2020101089_Q1.ipynb

{
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   "id": "186be3d3",
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   "source": [
    "# Assignment 2 - Question 1\n",
    "The objective of this assignment is to get you familiarize with  the  problem  of  `KNN Classifiers`.\n",
    "\n",
    "\n",
    "## Instructions\n",
    "- Do not Use Direct Inbuilt functions for the Task.\n",
    "- Numpy or other math libraries are allowed \n",
    "- Ensure that this notebook runs without errors when the cells are run in sequence.\n",
    "- Do not change the contents of the Given cells. Use new cells to Write your code.\n",
    "\n",
    "\n",
    "## Submission\n",
    "- Ensure that this notebook runs without errors when the cells are run in sequence.\n",
    "- Rename the notebook to `<roll_number>_Q1.ipynb`\n",
    "- Fill the Name and Roll number in the below markdown"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f6269f1",
   "metadata": {},
   "source": [
    "Name: Siddik Ayyappa Naraharisetti<br>\n",
    "Roll Number: 2020101089 <br>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edeabff5",
   "metadata": {},
   "source": [
    "### Dataset\n",
    "\n",
    "Use the code below to load the Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "69cac090",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e0fa6912",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Load data\n",
    "iris = pd.read_csv('Iris.csv')\n",
    "#data cleaning\n",
    "iris.drop(columns=\"Id\",inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1ca8135b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#features and labels\n",
    "X=iris.iloc[:,0:4].values\n",
    "y=iris.iloc[:,4].values\n",
    "\n",
    "#Train and Test split\n",
    "X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2,random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d14014cb",
   "metadata": {},
   "source": [
    "Write your Code below for KNN Classifier.<br>\n",
    "Use different values of K and test the accuracies."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13e8c2c2",
   "metadata": {},
   "source": [
    "### Beginning the code\n",
    "We shall visualise the dataset with the help of pandas dataframes, to get a feel of how the data is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6ca8c19d",
   "metadata": {},
   "outputs": [
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       "      <th>...</th>\n",
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       "      <th>115</th>\n",
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       "       0    1    2    3\n",
       "0    6.4  3.1  5.5  1.8\n",
       "1    5.4  3.0  4.5  1.5\n",
       "2    5.2  3.5  1.5  0.2\n",
       "3    6.1  3.0  4.9  1.8\n",
       "4    6.4  2.8  5.6  2.2\n",
       "..   ...  ...  ...  ...\n",
       "115  4.9  3.1  1.5  0.1\n",
       "116  6.3  2.9  5.6  1.8\n",
       "117  5.8  2.7  4.1  1.0\n",
       "118  7.7  3.8  6.7  2.2\n",
       "119  4.6  3.2  1.4  0.2\n",
       "\n",
       "[120 rows x 4 columns]"
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "bf4d7328",
   "metadata": {},
   "outputs": [
    {
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       "      <td>Iris-virginica</td>\n",
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       "      <td>Iris-versicolor</td>\n",
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       "                   0\n",
       "0     Iris-virginica\n",
       "1    Iris-versicolor\n",
       "2        Iris-setosa\n",
       "3     Iris-virginica\n",
       "4     Iris-virginica\n",
       "..               ...\n",
       "115      Iris-setosa\n",
       "116   Iris-virginica\n",
       "117  Iris-versicolor\n",
       "118   Iris-virginica\n",
       "119      Iris-setosa\n",
       "\n",
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "pd.DataFrame(y_train)\n"
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  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "91145651",
   "metadata": {},
   "outputs": [],
   "source": [
    "import statistics as stat\n",
    "\n",
    "class KNN():\n",
    "    def __init__(self, x_train, y_train, k):\n",
    "        self.X = x_train\n",
    "        self.y, self.y_key_forward, self.y_key_back = self.to_categorical(y_train)\n",
    "        self.y_train = y_train\n",
    "        self.k = k\n",
    "    def to_categorical(self, y):\n",
    "        y = np.array(y)\n",
    "        cat = np.unique(y)\n",
    "        n_cat = len(cat)\n",
    "        temp = dict()\n",
    "        temp_1 = dict()\n",
    "        for i in range(n_cat):\n",
    "            temp[cat[i]] = i\n",
    "            temp_1[i] = cat[i]\n",
    "        del cat\n",
    "        cat_labels = [temp[i] for i in y]\n",
    "        return cat_labels, temp,temp_1\n",
    "    def neighbours(self, sample):\n",
    "        min_distance, dist = np.inf, []\n",
    "        for idx, i in enumerate(self.X): # -> Time complexity - nd\n",
    "            dist += [(np.sum((sample - i)**2), idx)] \n",
    "        dist.sort(key=lambda pair:pair[0]) # sorting with the distance. Time complexity - n.log n\n",
    "        dist = np.array(np.array(dist))[:self.k]\n",
    "        labels = [self.y[int(i[1])] for i in dist]   # getting the labels of the nearest k points\n",
    "        return labels\n",
    "    def forward(self, X):\n",
    "        neighbours = []\n",
    "        for i in X:\n",
    "            neighbours += [self.neighbours(i)] # -> This would be repeating n times. time complexity for each time - nd + n.log(n)\n",
