Tarefa_02/292701.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dd71f212-b8dc-4f83-a4c9-4b2a5b7e8625",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "292701"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Place here the same 6-digit number you selected for the first coursework. \n",
    "# Make sure that you keep a copy of this number and avoid trivial numbers, such as 000000 or 123456 -- thank you!\n",
    "292701"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d05468eb-e9d9-44b3-80f7-d1e1dc7296b1",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Assignment 2 - Regression and Classification\n",
    "\n",
    "Second assessed coursework for the course: Técnicas e Algoritmos em Ciência de Dados\n",
    "\n",
    "This coursework aims to provide students with a comprehensive understanding of linear regression with polynomial basis functions and classification with K-nearest neighbours. Specifically, students will learn about key concepts related to the model's generalisation ability by changing the degree of the polynomial and the size of the dataset. In the second part of the coursework, students will delve into classification using the K-nearest neighbours algorithm. Finally, students will be introduced to the concept of using a validation set to select the optimal value of $K$ for their classification model. By the end of this coursework, students will have gained a solid understanding of these key concepts and be equipped with the skills to apply them in practical scenarios.\n",
    "\n",
    "## General guidelines:\n",
    "\n",
    "* This work must be entirely original. You are allowed to research documentation for specific libraries, but copying solutions from the internet or your classmates is strictly prohibited. Any such actions will result in a deduction of points for the coursework.\n",
    "* Please enter your code in the designated areas of the notebook. You can create additional code cells to experiment with, but __make sure to place your final solutions where they are requested in the notebook.__\n",
    "* Before submitting your work, make sure to rename the file to the random number that you created for the previous coursework (for example, 289479.ipynb).\n",
    "\n",
    "## Notebook Overview:\n",
    "\n",
    "1. [Polynomial Fitting Visualisation](#Polynomial-Fitting-Visualisation) (50%)\n",
    "2. [Classification with KNN](#Classification-with-KNN) (50%)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5bbccb7a-e176-497e-afe5-107d94f6ccf9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e1e05a8-860b-45c1-9e23-1e2ae348d7ee",
   "metadata": {},
   "source": [
    "# Polynomial Fitting Visualisation\n",
    "In this exercise you will explore the effect that the degree of the polynomial and the size of the training data has on the model's performance and generalisation ability.\n",
    "\n",
    "1. Generate a 2D dataset of 15 points $(x_i,y_i)$ for $i=1..15$ using a sine wave perturbed by a small gaussian noise --- this is very similar to what you did in the lab.\n",
    "    - The $x_i$ should be equally spaced in the $[0-10]$ interval \n",
    "    - Use: $y_i = 4*sin(x_i) + \\epsilon$, where $\\epsilon$ is gaussian noise (with $\\mu=0$ and $\\sigma=1$).\n",
    "    - To ensure reproducibility of your results, use (provided below): \n",
    "    `rng = np.random.default_rng(13)` and\n",
    "    `random_state = np.random.RandomState(13)`\n",
    "    \n",
    "2. Split the points randomly into a training and testing sets of size 10 and 5, respectively.\n",
    "    \n",
