : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PBRAND  : num  5 2 2 2 6 0 0 0 0 3 ...\n",
      " $ PZEILPL : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PPLEZIER: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PFIETS  : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PINBOED : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ PBYSTAND: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AWAPART : num  0 2 1 0 0 0 0 0 0 1 ...\n",
      " $ AWABEDR : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AWALAND : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ APERSAUT: num  1 0 1 1 0 1 1 0 1 0 ...\n",
      " $ ABESAUT : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AMOTSCO : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AVRAAUT : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AAANHANG: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ ATRACTOR: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AWERKT  : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ ABROM   : num  0 0 0 0 0 0 0 1 0 0 ...\n",
      " $ ALEVEN  : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ APERSONG: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AGEZONG : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AWAOREG : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ ABRAND  : num  1 1 1 1 1 0 0 0 0 1 ...\n",
      " $ AZEILPL : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ APLEZIER: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AFIETS  : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ AINBOED : num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ ABYSTAND: num  0 0 0 0 0 0 0 0 0 0 ...\n",
      " $ Purchase: Factor w/ 2 levels \"No\",\"Yes\": 1 1 1 1 1 1 1 1 1 1 ...\n"
     ]
    }
   ],
   "source": [
    "str(Caravan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>No</dt><dd>5474</dd><dt>Yes</dt><dd>348</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[No] 5474\n",
       "\\item[Yes] 348\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "No\n",
       ":   5474Yes\n",
       ":   348\n",
       "\n"
      ],
      "text/plain": [
       "  No  Yes \n",
       "5474  348 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(Caravan$Purchase)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "FALSE"
      ],
      "text/latex": [
       "FALSE"
      ],
      "text/markdown": [
       "FALSE"
      ],
      "text/plain": [
       "[1] FALSE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# check NA values\n",
    "any(is.na(Caravan))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "x <- Caravan %>% select(-Purchase)\n",
    "y <- Caravan %>% select(Purchase)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Standarization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "# standarization\n",
    "x.standarized  <- scale(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Train test split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(123)\n",
    "split <- sample.split(y, SplitRatio=0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "# \n",
    "x_train <- subset(x.standarized, split=TRUE)\n",
    "x_test <- subset(x.standarized, split=FALSE)\n",
    "# target\n",
    "y_train <- subset(y, split=TRUE) %>% pull()\n",
    "y_test <- subset(y, split=FALSE) %>% pull()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> knn() function\n",
    "\n",
    "arguments:\n",
    "\n",
    "- train\t: matrix or data frame of training set cases.\n",
    "\n",
    "- test : matrix or data frame of test set cases. A vector will be interpreted as a row vector for a single case.\n",
    "\n",
    "- cl : factor of true classifications of training set.\n",
    "    \n",