    "            # Hence the total time complexity - O(n(nd + n.log(n)))\n",
    "        labels = []\n",
    "        for neighbour in neighbours:\n",
    "            labels += [stat.mode(neighbour)] # this is the only line in which a third party library has been utilised, just for the mode of the array.\n",
    "            # The above line is run for n times, each, looking for the mode in an array of size k -\n",
    "            #  time complexity - O(nk)\n",
    "        labels = np.array(labels)\n",
    "        return labels\n",
    "    def evaluate(self, X, y):\n",
    "        labels = self.forward(X) # total time complexity - O(n(nd + n.log(n) + k))\n",
    "        if(len(labels) != len(y)):\n",
    "            raise ValueError(\"Check Labels\")\n",
    "        y_labels = [self.y_key_forward[i] for i in y]\n",
    "        score = 0\n",
    "        array = [\"=\",\"=\",\"=\",\"=\",\"=\",\"=\",\"=\",\"=\",\"=\",\">\"]\n",
    "        for i in range(len(y_labels)):\n",
    "            if(y_labels[i] == labels[i]):\n",
    "                score += 1\n",
    "        return(score/len(y)*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db5fe580",
   "metadata": {},
   "source": [
    "###  Math behind the code\n",
    "\n",
    "All the points in the initial set $X_{init}$ are firstly taken in the class. Then for each point $X_i$ in the test for which we calculate the label, we calculate the distance,\n",
    "<br> \n",
    "$(X_i - X_j)^2$  $\\forall X_j \\in X_{init}$ \n",
    "<br> \n",
    "<br> \n",
    "Which will ne stored in an array. Then we sort the array, take the first k points (neighbours), then we assign the major label in the k neighbours. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "92d82346",
   "metadata": {},
   "outputs": [],
   "source": [
    "accuracies = []\n",
    "for k in range(1, 110):\n",
    "    knn = KNN(X_train, y_train, k = k) # initialising the dataset, \n",
    "    accuracies += [knn.evaluate(X_test, y_test)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2217ca2e",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 768x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plot\n",
    "plot.figure(dpi=120)\n",
    "plot.plot(range(1, len(accuracies)+1), accuracies)\n",
    "# plot.xticks(range(0, len(accuracies), 8))\n",
    "# plot.yticks(range(0, len(accuracies), 8))\n",
    "plot.xlabel(\"K\")\n",
    "plot.ylabel(\"Accuracy\")\n",
    "plot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c3ac0ca",
   "metadata": {},
   "source": [
    "### Questions\n",
    "\n",
    "1) What are the Advantages and Disadvantages of KNN algorithm?\n",
    "   <br>\n",
    "   | Advantages | Disadvantages |\n",
    "   | --- | --- |\n",
    "   | The time complexity of training is <br>practically 0 | The time complexity of testing suggests that<br> for large dataset (or data with high number of <br>features) it is not feasible to use KNN|\n",
    "   | Easy to add new data | Noisy data influences the final labels |\n",
    "   | Easy to implement | The data must be normalized among all the features <br>individually (Data of similar nature could be recorded in <br>different units) else the accuracies are affected.| \n",
    "   \n",
    "   <br>\n",
    "2) What is the complexity of the KNN algorithm during Training and Testing?<br><br> \n",
    "   1) The answers are given assuming the values of k, n, d, being the number of neigbours, number of training samples and the number of features respectively.\n",
    "   2) The <b>training</b> phase, doesn't have much of computation to do (We are just storing the training data), hence \n",
    "      1) The time complexity - ```O(1)```\n",
    "      2) The space complexity - ```O(nd)```\n",
    "   3) The <b>testing</b> phase\n",
    "      1) The time complexity - ```O(n(nd + n.log(n) + k))```\n",
    "      2) The space complexity - ```O(nk)```\n",
    "<br><br>\n",
    "3) Is euclidian distance the only distance metric used in KNN?\n",
    "   <br><br>\n",
    "   No. Depending upon the space which the points are in and the problem being solved, we can use different metrics, like Minkowski, Chi-Squared, Cosine. [source](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4978658/)\n",
    "   <br><br>\n",
    "4) what K value gave the best accuracy?<br><br>\n",
    "   The values like 1, 5, 6, 11, .. 29, have been giving an accuracy of $100\\%$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "47958869",
   "metadata": {},
   "source": [
    "### Testing and Verification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ccfbab0e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.metrics import accuracy_score\n",
    "acc = []\n",
    "for i in range(1, 110):\n",
    "    model = KNeighborsClassifier(n_neighbors=i)\n",
    "    model.fit(X_train, y_train)\n",
    "    temp = model.predict(X_test)\n",
    "    acc += [(accuracy_score(temp, y_test))*100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d7e0f07c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot.plot(range(1, len(acc)+1), acc)\n",
    "plot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4cf9e43",
   "metadata": {},
   "source": [
    "The above plot, which has been taken from the actual classification, shows resemlence with the plot featuring in the above portions of the notebook, implying that the classification is indeed accurate. "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.6 64-bit",
   "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": "3.10.6"
  },
  "vscode": {
   "interpreter": {
    "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}