    "3. Learn the weights of the linear regression for  polynomial models of degree $M$ for $M = 0..9$ . For each value of $M$ calculate the Root Mean Squared Error (RMSE) for the training and testing sets and plot these values against $M$. Your figure should be similar to Figure 1 from the Coursework document.\n",
    "\n",
    "4. In the last part of this exercise, you will have to create more points for training (using the same sine wave perturbed by a small gaussian noise as described in point 1). For testing, you will continue to use the same 5 points you used in points 1 to 3. Learn the weights of the linear regression for  polynomial models of degree $M=9$ for training sets of size $N$ with $N=10:500:10$ (that is, from $N=10$ to $N=500$ in steps of $10$). For each value of $N$ calculate the Root Mean Squared Error (RMSE) for the training and testing sets and plot these values against $N$. Your figure should be similar to Figure 2 from the Coursework document.\n",
    "\n",
    "* Note that for parts 3 and 4 you are supposed to write your code from scratch and you cannot use existing functions such as `PolynomialFeatures`, `LinearRegression` or `mean_squared_error`.\n",
    "* _Observation: in this exercise we are not using the validation set because our goal is not to choose a specific model but rather to analyse the behaviour of the family of models._"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8da4fed1-c4ad-4b5d-914b-0debae29f1b6",
   "metadata": {},
   "source": [
    "### Generate the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "748c64e9-3c3e-4e25-88d5-ac8943bc4671",
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(13)\n",
    "random_state = np.random.RandomState(13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "11f869dc-1b96-4aaa-b2d9-d2ad0c709d84",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# your code goes here:\n",
    "# Using linspace to generate the x dataset, and creating a noise with normal distribution\n",
    "# by default the loc is 0 and scale is 1, then generate the y data\n",
    "x = np.linspace(0, 10, 15)\n",
    "noise = np.random.normal(loc=0, scale=1, size=15)\n",
    "\n",
    "y = 4*np.sin(x) + noise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51c1ce30-85ed-4c2b-8a16-0b9b3a5096b4",
   "metadata": {},
   "source": [
    "### Split the points into training and testing\n",
    "Feel free to use `train_test_split(x, y, test_size = ?, random_state = random_state)`, remember to calculate the right proportion for the `test_size` so that you end up with 5 points in the testing set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4d86279b-109e-4ff0-9f32-6f8c0a1b5f81",
   "metadata": {},
   "outputs": [],
   "source": [
    "# your code goes here:\n",
    "# Split the data in training and test with proportion 10:5\n",
    "x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=1/3, random_state=random_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "395409e1-7280-4420-88ed-2fc635b914d0",
   "metadata": {},
   "source": [
    "### Training set size vs. RMSE\n",
    "Generate the plot (as in __Figure 2__) of the RMSE during training and testing at different training set sizes $N$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "bc515bf6-c077-49c0-928d-a1300f3967e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show(close=None, block=None)>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your code goes here:\n",
    "# Let's use some functions to the next steps\n",
    "def linear_regression_PI(X, y):\n",
    "    # Let's calculate X pseudo-inverse\n",
    "    X_pi = np.linalg.inv(X.T @ X) @ X.T\n",
    "    # Then calculate w tha is X pseudo-inverse times y\n",
    "    w = X_pi @ y\n",
    "\n",
    "    return w\n",
    "\n",
    "def my_rmse(y_true:np.ndarray, y_pred:np.ndarray) -> float:\n",