    "- k\t: number of neighbours considered."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred <- knn(train=x_train, test= x_test, cl=y_train, k=3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 87</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>MOSTYPE</th><th scope=col>MAANTHUI</th><th scope=col>MGEMOMV</th><th scope=col>MGEMLEEF</th><th scope=col>MOSHOOFD</th><th scope=col>MGODRK</th><th scope=col>MGODPR</th><th scope=col>MGODOV</th><th scope=col>MGODGE</th><th scope=col>MRELGE</th><th scope=col>...</th><th scope=col>AGEZONG</th><th scope=col>AWAOREG</th><th scope=col>ABRAND</th><th scope=col>AZEILPL</th><th scope=col>APLEZIER</th><th scope=col>AFIETS</th><th scope=col>AINBOED</th><th scope=col>ABYSTAND</th><th scope=col>Purchase</th><th scope=col>Purchase.pred</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>...</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td> 0.68084775</td><td>-0.2725565</td><td> 0.4066617</td><td>-1.21685949</td><td> 0.7793384</td><td>-0.6942510</td><td> 0.2174254</td><td>-0.06870474</td><td>-0.1618019</td><td> 0.42763309</td><td>...</td><td>-0.08104764</td><td>-0.05991487</td><td> 0.764905</td><td>-0.02270383</td><td>-0.07364394</td><td>-0.1506075</td><td>-0.08734022</td><td>-0.1188063</td><td>No</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>2</th><td> 0.99221162</td><td>-0.2725565</td><td>-0.8594262</td><td>-1.21685949</td><td> 0.7793384</td><td> 0.3025256</td><td>-0.3653787</td><td>-0.06870474</td><td> 0.4641188</td><td>-0.09606902</td><td>...</td><td>-0.08104764</td><td>-0.05991487</td><td> 0.764905</td><td>-0.02270383</td><td>-0.07364394</td><td>-0.1506075</td><td>-0.08734022</td><td>-0.1188063</td><td>No</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>3</th><td> 0.99221162</td><td>-0.2725565</td><td>-0.8594262</td><td>-1.21685949</td><td> 0.7793384</td><td>-0.6942510</td><td>-0.3653787</td><td> 0.91409379</td><td> 0.4641188</td><td>-1.66717535</td><td>...</td><td>-0.08104764</td><td>-0.05991487</td><td> 0.764905</td><td>-0.02270383</td><td>-0.07364394</td><td>-0.1506075</td><td>-0.08734022</td><td>-0.1188063</td><td>No</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>-1.18733547</td><td>-0.2725565</td><td> 0.4066617</td><td> 0.01075374</td><td>-0.9708962</td><td> 1.2993023</td><td>-0.9481828</td><td> 0.91409379</td><td> 0.4641188</td><td>-0.61977113</td><td>...</td><td>-0.08104764</td><td>-0.05991487</td><td> 0.764905</td><td>-0.02270383</td><td>-0.07364394</td><td>-0.1506075</td><td>-0.08734022</td><td>-0.1188063</td><td>No</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>5</th><td> 1.22573452</td><td>-0.2725565</td><td> 1.6727497</td><td>-1.21685949</td><td> 1.4794323</td><td> 0.3025256</td><td>-0.3653787</td><td>-0.06870474</td><td> 0.4641188</td><td> 0.42763309</td><td>...</td><td>-0.08104764</td><td>-0.05991487</td><td> 0.764905</td><td>-0.02270383</td><td>-0.07364394</td><td>-0.1506075</td><td>-0.08734022</td><td>-0.1188063</td><td>No</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>-0.09756193</td><td>-0.2725565</td><td>-0.8594262</td><td>-2.44447272</td><td>-0.2708024</td><td>-0.6942510</td><td> 0.2174254</td><td>-1.05150327</td><td> 1.0900394</td><td>-3.23828168</td><td>...</td><td>-0.08104764</td><td>-0.05991487</td><td>-1.014271</td><td>-0.02270383</td><td>-0.07364394</td><td>-0.1506075</td><td>-0.08734022</td><td>-0.1188063</td><td>No</td><td>No</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 87\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & MOSTYPE & MAANTHUI & MGEMOMV & MGEMLEEF & MOSHOOFD & MGODRK & MGODPR & MGODOV & MGODGE & MRELGE & ... & AGEZONG & AWAOREG & ABRAND & AZEILPL & APLEZIER & AFIETS & AINBOED & ABYSTAND & Purchase & Purchase.pred\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ... & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <fct> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 &  0.68084775 & -0.2725565 &  0.4066617 & -1.21685949 &  0.7793384 & -0.6942510 &  0.2174254 & -0.06870474 & -0.1618019 &  0.42763309 & ... & -0.08104764 & -0.05991487 &  0.764905 & -0.02270383 & -0.07364394 & -0.1506075 & -0.08734022 & -0.1188063 & No & No\\\\\n",
       "\t2 &  0.99221162 & -0.2725565 & -0.8594262 & -1.21685949 &  0.7793384 &  0.3025256 & -0.3653787 & -0.06870474 &  0.4641188 & -0.09606902 & ... & -0.08104764 & -0.05991487 &  0.764905 & -0.02270383 & -0.07364394 & -0.1506075 & -0.08734022 & -0.1188063 & No & No\\\\\n",
       "\t3 &  0.99221162 & -0.2725565 & -0.8594262 & -1.21685949 &  0.7793384 & -0.6942510 & -0.3653787 &  0.91409379 &  0.4641188 & -1.66717535 & ... & -0.08104764 & -0.05991487 &  0.764905 & -0.02270383 & -0.07364394 & -0.1506075 & -0.08734022 & -0.1188063 & No & No\\\\\n",
       "\t4 & -1.18733547 & -0.2725565 &  0.4066617 &  0.01075374 & -0.9708962 &  1.2993023 & -0.9481828 &  0.91409379 &  0.4641188 & -0.61977113 & ... & -0.08104764 & -0.05991487 &  0.764905 & -0.02270383 & -0.07364394 & -0.1506075 & -0.08734022 & -0.1188063 & No & No\\\\\n",
       "\t5 &  1.22573452 & -0.2725565 &  1.6727497 & -1.21685949 &  1.4794323 &  0.3025256 & -0.3653787 & -0.06870474 &  0.4641188 &  0.42763309 & ... & -0.08104764 & -0.05991487 &  0.764905 & -0.02270383 & -0.07364394 & -0.1506075 & -0.08734022 & -0.1188063 & No & No\\\\\n",
       "\t6 & -0.09756193 & -0.2725565 & -0.8594262 & -2.44447272 & -0.2708024 & -0.6942510 &  0.2174254 & -1.05150327 &  1.0900394 & -3.23828168 & ... & -0.08104764 & -0.05991487 & -1.014271 & -0.02270383 & -0.07364394 & -0.1506075 & -0.08734022 & -0.1188063 & No & No\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 87\n",
       "\n",
       "| <!--/--> | MOSTYPE &lt;dbl&gt; | MAANTHUI &lt;dbl&gt; | MGEMOMV &lt;dbl&gt; | MGEMLEEF &lt;dbl&gt; | MOSHOOFD &lt;dbl&gt; | MGODRK &lt;dbl&gt; | MGODPR &lt;dbl&gt; | MGODOV &lt;dbl&gt; | MGODGE &lt;dbl&gt; | MRELGE &lt;dbl&gt; | ... ... | AGEZONG &lt;dbl&gt; | AWAOREG &lt;dbl&gt; | ABRAND &lt;dbl&gt; | AZEILPL &lt;dbl&gt; | APLEZIER &lt;dbl&gt; | AFIETS &lt;dbl&gt; | AINBOED &lt;dbl&gt; | ABYSTAND &lt;dbl&gt; | Purchase &lt;fct&gt; | Purchase.pred &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 |  0.68084775 | -0.2725565 |  0.4066617 | -1.21685949 |  0.7793384 | -0.6942510 |  0.2174254 | -0.06870474 | -0.1618019 |  0.42763309 | ... | -0.08104764 | -0.05991487 |  0.764905 | -0.02270383 | -0.07364394 | -0.1506075 | -0.08734022 | -0.1188063 | No | No |\n",
       "| 2 |  0.99221162 | -0.2725565 | -0.8594262 | -1.21685949 |  0.7793384 |  0.3025256 | -0.3653787 | -0.06870474 |  0.4641188 | -0.09606902 | ... | -0.08104764 | -0.05991487 |  0.764905 | -0.02270383 | -0.07364394 | -0.1506075 | -0.08734022 | -0.1188063 | No | No |\n",
       "| 3 |  0.99221162 | -0.2725565 | -0.8594262 | -1.21685949 |  0.7793384 | -0.6942510 | -0.3653787 |  0.91409379 |  0.4641188 | -1.66717535 | ... | -0.08104764 | -0.05991487 |  0.764905 | -0.02270383 | -0.07364394 | -0.1506075 | -0.08734022 | -0.1188063 | No | No |\n",
       "| 4 | -1.18733547 | -0.2725565 |  0.4066617 |  0.01075374 | -0.9708962 |  1.2993023 | -0.9481828 |  0.91409379 |  0.4641188 | -0.61977113 | ... | -0.08104764 | -0.05991487 |  0.764905 | -0.02270383 | -0.07364394 | -0.1506075 | -0.08734022 | -0.1188063 | No | No |\n",
       "| 5 |  1.22573452 | -0.2725565 |  1.6727497 | -1.21685949 |  1.4794323 |  0.3025256 | -0.3653787 | -0.06870474 |  0.4641188 |  0.42763309 | ... | -0.08104764 | -0.05991487 |  0.764905 | -0.02270383 | -0.07364394 | -0.1506075 | -0.08734022 | -0.1188063 | No | No |\n",
       "| 6 | -0.09756193 | -0.2725565 | -0.8594262 | -2.44447272 | -0.2708024 | -0.6942510 |  0.2174254 | -1.05150327 |  1.0900394 | -3.23828168 | ... | -0.08104764 | -0.05991487 | -1.014271 | -0.02270383 | -0.07364394 | -0.1506075 | -0.08734022 | -0.1188063 | No | No |\n",
       "\n"
      ],
      "text/plain": [
       "  MOSTYPE     MAANTHUI   MGEMOMV    MGEMLEEF    MOSHOOFD   MGODRK    \n",
       "1  0.68084775 -0.2725565  0.4066617 -1.21685949  0.7793384 -0.6942510\n",
       "2  0.99221162 -0.2725565 -0.8594262 -1.21685949  0.7793384  0.3025256\n",
       "3  0.99221162 -0.2725565 -0.8594262 -1.21685949  0.7793384 -0.6942510\n",
       "4 -1.18733547 -0.2725565  0.4066617  0.01075374 -0.9708962  1.2993023\n",
       "5  1.22573452 -0.2725565  1.6727497 -1.21685949  1.4794323  0.3025256\n",
       "6 -0.09756193 -0.2725565 -0.8594262 -2.44447272 -0.2708024 -0.6942510\n",
       "  MGODPR     MGODOV      MGODGE     MRELGE      ... AGEZONG     AWAOREG    \n",
       "1  0.2174254 -0.06870474 -0.1618019  0.42763309 ... -0.08104764 -0.05991487\n",
       "2 -0.3653787 -0.06870474  0.4641188 -0.09606902 ... -0.08104764 -0.05991487\n",