    "    # Calculate the squared diff between pred and true values\n",
    "    diff_y = (y_true - y_pred) ** 2\n",
    "    rmse = np.sqrt(np.mean(diff_y))\n",
    "\n",
    "    return rmse\n",
    "\n",
    "def make_polynomial_phi(data:np.ndarray, polynomial_base:int):\n",
    "    # Create the polynomial matrix\n",
    "    phi_matrix = np.ones((data.shape[0], polynomial_base+1))\n",
    "\n",
    "    for i in range(1, polynomial_base +1):\n",
    "        phi_matrix[:,i] = np.power(data, i)\n",
    "\n",
    "    return phi_matrix\n",
    "\n",
    "bases = np.arange(10)\n",
    "rmse_train = dict()\n",
    "rmse_test = dict()\n",
    "# Let's make the prediction for each base from 0 to 9 and check it's rmse\n",
    "for base in bases:\n",
    "    # Prepare the data\n",
    "    x_train_poly = make_polynomial_phi(x_train, base)\n",
    "    x_test_poly = make_polynomial_phi(x_test, base)\n",
    "    # Train the model\n",
    "    w_pi = linear_regression_PI(x_train_poly, y_train)\n",
    "    # make our predictions\n",
    "    y_pred_train = x_train_poly @ w_pi\n",
    "    y_pred_test = x_test_poly @ w_pi\n",
    "    # save the bases and associate rmse\n",
    "    rmse_train[base] = my_rmse(y_train, y_pred_train)\n",
    "    rmse_test[base] = my_rmse(y_test, y_pred_test)\n",
    "# Finally plot our results\n",
    "plt.plot(rmse_train.keys(), rmse_train.values(), linestyle=\"-\", marker=\"o\", color=\"blue\", label=\"Train Results\")\n",
    "plt.plot(rmse_test.keys(), rmse_test.values(), linestyle=\"--\", marker=\"o\", color=\"orange\", label=\"Test Results\")\n",
    "plt.xlabel(\"Polynomial Degree\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.xticks(bases)\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "\n",
    "plt.show"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c4953804",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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V4ON69+6N3r17Y8aMGcjOzsaCBQswcOBAJCYmYs+ePU7L7ty5E3q9vsHnMhgMLtuenp6Ohx9+GHfffTfmzZuH99577/ILKsuWLcOIESNwxx13YP369WjVqhV+//vfOw3oqc1kMsFkMjnmi4uLAci06Eti9JXGZkPtoVJqrrulsdeONfQv1lkdl0udzWYzhBCw2Wyw2Wyqr9/eY2Bvgy/sj7NfPvPMM3jssccQFRWFESNGwGQyYdu2bbh48SKmTZuGV199FSkpKejduzc0Gg0WL16MlJQUREVFOcaZrF69GtnZ2TAajY3uGahbt6lTp2LcuHGYPn067rrrLrz44osYM2YMZs2ahdatW+PYsWNYunQpnnzySZjNZrz33nsYPXo00tLSsH//fhw8eBD33HMPbDYbhgwZghdffBEffPABsrOz8fHHH2PPnj3o3bu30zpr1y4jIwPr16/HnXfeCaPRiISEBEybNg0jR45EVlYWTpw4gbVr16JTp05e1dtms0EIAbPZXG+AsTf/IwENKocPH8Y777yDxx9/HH/605+wdetWTJ06FQaDARMnTqy3/Ny5czF79ux6t69atQphYU3r+vNG+6pf0bXWfE5OjmrrbqlYQ3Wwzupo6XXW6XRISUlBaWkpqqqqAtaOkpISnx9bWVkJIYTjC++dd94JRVHw5ptv4qmnnkJYWBi6dOmCRx55BMXFxdDpdHj++edx+PBhaDQaR8+HfbfR7Nmz8Ze//AXvv/8+UlNTGx3TUVFR4VgvAAwaNAgZGRmYNWsWXn75ZXz11VeYNWsWxo0bh9LSUqSmpuLaa68FAFitVuzZswcffvghzp8/j+TkZNx///246667UFxcjOzsbDz55JP44x//iMrKStxzzz0YP3489u7d61inxWJBVVWVY/6pp57CtGnTkJWVBZPJhAsXLqCiogKTJ0/GyZMnERkZiRtuuAHPPfecU7vdqaqqQkVFBTZs2ACLxeJ0X3m550eIKaLuziwVGQwG9OvXD5s2bXLcNnXqVGzduhWbN2+ut7yrHpX09HScPXu20S6y5qbZ/zK0u2YAAL4M/wLDhg1rtFuNGmY2m5GTk8Ma+hnrrI7Lpc6VlZXIz89HZmYmQkJCVF+/EAIlJSWIjIz0+bBc8kxTal1ZWYmjR48iPT293vukuLgYCQkJKCoqcrv9DmiPSmpqKrp06eJ0W+fOnfH555+7XN5oNMJoNNa7Xa/Xq/uhoHHuwlJ9/S0Qa6gO1lkdLb3OVqsViqJAo9EE5JBV++4HexvIf5pSa41GA0VRXP4/ePP/EdC/8ODBg7F//36n2w4cOOB0fHpQYoInIiJSRUCDyrRp07BlyxY899xzOHToEBYsWIB//etfmDx5ciCbRUREREEioEGlf//+WLp0KT755BN069YNzz77LF577bVGDw8LCjzhGxERkSoCfgr9m2++GTfffHOgm0FERF4K4LEYdAlorvcHRyH5gmNUiOgyZh8I6c0hpnT5sb8/mjqwPOA9KkREdGnRarWIiYlBYWEhACAsLEzVw4RtNhuqqqpQWVnJo378zJdaCyFQXl6OwsJCxMTEePxr0g1hUPEFuzuJ6DJn/6Vde1hRkxACFRUVCA0N5XlU/Kwptfb016TdYVAhIiKvKYqC1NRUJCUlqf6TAWazGRs2bMA111zTos9XEwx8rbVer29yT4odg4ovmOCJiADI3UDNtUHyZp0WiwUhISEMKn4WDLXmzj0iIiIKWgwqREREFLQYVHzBwbRERESqYFAhIiKioMWg4gsOpiUiIlIFgwoREREFLQYVX3CMChERkSoYVIiIiChoMaj4gmNUiIiIVMGg0lTcDUREROQ3DCpNxqBCRETkLwwqREREFLQYVJqMPSpERET+wqDSRBxWS0RE5D8MKk3GHhUiIiJ/YVAhIiKioMWg0mTsUSEiIvIXBpUm4hgVIiIi/2FQaTL2qBAREfkLg0qTMagQERH5C4MKERERBS0GlSbiGBUiIiL/YVBpMu76ISIi8hcGlSZjUCEiIvIXBhUiIiIKWgwqTcQxKkRERP7DoNJk3PVDRETkLwwqTcagQkRE5C8MKk3GoEJEROQvDCpEREQUtBhUmoiDaYmIiPyHQaXJuOuHiIjIXxhUmoxBhYiIyF8YVHyiuLhGREREzY1BxSfsRSEiIlIDg0qTMbQQERH5S0CDyqxZs6AoitPUqVOnQDbJBwwqRERE/qILdAO6du2K1atXO+Z1uoA3yT1RE044RoWIiMh/Ap4KdDodUlJSPFrWZDLBZDI55ouLiwEAZrMZZrPZL+1zRWO1QFtrXs11tzT22rGG/sU6q4N1VgfrrB5/1dqb5wt4UDl48CDS0tIQEhKC7OxszJ07F23atHG57Ny5czF79ux6t69atQphYWH+bqpD+6p96GqfEQI5OTmqrbulYg3VwTqrg3VWB+usnuaudXl5ucfLKkKIgA2yWLFiBUpLS9GxY0cUFBRg9uzZOHHiBPbs2YPIyMh6y7vqUUlPT8fZs2cRFRWlWrs1+16EdvefAQArQ/+Da0aMh16vV239LYnZbEZOTg6GDRvGGvoR66wO1lkdrLN6/FXr4uJiJCQkoKioyO32O6A9KjfeeKPjeo8ePTBgwABkZGRg8eLFuP/+++stbzQaYTQa692u1+vVfbNqasYgK4FYfwvEGqqDdVYH66wO1lk9zV1rb54rqA5PjomJQYcOHXDo0KFAN8UN0cB1IiIiak5BFVRKS0uRm5uL1NTUQDfFDYYTIiIiNQQ0qEyfPh3r16/H0aNHsWnTJowdOxZarRZ33XVXIJvlJYYWIiIifwnoGJXjx4/jrrvuwrlz55CYmIirrroKW7ZsQWJiYiCb5Z7grh8iIiI1BDSoLFy4MJCrbwKe8I2IiEgNQTVG5ZIRuCO6iYiILisMKj7hrh8iIiI1MKg0GYMKERGRvzCo+IRjVIiIiNTAoOILHvVDRESkCgYVnzCcEBERqYFBpckYWoiIiPyFQcUnHKNCRESkBgYVX3CMChERkSoYVHzCcEJERKQGBpUmY2ghIiLyFwYVn3CMChERkRoYVHzBMSpERESqYFDxCYMKERGRGhhUiIiIKGgxqPiEY1SIiIjUwKDiC45RISIiUgWDik8YVIiIiNTAoEJERERBi0HFJ+xRISIiUgODii8EB9MSERGpgUHFJ7V6UQR7VIiIiPyFQcUXPOqHiIhIFQwqREREFLQYVHzCMSpERERqYFDxCXf9EBERqYFBxRcco0JERKQKBhUiIiIKWgwqPuEYFSIiIjUwqPiEu36IiIjUwKDiC45RISIiUgWDShNx1w8REZH/MKj4hL0oREREamBQ8Ql3/RAREamBQcUXHKNCRESkCgYVIiIiCloMKj6pfR4V9qgQERH5C4OKTxhOiIiI1MCg4guOUSEiIlIFg0qTMagQERH5S9AElXnz5kFRFDz22GOBbooH+Fs/REREagiKoLJ161a8++676NGjR6Cb4iH2ohAREakh4EGltLQUEyZMwHvvvYfY2NhAN8czHKNCRESkCl2gGzB58mTcdNNNGDp0KObMmdPosiaTCSaTyTFfXFwMADCbzTCbzX5tZ21am7VWwhOqrrulsdeONfQv1lkdrLM6WGf1+KvW3jxfQIPKwoUL8dNPP2Hr1q0eLT937lzMnj273u2rVq1CWFhYczevQb1Mx5FRfV0BkJOTo9q6WyrWUB2sszpYZ3Wwzupp7lqXl5d7vGzAgkp+fj4effRR5OTkICQkxKPHzJgxA48//rhjvri4GOnp6Rg+fDiioqL81dR6tFuXAEftcwLDhg2DXq9Xbf0tidlsRk5ODmvoZ6yzOlhndbDO6vFXre17RDwRsKCyfft2FBYWok+fPo7brFYrNmzYgLfeegsmkwlardbpMUajEUajsd5z6fV6dd+sivOxPqqvvwViDdXBOquDdVYH66ye5q61N88VsKByww03YPfu3U633XfffejUqRP++Mc/1gspwYWDaYmIiNQQsKASGRmJbt26Od0WHh6O+Pj4ercHM55HhYiIyH8CfnjyJYmHJxMREaki4Icn17Zu3bpAN8FDDCdERERqYI+KT2oFFcHQQkRE5C8MKkRERBS0GFR8IWr/KCF7VIiIiPyFQcUnHExLRESkBgYVnzCcEBERqYFBpckYWoiIiPyFQcUXTmNUiIiIyF8YVBoiBHBuG2A1ubqzgetERETUnBhUGpK3GPi2P7Blkos7GU6IiIjUwKDSkL3Py8tjC90syNBCRETkLwwqDYlsX3O99IjzfRyjQkREpAoGlYaYS2qun1pT506OUSEiIlIDg0pDKk/VXC/aW+dOBhUiIiI1MKg0pKKg5rqlNHDtICIiuowxqLhiswKmMzXzdYMKx6gQERGpwqugUlhY2Oj9FosFP/74Y5MaFBRMZwBhq5mv16PCXT9ERERq8CqopKamOoWV7t27Iz8/3zF/7tw5ZGdnN1/rAqX2bh+AQYWIiChAvAoqQjhvlI8ePQqz2dzoMpek2gNpAcDc8K4fIiIi8p9mH6OiKC1g1EZFdVDRhshLDqYlIiIKCF2gGxCU0m8ForsAF3cBPz7U6K4fhbt+iIiI/MaroKIoCkpKShASEgIhBBRFQWlpKYqLiwHAcXnJM8QCCQMAfbScb+SoH45RISIi8h+vgooQAh06dHCa7927t9N8i9j1Y6ePkJeNDqYlIiIif/EqqKxdu9Zf7QhOuuqgYjMD1ipAawhse4iIiC4zXgWVa6+91l/tCE668JrrllJAG1c9wzEqREREavAqqFgsFlitVhiNRsdtp0+fxj//+U+UlZXhlltuwVVXXdXsjQwYjR7QGAGbCbCUAMbqoMIxKkRERKrwKqg8+OCDMBgMePfddwEAJSUl6N+/PyorK5GamopXX30VX375JUaNGuWXxgaEPhIwmeqcS4VBhYiISA1enUfl+++/x7hx4xzzH330EaxWKw4ePIiff/4Zjz/+OF588cVmb2RA6RoaUCu1oKHDREREQceroHLixAlkZWU55tesWYNx48YhOloexjtx4kT88ssvzdvCQHMZVNiLQkREpAavgkpISAgqKioc81u2bMGAAQOc7i8tbWFncXUVVDhGhYiISBVeBZVevXrh//7v/wAA//vf/3D69Glcf/31jvtzc3ORlpbWvC0MNPu5VBoao8Lf/SEiIvIbrwbTzpw5EzfeeCMWL16MgoICTJo0CampqY77ly5disGDBzd7IwOKY1SIiIgCxuvzqGzfvh2rVq1CSkoK7rjjDqf7e/XqhSuvvLJZGxhw2jB5aSmrdSN7UYiIiNTg9Y8Sdu7cGZ07d3Z530MPPdTkBgUdTXWJhLXmNo5RISIiUoVXQWXDhg0eLXfNNdf41JigpNiH8dhq3cigQkREpAavgsqQIUMcPzooGhhEqigKrFary/suSYpWXgrXr4ljVIiIiPzHq6ASGxuLyMhITJo0Cb/5zW+QkJDgr3YFkeoeFcEeFSIiIrV5dXhyQUEBnn/+eWzevBndu3fH/fffj02bNiEqKgrR0dGOqUVx1aPCQ5KJiIhU4VVQMRgMGD9+PL799lvs27cPPXr0wJQpU5Ceno4///nPsFgs/mpn4DiCCntUiIiI1OZVUKmtTZs2mDlzJlavXo0OHTpg3rx5KC4ubs62BQf7YFqnMSoMJ0RERGrwKaiYTCYsWLAAQ4cORbdu3ZCQkIBvvvkGcXFxzd2+wHPZo1LrboYWIiIiv/FqMO2PP/6I+fPnY+HChcjMzMR9992HxYsXt8yAYueqR4VjVIiIiFThVVAZOHAg2rRpg6lTp6Jv374AgI0bN9Zb7pZbbvHo+d555x288847OHr0KACga9eujtP0Bw17jwrPo0JERKQ6r89Mm5eXh2effbbB+705j0rr1q0xb948ZGVlQQiBDz/8EGPGjMGOHTvQtWtXb5vmH/YeFRvHqBAREanNq6Bis7kep1FbeXm5x883evRop/m///3veOedd7BlyxaXQcVkMsFkMjnm7YN3zWYzzGazx+v1hsYGaAFYbRbYqtehtQnH4B4Fwm/rvhzYa8ca+hfrrA7WWR2ss3r8VWtvns/rHpWGmEwm/OMf/8ALL7yAU6dOef14q9WKTz/9FGVlZcjOzna5zNy5czF79ux6t69atQphYWFer9MTnaoOoyOAY0dysfvkcgDAVRXnEe9YQiAnJ8cv676csIbqYJ3VwTqrg3VWT3PX2ptODa+CislkwqxZs5CTkwODwYCnnnoKt956K/7zn//gL3/5C7RaLaZNm+ZVY3fv3o3s7GxUVlYiIiICS5cuRZcuXVwuO2PGDDz++OOO+eLiYqSnp2P48OGIioryar2e0vyyDdgLZGSkI73PKACA9rt5wLmaZYYNGwa9Xu+X9bd0ZrMZOTk5rKGfsc7qYJ3VwTqrx1+19uZ0Jl4FlZkzZ+Ldd9/F0KFDsWnTJtxxxx247777sGXLFrzyyiu44447oNVq3T9RLR07dsTOnTtRVFSEzz77DBMnTsT69etdhhWj0Qij0Vjvdr1e7783q1Y+r1YBtC7XIfy7/ssEa6gO1lkdrLM6WGf1NHetvXkur4LKp59+io8++gi33HIL9uzZgx49esBiseDnn392/FihtwwGA9q3bw8A6Nu3L7Zu3YrXX38d7777rk/P1+z4o4REREQB49UJ344fP+44LLlbt24wGo2YNm2azyHFFZvN5jRgNuAU/ighERFRoHjVo2K1WmEwGGoerNMhIiLC55XPmDEDN954I9q0aYOSkhIsWLAA69atw7fffuvzczY7lz0qDCdERERq8CqoCCEwadIkxziRyspKPPzwwwgPD3dabsmSJR49X2FhIe69914UFBQgOjoaPXr0wLfffothw4Z50yz/cnUKfcEeFSIiIjV4FVQmTpzoNH/PPfc0aeX//ve/m/R4Vbj8UcJad6vYFCIiosuNV0Fl/vz5/mpH8OIp9ImIiALGp19Pvry46lFhUCEiIlIDg4o7GndjVIiIiMhfGFTcanyMChEREfkPg4o7ro76qbW7R+GuHyIiIr9hUHHH5VE/HKNCRESkBgYVd9yeR4WIiIj8hUHFHbc9KkREROQvDCruuPtRQvauEBER+Q2Dilv2EvGEb0RERGpjUHFH46JHhb0oREREqmBQccfN4clERETkPwwqbrn7UUKGFiIiIn9hUHHHbY8KgwoREZG/MKi44+rwZMGgQkREpAYGFXc4RoWIiChgGFTccXnCt1p3q9gUIiKiyw2Dijv2HhWeR4WIiEh1DCrucIwKERFRwDCouMMxKkRERAGjC3QDgpEQwLZtgF4P9EprfIwKERER+Q97VFx4/nngyiuB2bPh+kcJa+364QnfiIiI/IdBxYWbb5aXX38NXCiy96hwMC0REZHaGFRc6NYN6NcPsFiAl15y0aPCcEJERKQKBpUGTJ4sL5evdDWYtgZ3/RAREfkPg0oDJk4ERo0CbMLd4clERETkLwwqDVAU4PbbAauNJ3wjIiIKFAaVRiQnN9CjwnBCRESkCgaVRqSk1OpR4RgVIiIi1TGoNCI5GbDZZIkEx6gQERGpjkGlEUlJNT0qwsYxKkRERGpjUGmEXg9Ex1SXyMYxKkRERGpjUHEjPr66R6X2GBWeQp+IiEgVDCpuxCfKEikN/ighgwoREZG/MKi4ERsne1QUcNcPERGR2hhU3DAaq3tUFFFrlw8H0xIREamBQcUNrU5bM2Mfp8LDk4mIiFTBoOKGTl+7RPVP+qYwtBAREfkNg4obzj0q9nEqDCdERERqYFBxQ6d3seuHY1SIiIhUEdCgMnfuXPTv3x+RkZFISkrCrbfeiv379weySfU47fqx96hwdw8REZEqAhpU1q9fj8mTJ2PLli3IycmB2WzG8OHDUVZWFshmOXHdo1KDJ3wjIiLyH10gV75y5Uqn+Q8++ABJSUnYvn07rrnmmgC1ypnLHhXu+iEiIlJFQINKXUVFRQCAuLg4l/ebTCaYTCbHfHFxMQDAbDbDbDb7pU0areK4bjabAI0ZOiGg1FrGX+u+HNhrxxr6F+usDtZZHayzevxVa2+eTxEiOAZc2Gw23HLLLbh48SI2btzocplZs2Zh9uzZ9W5fsGABwsLC/NKur79ui/eu6wkAWBn2AUxKDG4s+w0MKAEA5Opuxh7jA35ZNxERUUtUXl6Ou+++G0VFRYiKimp02aAJKo888ghWrFiBjRs3onXr1i6XcdWjkp6ejrNnz7p9ob567z0NHoo0Qqe1wnzzMSA0FbovU6BUnQcAHNbdhJSbF0Ov1/tl/S2d2WxGTk4Ohg0bxhr6EeusDtZZHayzevxV6+LiYiQkJHgUVIJi18+UKVPw9ddfY8OGDQ2GFAAwGo0wGo31btfr9X57s4aEADahAWCFXqcB9HrUHaPiz/VfLlhDdbDO6mCd1cE6q6e5a+3NcwX0qB8hBKZMmYKlS5fiu+++Q9u2bQPZHJcMBsBqqz7yh6fQJyIiUlVAe1QmT56MBQsW4Msvv0RkZCROnToFAIiOjkZoaGggm+ag1wO2quo8xzPTEhERqSqgPSrvvPMOioqKMGTIEKSmpjqmRYsWBbJZTgwGwCrsPSrWevfzPCpERET+E9AelSAZx9sovR6w2ew9KjyFPhERkZr4Wz9uOI9R4Sn0iYiI1MSg4oZe72IwLXtRiIiIVMGg4obBYD88GTyFPhERkcoYVNxw6lEBf5SQiIhITQwqbrjsURHsUSEiIlIDg4obHKNCREQUOAwqbrgfo0JERET+wqDihuselRoco0JEROQ/DCpuGAy1T/jGMSpERERqYlBxQ6+vOYW+zcYxKkRERGpiUHGjdo+KxcwxKkRERGpiUHGj9hgVq5k/SkhERKQmBhU3ah/1YzFX7/rhGBUiIiJVMKi4odXW9KhYLNz1Q0REpCYGFTcUBbBVD6aN3n07YKkAgwoREZE6GFQ8IKrLpLFVAMe/dLqPY1SIiIj8h0HFA+nxeTUzWqPzGBXBoEJEROQvDCoeSIs5WecWhhMiIiI1MKh4y2qqcwNDCxERkb8wqHjgTElyzYytMnANISIiuswwqHjg3o/W18zU6VHhYFoiIiL/YVDxwImSjli4ebycsVYEtjFERESXEQYVD+j1QKU5RM5Y6+76YY8KERGRvzCoeMBgAExmo5yp06PCXT9ERET+w6DigcZ7