       "3 -0.3653787  0.91409379  0.4641188 -1.66717535 ... -0.08104764 -0.05991487\n",
       "4 -0.9481828  0.91409379  0.4641188 -0.61977113 ... -0.08104764 -0.05991487\n",
       "5 -0.3653787 -0.06870474  0.4641188  0.42763309 ... -0.08104764 -0.05991487\n",
       "6  0.2174254 -1.05150327  1.0900394 -3.23828168 ... -0.08104764 -0.05991487\n",
       "  ABRAND    AZEILPL     APLEZIER    AFIETS     AINBOED     ABYSTAND   Purchase\n",
       "1  0.764905 -0.02270383 -0.07364394 -0.1506075 -0.08734022 -0.1188063 No      \n",
       "2  0.764905 -0.02270383 -0.07364394 -0.1506075 -0.08734022 -0.1188063 No      \n",
       "3  0.764905 -0.02270383 -0.07364394 -0.1506075 -0.08734022 -0.1188063 No      \n",
       "4  0.764905 -0.02270383 -0.07364394 -0.1506075 -0.08734022 -0.1188063 No      \n",
       "5  0.764905 -0.02270383 -0.07364394 -0.1506075 -0.08734022 -0.1188063 No      \n",
       "6 -1.014271 -0.02270383 -0.07364394 -0.1506075 -0.08734022 -0.1188063 No      \n",
       "  Purchase.pred\n",
       "1 No           \n",
       "2 No           \n",
       "3 No           \n",
       "4 No           \n",
       "5 No           \n",
       "6 No           "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_test_pred <- data.frame(x_test,'Purchase'= y_test, 'Purchase.pred'= y_pred)\n",
    "head(x_test_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.946753692889042"
      ],
      "text/latex": [
       "0.946753692889042"
      ],
      "text/markdown": [
       "0.946753692889042"
      ],
      "text/plain": [
       "[1] 0.9467537"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# precision of the model\n",
    "precision <- mean(x_test_pred$Purchase == x_test_pred$Purchase.pred)\n",
    "precision "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Selecting the best k value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [],
   "source": [
    "precision <- numeric()\n",
    "k = 2:20\n",
    "for(i in 1:length(k)){\n",
    "    y_pred_i <- knn(train=x_train, test= x_test, cl=y_train, k=i)\n",
    "    precision[i] <- mean(y_test == y_pred_i)\n",
    "    #cat(paste0('k = ', i, ', precision = ', precision[i], '\\n'))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 960
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make dataframe\n",
    "df_k  <- data.frame('k'= k, 'precision'= precision)\n",
    "\n",
    "# plot\n",
    "p1 <- ggplot(df_k, aes(x=k, y=precision)) +\n",
    "geom_line(lty='dotted', color='blue') +\n",
    "geom_point(col='black') +\n",
    "labs(x='k', y='Precision', title='Selectiong best k')\n",
    "p1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Conclusions:\n",
    "\n",
    "When we observe the above plot, we can see clearly that the best choise of $k$ is when the line of the precision is flat, so this happend whe $k=4$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## k fold cross validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#install.packages(\"caret\")\n",
    "library(\"caret\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 86</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>MOSTYPE</th><th scope=col>MAANTHUI</th><th scope=col>MGEMOMV</th><th scope=col>MGEMLEEF</th><th scope=col>MOSHOOFD</th><th scope=col>MGODRK</th><th scope=col>MGODPR</th><th scope=col>MGODOV</th><th scope=col>MGODGE</th><th scope=col>MRELGE</th><th scope=col>...</th><th scope=col>APERSONG</th><th scope=col>AGEZONG</th><th scope=col>AWAOREG</th><th scope=col>ABRAND</th><th scope=col>AZEILPL</th><th scope=col>APLEZIER</th><th scope=col>AFIETS</th><th scope=col>AINBOED</th><th scope=col>ABYSTAND</th><th scope=col>Purchase</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>...</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>33</td><td>1</td><td>3</td><td>2</td><td> 8</td><td>0</td><td>5</td><td>1</td><td>3</td><td>7</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>37</td><td>1</td><td>2</td><td>2</td><td> 8</td><td>1</td><td>4</td><td>1</td><td>4</td><td>6</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>37</td><td>1</td><td>2</td><td>2</td><td> 8</td><td>0</td><td>4</td><td>2</td><td>4</td><td>3</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 9</td><td>1</td><td>3</td><td>3</td><td> 3</td><td>2</td><td>3</td><td>2</td><td>4</td><td>5</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>40</td><td>1</td><td>4</td><td>2</td><td>10</td><td>1</td><td>4</td><td>1</td><td>4</td><td>7</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>23</td><td>1</td><td>2</td><td>1</td><td> 5</td><td>0</td><td>5</td><td>0</td><td>5</td><td>0</td><td>...