VIiIiMhfGFQ8EB0NmCz2HhXu+iEiIlILg4oHxo8HKqtkj4rVzB4VIiIitTCoeODOOwGdQfaonCt0Dioco0JEROQ/DCoeMBgAY7gMKjYLe1SIiIjUwqDiIavg4clERERqY1DxkA2yR0Vj4wnfiIiI1MKg4iErZI+KIjhGhYiISC0MKh6yKbJHRan3o4RBFFRKjwCW8kC3goiIqNkwqHjIpsgeFY0IwsG01ipg++PAsnbAqmzAwt1TRETUMjCoeEhU96hoEWRBpfQwkHMVsP9VOX9xF7Dzj4FtExERUTNhUPGQ0FQPpkXd3ooA7vrJ+wxY0Rs4vxUwxAJd/yJvP/AmcHJF4NpFRETUTBhUPCSqd/3U7VEJyGBaayWwdTKw8Q7AXAwkDAJu3An0fBboMFUus+U+oLJQ/bYRERE1IwYVD9l7VHSB3vVTfAD4diBw8G053+VpYOg6ILyNnO/9PBDdDag8DWy5HxBBNNg30FgLIqJLDoOKp7TVPSpKAIPK0QXAyr7AxZ8BYyIwZAXQay6g0dcsow0BBi8ANEbg5NfAoX8Grr3B5NQa4Kss4JtuQN6ngLAFukVEROQBBhVPVfeoaBVLnTtU+JZuqQB+eADYNAGwlAJJQ+SunrSRrpeP6Q70miev//Q4UPSr/9sYrCzlwLapwHdDgdJcoOgXYOOdwMp+wInlwd3LIgRQsCr42xlINovc/UlELRaDiqeqe1Tq8vsYldIjQM5gIPffABSg20zg+tVAWFrjj+s4FUgZLsezbLobsJr8285gdPYHOdj4wJtyvv3DQLdnAF0kcGEHsP4mYPXVwOn1gW2nKxd/Ab4bBqwdIdu5YQxQfjLQrQoux78Cll0BLEkFTnwT6NZIwgqdKA10K4halIAGlQ0bNmD06NFIS0uDoij44osvAtmcRml0RvVXWrBKfvO/sAMwJgDX5wA9ZgMarfvHKhog+wPAGA9c2Ans+qu/Wxs8rFXAz38BcgYBJQeA0DRgyErgyneAHrOAWw4DnafL8Hnme2DNEOC7EcC5bYFuOVB1QfYAregJnF4je/I0euDEV8A3XYDc+exdKcsDNowFNtwClOcB1nLgf2OB/KWBa1PVRWDvi9B9k4Wbyu+B7psOwKZ7gANvAxd+BmzWwLUtmBT+D9jzd+DMZr6PyWO6QK68rKwMPXv2xG9/+1vcdtttgWyKW4qaQUUIYO9cubGFAOL6A1d/VjNg1lOhqcCAfwMbbgV+fRFIHQGk3ODdc1irgKpzgOls9VR9veo8EJICJA4GIjsAiuLd8/rLxd3A5ntlOAOAzAlAvzfl4dt2IQlA7xeBjtOAX+YAh94DTq2SU+uxQPdngNie6rbbZgVy/yUDpemcvK31WKDPS3L31ZbfysPQf/gtcGwhMOBfQHiGum1sKiGA4l+BvM+B41/I3ZhtbgfaTgSiOrh/vM0M7H8D2P0MYCkDFB3Q+QnZ65i3WB4FN+hjIGO831+KQ0kusP914PB/AEsZ7P8FSvlR4OhR4OjH8gZdJJAwUP6/JAwC4vsD+uim/d8IAQiL8xi15mQpB0oOAsX75WQpATL+HxDXx/vnKt4vz+90/Mua26K7Au0fAjLvAYxxnj+XzQrl/Da0sqwHKnoB+kvs/6A2SwVQni+nsjx5WXESsFXJ3ZrCWj1VX7ffBshd/Pb3U0hCYF+HnylCBEesVRQFS5cuxa233trgMiaTCSZTzS6M4uJipKen4+zZs4iKivJr+56dbcPfutTf/XNa2xuRozdCr2+mDwtzMbQ//haak8sAALa2v4W192sN7nryhGb776E9/D5EaCtYhm2TvSx1WcqhnNsM5cx6KGe+h1JxHDCdhWIpcfv8whAPET8AImEQRHw2RGxfQBfmUdvMZjNycnIwbNiwptVQWKHZ/yo0v8yCYquCMMTD2vctiNbj3D+29DC0e+dAObYACuQgW1t8Nmzt7odIvwPQhvreLg8oZzZAu2MalKLdAAAR1QXWXq9AJF9fs5DNAs3B16HZMwuKzQShi4Ctx1zY2j0oe8/caLY6e0sIKBd+gnJiKTQnvoBScsDlYrb4bNgy74VIv11uwOtQzm2BdvtkR41sCYNh7fOW3NjZLNBuexCaYx9DQAPrle9DZNzjXRtPfgXlwjaI8HZAVCeIyE6AIabh5c9uhObA6/Jx1bt/RVRXVF0xGd/tD8N1veKgv/gjlHNboJz7weX/kdCEACFJEMYkICQJMCZCGBOrb0sEdOGA6RwU0xnAdEZeVp6BYiqs/tJwBoqwQBiTIMLaAOFtIMIygLB0iLA2EOFtgLAMQF/9OmxVgK1S7ga2VcrdwjYTFKsJqLoApfQgUHIAin0qz3P9t0q8FrYOj0KkjnL/3jOdgeaXOdAc/hcUYYVQtBBJ10E5+z0Ua0V1HYwQrW+T/28JV9cPb0IAZbnQnP4OyunVUArXQTFflHdBA5E8FLbMCRBpYzz+3PGYELLHruqCDNbWciiWUhmULaXyc9Nacx2wyYH6wgZAVPca2WoubVVQKk5AKT8OlB+HUnW2eZoZ2QEifhBsCYMgErKBiOb78uivz47i4mIkJCSgqKjI7fb7kgoqs2bNwuzZs+vdvmDBAoSFNfMbtI5PP+2A/47qUu/2Qm0vbA6Z1SzriLTlo3/lPESKE7BCh92Gh3BMP7zJz6sVlRhS8TgixEmc1GZjq/EpaFCFONs+JFj3IMG6B7G2g9Cg7kBhSUCDKkSiSqmZzEoEwmynEGs7BC2qnJa3QYsiTTuc13RCvm4IirRXNPk1NCbcVoDepjcQb5ODhk9p+2GnYTJMmlg3j3QWactHh6pFSLNuhgbyW0sVwnFcNwRH9SNQovGyR8uDdneu+j+0sm5yrGuf4S4c1d0IobjevRdhO4Feprccr/WMpht2GiejXJParG1rEmFFvG0fUi2bkWrdgjBR82FshQ5ntL1QoB0IixKCdMtaJFt3OAKiFQYUaAcgT3c9zmh7QI9ydKn6CJmWHACACZHYa5iEPN11zhtJYUWvqneQYVkNAQU7Db9Hnn6Y26ZGWQ+je9W/kWD7pd59lUosSpTWKNW0QommNUo16TCKi7jCvAwxtlzHcqe1fZCrH4Mzmh6uNw7CiihbHuJsvyLOuh9xtl8RLtQ7x5ENugb/t92pQgRKNa1QqkmDVlQh1boZmuq/VamShlz9aOTrrodVce5x1ggTrjB/hSzz59BXnySzQNsfew33olSTDp0oRWvLBmRaViHadtTxuBKlFY7ph+GUtj9ibIeRaP0ZidafESbOOD2/GWEo1yQ5PdaMUJzUDUK+7jqc03RpNERpRSUibCcRIY4j3HYaelECA0qgF6UwiFIYRAn0KINelEDrY+08ZUEIKpQEVGgSUK4kolKJgw0G2BQtBDQANLBBAwE5L6CBBhbE2g4izroPkeJ4vec0IQrntR1RrqSgUolDpSYOlUqsvK7EwYJQ5/eqsMEoLiJMnEWoKESY7QxChZzCxBmc1vbFr4bfNOvrLi8vx913393ygkoge1ReekmDGRn195QVanoi4pZNTU6ayvEl0G59AIqlFCK0NayDFkHE9W/Sczq58BN0a66S38BiegLFv0KxOQcMEdoaIula2BKvAaI6Qxji5dgYfXTD//S2KigXf4ZydpPskTm7GUplQc1zaoywDl4CkeJ6o9GktC5s0OT+E5pdf4JiLYfQRcLa62WIzIlN+zZReQqaIx9Cc/jfsgu/muxleUB+6/ell6U8H8qZ9dAUboByZgOUssPyZUADW7sHYOs2S9bbHWGD5tA70Oz+s3zd2lDYrvgdENoKwhArv0EbYiEMMYA+FjDEwmzTI2f1allnLeS3aWtF9TfrCsBaAcVqgtCFA5Edvd+dUHkKyqlV0JxaJb/1Vp2vaa42HCJ1JGytboVIvRHQ1/lfrSiAJu8TaI5+CKW45gg1EdpKvr9MciNly5wEa4/nGq6RsEGz4zFoc+Uh+dbeb8DW/uEG2lsI7Z5noBz5DxQICE0IROvb5Oso2Q+l4kSjL1doQmDL/A1sWVOAqM6O2z1+P1vKAFMhlMozgKkQqCys7ik5A6VSXsJSKl+rvafFmAgRUn1pTJL3aUPkN/PyPNkDUlZ9WT1vr1399hvlY+2XunCIiCvkN/PIjkBkB4jIDoAhwfl/qTwfmkNvQ3P4fSjmIvlchjjY2j0IW/tHgJAUKHkLoN39DJSKfHl/TG9Yez4PkTTERUMElAvb5fPlLZK9E67aq+ghErIhkm+ASLoBVRHdkbNmLYYPugKGE4ugOfYxlLIjNcuHZcCWcTdsrcZAMZ2TPXkl+2t6iyrqb9wbIxSd3H2nCwd0YRC6CEAb7piHLgJCGyp3RyoyXMi6VV86btMCoanyszYsHQhLl/+vTfm8Mp2r/uyt/gw+vw2KrfGDJ4Q2XLbDmADFdFa+X+psD2or0F6J6NFr2aPiSVCpq7i4GNHR0R690KZ69VXgFlyBK5IPO91eqOmJ2HFbvf8DVhUBZceAsqPAqRzgwFvy9uTrgMELZVdwc/tlHvDzjJr50FZyfclD5GV426Z3FwohX9fZTcDh+cCp1fKD8JplQGr9sGI2m7F8+XKMGjXKuxqWHpXjNU6vlfPJ1wED/gNEZDat/bUJG1CQI8eOHP+yZt+wPgZIGQqEpsjz2VR32yMkETAmyUtDLFBRINtXuA44vU4eHl2bogWSbwB6v+DbmJjSw8APDwKnv3P/UhQ9rEILrWKGItwM7NQYgZhuQGxvILaXnGJ6AvqImmVsZuDMJqBgpZzsY4Ls9DFA61uA9Nvk0Wc6D4KdEMD57cDhD4Bjn8hxUIDcvdP/HSDpas+e46cnan77qs+rQKfHau63VgEH3gD2PFtzWHPG/wN6Pe88BsxcDBTtk2Nqiqsvi36V74F29wHtf+dyXIDP72d/sZTLMU/aWsFEY2j6/7m5VP5/739Nvg8BGW7DMoDSQ3I+rA3Q8+9A5t0e7Z6EuUT+3Q+9B5zfJt9zKUPllHS1DAX2RevWWQjgzEbgyEdyvJInh6wbE4CojkBklvy/NcYBhuqp7nVtWPCMw3PHagLO/yTHtJWfkGNeak8N1UbRyAMPwjPk3zG8DRCeAYsxDeu2n8S1N9/f7EHF0+13QAfTXkoMBqDvU9tx/l9x0CgeZjsh5Ib64q7qUFIdTMqOAdXfRpx0ng70nAto/PRn6fyk3IAqWrlhj2jX/P98iiLDQkQmkH47sPF2ecTKhluAa7+SHzpNIQSQ+57cGFlK5QdI7xeArEc8+zD0hqIB0kbIqaJAfjAfek/+DfM/c/NYbU2wqf18cf3keXCShwCJVwH6SN/bF9FOHqp+dIEMhlUXXE/CAkWYoYO5/ml/NEbZO6QNkZems3LQ5PntcqppPBDZXoYXW5U8gV7dcRdx/YDUkfL8PvEDvH8fKwoQ309OfV4GTi6X62o9FtAaPH+OPi/LDfPeecBP0wCbCej8FHDia3leIfuGNK4v0Oc1IOmq+s+jjwISrpTTpUwX1vzjNgAZWjv+Acj6PXBiGbDvFRkUSg/J2nX9k/w5D08CquM5I+Xg2vYPyUGj3rx/FEWGmaSrgb5vyDYd+UgeZRTWCojqVB1KOsrLqI6ux+q1BFojkJgtJ1csZfLzrOKk/JkVY2J1OGnlsidVmM0o0yz3c6Mbx6DiIb0eKCqPwYmSjkiP2ue4vcHzqFQVAT/cD+R/3vCTGhPkGyQ8A2h7L9B6TDO3ug6NFsj6nX/XUZvWAFz1KfC/2+VZctePBq792vsjj+zKj8sT3xV8K+cTrwIGzpcbUH8LTZUfvl2elj0YF3+R3fP2bnrH5RnAfFGGFEUDxPaRoTBpiNwg1t3t0VSKArSdICdXhAAspTCXF2LddzkYcsON0IdEAZoQ+YFWN9wJmwxi53fIXpIL1ZcVJ+QRICUHa5Y1JsojyVJHyt6y5uwF1BqB9LG+PVZRgJ7PyfC1exaw82l59M1FORAXIcnyC0G7ic0fbi83Gq38O6WPBc5tBS7uAVrdLHsVm/S8Tdg06ULlkV9qHv11KdGFy89MNT43m0lAg0ppaSkOHTrkmD9y5Ah27tyJuLg4tGnTvAMXm8re41VprvvtxEVQubAT+N8d8tuFRg+0vlV++w3PAMIzq9NrG+eu9JZKa5SHVv9vHHDym1ph5Xr3j7UTAjjyIbD9MdkTpQ2RG6IOUz07p0xzUjQ13dENsVbJngl9RPMHE28pivymGhYiB9yGptW8mV0ur5Hv1Yh2QJtaR0xVnqkJLhDy9cf2Dt4NvaLIw8w1BuDnP8mQojEAnabJwBnov0tLFN9fTkTNLKBBZdu2bbjuuusc848//jgAYOLEifjggw8C1CrXDNU9z/WDSi1CyDPIbpsiu5vD2sgehUu9+7iptEbg6s+B/90mu/PX3wwMWS53fzTGZpa9J/vflOc4AeQuhYEfANGd/N1q32kN7s8cfKkJSZS9Ji7GGQW1rjNkb9jZH+Su1Uj/HoFGRM0voEFlyJAhCJKxvG7Zv4RWNBRULGXA1t/L/aIAkHYTkP2RdycyasnsYWXDbUDBCmDdTTKsxA2qv+zF3XJA5dGP5a9AA/LbcPfZcmPjrzE81DK1myQnIrok8RPfQ46gUuVi10/xPmDLXfIH7xQN0OPvQJengrdbPFC0IcA1S+TpzwtWAutGQbn6K3mf6Sxw+FMZUC7sqHmMMVGeuTLrd3IAHBERXVYYVDxk3/VTN6hEiuPQrc4GrGXylPKDFwLJ1waghZcIbQhwzVJ5Wv+Cb6H93y24El2g+2onIMxyGY0eaDUaaDtJHkHir1OEExFR0GNQ8ZC9R6W8TlAJERcBK+SRHYMWyHNrUOO0IcA1XwDrx0A5tQqp2Cpvj+srw0nG/2vxv11BRESeYVDxkCOomOqfF8Da+Wloe85R/wiUS1l1WLHumIHDR/OQed1foU/oHehWERFRkGFQ8ZB910+ZqaZHxdr1GWzJ1eLKbk9Dy5DiPV0obL1exN6Ty5EZ3S3QrSEioiDE0Z4esveo1A4qti5/xlltjwC1iIiIqOVjUPGQPaiUVvj3V5qJiIioBoOKh+y7fkorGVSIiIjUwqDioZoeFS9+ZIuIiIiahEHFQ/agUsJdP0RERKphUPGQfddPcVl4YBtCRER0GWFQ8ZC9R2VPfufANoSIiOgywvOoeMgeVA4XXgHz1TnQh8cHtkFERESXAQYVD+lr/dxMVdxQ6MMBmM0Baw8REdHlgLt+PGQfowIAVVWBawcREdHlhD0qHqrdo8KOFKLg8OuvwC+/ADqd/B9t6DI2FmjTBlCUQLeYiLzFoOIhRQG0WsBqZVAh/7PZgJ9+ApYvB86fB1q3BtLTay5TU53D8+Xk1Cngk0+A//5X1shTCQnAlVfWTP37y9taEiGAc+eAY8dqptJSoFcvYMAAICnJ9+ctKwPKy4HKSqCiwvWl2QwYjUBoaM