</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 86\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & MOSTYPE & MAANTHUI & MGEMOMV & MGEMLEEF & MOSHOOFD & MGODRK & MGODPR & MGODOV & MGODGE & MRELGE & ... & APERSONG & AGEZONG & AWAOREG & ABRAND & AZEILPL & APLEZIER & AFIETS & AINBOED & ABYSTAND & Purchase\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ... & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 33 & 1 & 3 & 2 &  8 & 0 & 5 & 1 & 3 & 7 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t2 & 37 & 1 & 2 & 2 &  8 & 1 & 4 & 1 & 4 & 6 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t3 & 37 & 1 & 2 & 2 &  8 & 0 & 4 & 2 & 4 & 3 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t4 &  9 & 1 & 3 & 3 &  3 & 2 & 3 & 2 & 4 & 5 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t5 & 40 & 1 & 4 & 2 & 10 & 1 & 4 & 1 & 4 & 7 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t6 & 23 & 1 & 2 & 1 &  5 & 0 & 5 & 0 & 5 & 0 & ... & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 86\n",
       "\n",
       "| <!--/--> | MOSTYPE &lt;dbl&gt; | MAANTHUI &lt;dbl&gt; | MGEMOMV &lt;dbl&gt; | MGEMLEEF &lt;dbl&gt; | MOSHOOFD &lt;dbl&gt; | MGODRK &lt;dbl&gt; | MGODPR &lt;dbl&gt; | MGODOV &lt;dbl&gt; | MGODGE &lt;dbl&gt; | MRELGE &lt;dbl&gt; | ... ... | APERSONG &lt;dbl&gt; | AGEZONG &lt;dbl&gt; | AWAOREG &lt;dbl&gt; | ABRAND &lt;dbl&gt; | AZEILPL &lt;dbl&gt; | APLEZIER &lt;dbl&gt; | AFIETS &lt;dbl&gt; | AINBOED &lt;dbl&gt; | ABYSTAND &lt;dbl&gt; | Purchase &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 33 | 1 | 3 | 2 |  8 | 0 | 5 | 1 | 3 | 7 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 2 | 37 | 1 | 2 | 2 |  8 | 1 | 4 | 1 | 4 | 6 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 3 | 37 | 1 | 2 | 2 |  8 | 0 | 4 | 2 | 4 | 3 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 4 |  9 | 1 | 3 | 3 |  3 | 2 | 3 | 2 | 4 | 5 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 5 | 40 | 1 | 4 | 2 | 10 | 1 | 4 | 1 | 4 | 7 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 6 | 23 | 1 | 2 | 1 |  5 | 0 | 5 | 0 | 5 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "\n"
      ],
      "text/plain": [
       "  MOSTYPE MAANTHUI MGEMOMV MGEMLEEF MOSHOOFD MGODRK MGODPR MGODOV MGODGE MRELGE\n",
       "1 33      1        3       2         8       0      5      1      3      7     \n",
       "2 37      1        2       2         8       1      4      1      4      6     \n",
       "3 37      1        2       2         8       0      4      2      4      3     \n",
       "4  9      1        3       3         3       2      3      2      4      5     \n",
       "5 40      1        4       2        10       1      4      1      4      7     \n",
       "6 23      1        2       1         5       0      5      0      5      0     \n",
       "  ... APERSONG AGEZONG AWAOREG ABRAND AZEILPL APLEZIER AFIETS AINBOED ABYSTAND\n",
       "1 ... 0        0       0       1      0       0        0      0       0       \n",
       "2 ... 0        0       0       1      0       0        0      0       0       \n",
       "3 ... 0        0       0       1      0       0        0      0       0       \n",
       "4 ... 0        0       0       1      0       0        0      0       0       \n",
       "5 ... 0        0       0       1      0       0        0      0       0       \n",
       "6 ... 0        0       0       0      0       0        0      0       0       \n",
       "  Purchase\n",
       "1 No      \n",
       "2 No      \n",
       "3 No      \n",
       "4 No      \n",
       "5 No      \n",
       "6 No      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "df <- Caravan\n",
    "head(Caravan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x <- df %>% select(-Purchase)\n",
    "y <- df %>% select(Purchase)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# standarization\n",
    "x.standarized  <- scale(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(123)\n",
    "split <- sample.split(y, SplitRatio=0.8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# train\n",
    "x_train <- subset(x.standarized, split=TRUE)\n",
    "x_test <- subset(x.standarized, split=FALSE)\n",
    "# target\n",
    "y_train <- subset(y, split=TRUE) %>% pull()\n",
    "y_test <- subset(y, split=FALSE) %>% pull()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'Fold01'</li><li>'Fold02'</li><li>'Fold03'</li><li>'Fold04'</li><li>'Fold05'</li><li>'Fold06'</li><li>'Fold07'</li><li>'Fold08'</li><li>'Fold09'</li><li>'Fold10'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'Fold01'\n",
       "\\item 'Fold02'\n",
       "\\item 'Fold03'\n",
       "\\item 'Fold04'\n",
       "\\item 'Fold05'\n",
       "\\item 'Fold06'\n",
       "\\item 'Fold07'\n",
       "\\item 'Fold08'\n",
       "\\item 'Fold09'\n",
       "\\item 'Fold10'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'Fold01'\n",
       "2. 'Fold02'\n",
       "3. 'Fold03'\n",
       "4. 'Fold04'\n",
       "5. 'Fold05'\n",
       "6. 'Fold06'\n",
       "7. 'Fold07'\n",
       "8. 'Fold08'\n",
       "9. 'Fold09'\n",
       "10. 'Fold10'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"Fold01\" \"Fold02\" \"Fold03\" \"Fold04\" \"Fold05\" \"Fold06\" \"Fold07\" \"Fold08\"\n",
       " [9] \"Fold09\" \"Fold10\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "folds <- createFolds(y_train, k = 10)\n",
    "names(folds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# loop\n",
    "precision <- numeric()\n",
    "for(i in 1:length(folds)){\n",
    "    fold_i <- folds[[i]]\n",
    "    # train\n",
    "    x_train_fold <- x_train[-fold_i,]\n",
    "    y_train_fold <- y_train[-fold_i]\n",
    "    # test\n",
    "    x_validation_fold <- x_train[fold_i,]\n",
    "    y_validation_fold <- y_train[fold_i]\n",
    "    #\n",
    "    y_pred_fold <- knn(train=x_train_fold, test= x_validation_fold, cl=y_train_fold, k=10)\n",
    "    #cm <- table(y_test_fold, y_pred_fold)\n",
    "    #precision[i] <- (cm[1,1] + cm[2,2]) / (cm[1,1] + cm[2,2] +cm[1,2] + cm[2,1])\n",
    "    precision[i] <- mean(y_validation_fold == y_pred_fold)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.93955"
      ],
      "text/latex": [
       "0.93955"
      ],
      "text/markdown": [
       "0.93955"
      ],
      "text/plain": [
       "[1] 0.93955"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# \n",
    "precision2 <- mean(round(precision,4))\n",
    "precision2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Easy way"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 86</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>MOSTYPE</th><th scope=col>MAANTHUI</th><th scope=col>MGEMOMV</th><th scope=col>MGEMLEEF</th><th scope=col>MOSHOOFD</th><th scope=col>MGODRK</th><th scope=col>MGODPR</th><th scope=col>MGODOV</th><th scope=col>MGODGE</th><th scope=col>MRELGE</th><th scope=col>...</th><th scope=col>APERSONG</th><th scope=col>AGEZONG</th><th scope=col>AWAOREG</th><th scope=col>ABRAND</th><th scope=col>AZEILPL</th><th scope=col>APLEZIER</th><th scope=col>AFIETS</th><th scope=col>AINBOED</th><th scope=col>ABYSTAND</th><th scope=col>Purchase</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>...</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>33</td><td>1</td><td>3</td><td>2</td><td> 8</td><td>0</td><td>5</td><td>1</td><td>3</td><td>7</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>37</td><td>1</td><td>2</td><td>2</td><td> 8</td><td>1</td><td>4</td><td>1</td><td>4</td><td>6</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>37</td><td>1</td><td>2</td><td>2</td><td> 8</td><td>0</td><td>4</td><td>2</td><td>4</td><td>3</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>4</th><td> 9</td><td>1</td><td>3</td><td>3</td><td> 3</td><td>2</td><td>3</td><td>2</td><td>4</td><td>5</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>40</td><td>1</td><td>4</td><td>2</td><td>10</td><td>1</td><td>4</td><td>1</td><td>4</td><td>7</td><td>...</td><td>0</td><td>0</td><td>0</td><td>1</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>23</td><td>1</td><td>2</td><td>1</td><td> 5</td><td>0</td><td>5</td><td>0</td><td>5</td><td>0</td><td>...</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>No</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 86\n",
       "\\begin{tabular}{r|lllllllllllllllllllll}\n",
       "  & MOSTYPE & MAANTHUI & MGEMOMV & MGEMLEEF & MOSHOOFD & MGODRK & MGODPR & MGODOV & MGODGE & MRELGE & ... & APERSONG & AGEZONG & AWAOREG & ABRAND & AZEILPL & APLEZIER & AFIETS & AINBOED & ABYSTAND & Purchase\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & ... & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 33 & 1 & 3 & 2 &  8 & 0 & 5 & 1 & 3 & 7 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t2 & 37 & 1 & 2 & 2 &  8 & 1 & 4 & 1 & 4 & 6 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t3 & 37 & 1 & 2 & 2 &  8 & 0 & 4 & 2 & 4 & 3 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t4 &  9 & 1 & 3 & 3 &  3 & 2 & 3 & 2 & 4 & 5 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t5 & 40 & 1 & 4 & 2 & 10 & 1 & 4 & 1 & 4 & 7 & ... & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\t6 & 23 & 1 & 2 & 1 &  5 & 0 & 5 & 0 & 5 & 0 & ... & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & No\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 86\n",
       "\n",
       "| <!--/--> | MOSTYPE &lt;dbl&gt; | MAANTHUI &lt;dbl&gt; | MGEMOMV &lt;dbl&gt; | MGEMLEEF &lt;dbl&gt; | MOSHOOFD &lt;dbl&gt; | MGODRK &lt;dbl&gt; | MGODPR &lt;dbl&gt; | MGODOV &lt;dbl&gt; | MGODGE &lt;dbl&gt; | MRELGE &lt;dbl&gt; | ... ... | APERSONG &lt;dbl&gt; | AGEZONG &lt;dbl&gt; | AWAOREG &lt;dbl&gt; | ABRAND &lt;dbl&gt; | AZEILPL &lt;dbl&gt; | APLEZIER &lt;dbl&gt; | AFIETS &lt;dbl&gt; | AINBOED &lt;dbl&gt; | ABYSTAND &lt;dbl&gt; | Purchase &lt;fct&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 1 | 33 | 1 | 3 | 2 |  8 | 0 | 5 | 1 | 3 | 7 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 2 | 37 | 1 | 2 | 2 |  8 | 1 | 4 | 1 | 4 | 6 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 3 | 37 | 1 | 2 | 2 |  8 | 0 | 4 | 2 | 4 | 3 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 4 |  9 | 1 | 3 | 3 |  3 | 2 | 3 | 2 | 4 | 5 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 5 | 40 | 1 | 4 | 2 | 10 | 1 | 4 | 1 | 4 | 7 | ... | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "| 6 | 23 | 1 | 2 | 1 |  5 | 0 | 5 | 0 | 5 | 0 | ... | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | No |\n",
       "\n"
      ],
      "text/plain": [
       "  MOSTYPE MAANTHUI MGEMOMV MGEMLEEF MOSHOOFD MGODRK MGODPR MGODOV MGODGE MRELGE\n",
       "1 33      1        3       2         8       0      5      1      3      7     \n",
       "2 37      1        2       2         8       1      4      1      4      6     \n",
       "3 37      1        2       2         8       0      4      2      4      3     \n",
       "4  9      1        3       3         3       2      3      2      4      5     \n",
       "5 40      1        4       2        10       1      4      1      4      7     \n",
       "6 23      1        2       1         5       0      5      0      5      0     \n",
       "  ... APERSONG AGEZONG AWAOREG ABRAND AZEILPL APLEZIER AFIETS AINBOED ABYSTAND\n",
       "1 ... 0        0       0       1      0       0        0      0       0       \n",
       "2 ... 0        0       0       1      0       0        0      0       0       \n",
       "3 ... 0        0       0       1      0       0        0      0       0       \n",
       "4 ... 0        0       0       1      0       0        0      0       0       \n",
       "5 ... 0        0       0       1      0       0        0      0       0       \n",
       "6 ... 0        0       0       0      0       0        0      0       0       \n",
       "  Purchase\n",
       "1 No      \n",
       "2 No      \n",
       "3 No      \n",
       "4 No      \n",
       "5 No      \n",
       "6 No      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df <- Caravan\n",
    "head(Caravan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(12345)\n",
    "split <- sample.split(df$Purchase, SplitRatio=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [],
   "source": [
    "# train and test\n",
    "train <- subset(df, split=TRUE)\n",
    "test <- subset(df, split=FALSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "k-Nearest Neighbors \n",
       "\n",
       "5822 samples\n",
       "  85 predictor\n",
       "   2 classes: 'No', 'Yes' \n",
       "\n",
       "Pre-processing: centered (85), scaled (85) \n",
       "Resampling: Cross-Validated (10 fold, repeated 3 times) \n",
       "Summary of sample sizes: 5240, 5240, 5239, 5240, 5240, 5240, ... \n",
       "Resampling results across tuning parameters:\n",
       "\n",
       "  k   Accuracy   Kappa       \n",
       "   5  0.9347887   0.032917215\n",
       "   7  0.9382796   0.022994581\n",
       "   9  0.9394251   0.013024030\n",
       "  11  0.9397691   0.008784034\n",
       "  13  0.9398836   0.002613169\n",
       "  15  0.9401698  -0.000111739\n",
       "  17  0.9402271   0.000000000\n",
       "  19  0.9402271   0.000000000\n",
       "  21  0.9402271   0.000000000\n",
       "  23  0.9402271   0.000000000\n",
       "  25  0.9402271   0.000000000\n",
       "  27  0.9402271   0.000000000\n",
       "  29  0.9402271   0.000000000\n",
       "  31  0.9402271   0.000000000\n",
       "  33  0.9402271   0.000000000\n",
       "  35  0.9402271   0.000000000\n",
       "  37  0.9402271   0.000000000\n",
       "  39  0.9402271   0.000000000\n",
       "  41  0.9402271   0.000000000\n",
       "  43  0.9402271   0.000000000\n",
       "\n",
       "Accuracy was used to select the optimal model using the largest value.\n",
       "The final value used for the model was k = 43."
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(400)\n",
    "ctrl <- trainControl(method=\"repeatedcv\", repeats = 3) #,classProbs=TRUE,summaryFunction = twoClassSummary)\n",
    "knnFit <- train(Purchase ~ ., data = train, method = \"knn\", trControl = ctrl, preProcess = c(\"center\",\"scale\"), tuneLength = 20)\n",
    "\n",
    "# Output of kNN fit\n",
    "knnFit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 360,
       "width": 960
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(knnFit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Confusion Matrix and Statistics\n",
       "\n",
       "          Reference\n",
       "Prediction   No  Yes\n",
       "       No  5474  348\n",
       "       Yes    0    0\n",
       "                                          \n",
       "               Accuracy : 0.9402          \n",
       "                 95% CI : (0.9338, 0.9462)\n",
       "    No Information Rate : 0.9402          \n",
       "    P-Value [Acc > NIR] : 0.5143          \n",
       "                                          \n",
       "                  Kappa : 0               \n",
       "                                          \n",
       " Mcnemar's Test P-Value : <2e-16          \n",
       "                                          \n",
       "            Sensitivity : 1.0000          \n",
       "            Specificity : 0.0000          \n",
       "         Pos Pred Value : 0.9402          \n",
       "         Neg Pred Value :    NaN          \n",
       "             Prevalence : 0.9402          \n",
       "         Detection Rate : 0.9402          \n",
       "   Detection Prevalence : 1.0000          \n",
       "      Balanced Accuracy : 0.5000          \n",
       "                                          \n",
       "       'Positive' Class : No              \n",
       "                                          "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "knnPredict <- predict(knnFit, newdata = test)\n",
    "# Get the confusion matrix to see accuracy value and other parameter values\n",
    "confusionMatrix(knnPredict, test$Purchase)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.1.0"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}