0UEuI8Hx7u3EPdnMxm4ORJIC8PyM8HTp+W6woJaXyyt7P2pGlgf4PNJl9rebnzZDYDGRlAcnLLCcQ2G1BYCFy8aAxoOxhUvGAwyH/I0tJAt+TyUFEhvzHv3Ss/BOLi5Dfj2lNYWP0PhdJS+QF1+rTcqNmvnz4t74+OrpliYpzno6OBqCggIkJ+G1dTWRmwejXw1VfAN9/ItjdEUWRYad1aTp07A0OHAtnZckOhFptNbhD27pV/K/tUXCz/XnFxQHy882S/LTlZ9nKEhLhfT1kZ8MUXMpysWiXXC8i/Ud++cqNiNgMWi/Ol/frZs3JavlxOdu3a1QSXfv2Arl1l+3xhNtt7eOLRvj2QmSk3yp6oqAD275d1tE8nT8oNaFhYzVR3Xgi5UbaHkrw8udFsSNu2MrDYp969nesvBHD8eM3/Xe3Lc+d8q0tdGo38m113nZwGDwYiIz1//NmzwPbtCr7+ui02bNDg+HH5HszLAwoKat4bTaXX14QYvb4mnFRUNP64qCigQ4eaqWNHeZmVJV+nzSZfQ0GB/BvXvTx7Vv5/pKYCaWk1k30+IaHhEOWO1Srbb59KS+XnzMmTwIkTcrJft7fJbNZj2LBOuPtu39bZHBQhhAjc6pumuLgY0dHRKCoqQlRUlN/XFx8vv922aQMcOABoNGYsX74co0aNgv5y/XrbRGazGV9+uRJt247E/v16/PILHFNurvzgbIzBUBNaTCYZRhr7oPaG0SgDi6spI0N+wA4eDLRq5fs68vKAr7+W03ffyddgFxEBDB8OXHGF/ODIz5cbkePHG+7VCwsDrr1WhpZhw4Bu3WSoMZtdv1fLy4GDB4F9++SG8vx5+aFce7dJ3en8+ZpAsm9f0+udkiLrmZlZ//LECeD//g9YskSGFbuBA4F77gHuvBNITHS/DpMJ+Pln4Mcfa6b9+10vm5oqA0u3bvLSPtk/YqxW4PBhYM+emvfqnj3y+er+XWJi5Puj7mQ0ytrZQ8mRI+7f696w1zQjQ65r2zb596pLrwd69gTat5f/b7/+6v6LWN1eiNqXOp2sde2NYe3JVYjQamXv1nXXAUOGyP+p8HAZMA8cAHbtkn87+3TyZOPtMxhkeG/TRtbBapUho/Zk7wGyX7e32Wr1uMQAZG3toVGjke/XxoJSfDxQVCRfm690Ohny9Xq5TkWRU93rQM3rq6iQ/6e+jK9UFIGrrjqBNWuSm3U75832m0HFC2+/DUyeLK9/+ikwZgyDiiesVpnMjx6V07FjNdePHhU4fFjAZnP9FSE+Xm4kwsPlBvLCBTmdP9/4h0pYmPxntk8pKfJSowEuXpQfFkVFztft897u2svIAK66qia4dO0qP3ztbDb54bp/v/zgPXBAXt+/X27wasvMBEaPBm6+WQYOV70jNhtw5kxNcMnLkxve1atreo3sUlJkaBkyxIITJ35AbOxAHDyodaz/2DHvXqsrer38xti5c82UkCD/RufO1Ux15wsKnMOHO+3ayXByzz3y22lTXbwoN+D24LJjh6xlQ9LTZSA+cEBuAFyJiBCIiChDSUk4ysq86/+PiwO6dKmZ2rSRG5bauxfsGxz7ZLPJdtlDSUaG3Ei76qUqKgK2bgW2bAF++EFOZ87UX06nk8HF3o7OneVl+/Y1G2Rf2XfNbNgArF0LrFsnQ1rd9WdlydsbqvMVVwjEx59CdnYSMjK0aNNG1is9Xe7e8rWNFovrUFNV5bp3q/b/OSADT26u8/+5/XphofOySUk1vSSpqTXX4+PlZ9zJkzWTvbel7nM0hT1kpaTI9bZq5foyPt6MnJzm384xqPjRn/8MPPccMHIksGzZ5RVUKivlh8s338ju9wsXXA9etF/XamU3Zn6++41/TIxA165KvW+ySUmu9/cKIb/52UPLhQvym5Q9kERE+PYahZAfSqWlDU8lJfJb9Pffy294db9BRUUBgwbJbt4DB2SPRUO9DhqNXPbmm+XUpYvv+7eFkN/sc3LktH69+25qQG58O3WSU1JSzTgsV7tQzGb54VY7lFxxhW+7yYSQfzt7eLUH2NqXOh1wxx0ynGRn+3/ff3Gx7OGo3bO3Z0/9b/GhofK11+11SU01Y+XK5bjxxlGoqNA7utPrTuXlcpdA7WCSmKju2AYhZJ1/+EHWun17+Zrat/ffGBJXjh6VgWXdOvn5UjsshocD3bvLXh/71L07EBJy6X32XrggPwvj4mp6RLxlNtfsxrZY5N/QZpOXda8L4Tw+qPauw8bG4NRfp39qzaDiR7t3Az16yD/2xYuX3j9LSYn88A/18LcVjx+XweSbb4A1a3zv5tdq5Tee2t36mZlA69YWHDu2Bvfccz0MhkujhrWVlMhvqN9/L6ctW1x3net0skeg9j7rDh3kh268n84daDIBmzbZg4sNJ0+Wo3fvMHTurEGnTrIdHTvK3o+WMvjPXy5ckAHm4kUZ6DIz63+bBvz3oX65EEL2pOzbJ/8/2rVzvUFlndUTDEGFg2m9lJwsL+3drsHIapXfkOzjDuyX+/fXDNCMjKzpfai7iyQ+XnaDf/217DGorVUr4Kab5HTFFfUHL1oszt/C4+JkMElLc/2t22wWWL688pLdUEZGyrEgw4bJeYtF7lPftEn2zNiDSWam+kfpGI01AxZnz7Zi+fI11R82PH2St2Jj5W498i9FkeGkXbtAt4SCCYOKl8Jq/XhyQ/tP7UpKgEcflfvh4+PlN9eGLr0Z9V7XyZPAt9/Kb867d8tdDbUHZTbUtpISuWxjFEUOXLzpJrlrokcPfvtujE4H9OkjJyIiajoGFS/VDiruBgK++iowf75nz5uWJke+28/v0K+f/Bbnitksv7GvWAGsXFm/1wOQ36azsuDo4rdfdugg76972G7t+cJC2QNw001yLI4nR1UQERH5A4OKlzQaORDJfkx9Q8rLgTfflNcnT5a7QM6dk4NL7Zf2yWSSvSJffiknu6wsGVr695fnOzhwQIaT1atlb4idoshgM3Kk7P3o1EnubnG1D90uOloGFyIiomDGoOKDsDD3QeWDD2QIycwEXnut4aMihJCh4+ef5aGD9ik3V+6WOXgQWLCg/uMSE4ERI2Q4GT6cvR5ERNQyMaj4ICxMHlbZ0KGfVivw8svy+hNPNH7opqLIw1mvvlpOdufOyXM8bN0qz/Hw889yIOuNN8qpT5+mnc+AiIjoUsCg4gP7abHLy12PKl2yRJ7IKz4euO8+39YRHy97TEaM8LGRRERELQC/k/vAPqDW1WBaIYDnn5fXp0zx/Lc+iIiIqD4GFR/Yg4qrMSrr1gHbt8sTqtlPt09ERES+YVDxQWNB5YUX5OV993GAKxERUVMxqPjAHlTqDqbdtUue10SjAR5/XP12ERERtTQMKj6wjzup++uoL74oL2+/XZ5enoiIiJqGQcUHrnb95OUBCxfK608+qX6biIiIWiIGFR+4CiqvvSZ/kO766+VZYomIiKjpGFR8UHeMyoULwL/+Ja8/9VRg2kRERNQSMaj4oO4YlXff1aCsTP6y8PDhAWwYERFRC8Og4oPau36qqjR46y1ZxieflKfEJyIioubBoOKD2kFl7dp0FBYqSE8Hxo8PbLuIiIhamqAIKv/4xz+QmZmJkJAQDBgwAD/++GOgm9Qoe1ApLQW+/LI9AHneFL0+gI0iIiJqgQIeVBYtWoTHH38czzzzDH766Sf07NkTI0aMQGFhYaCb1iD7GJU1azQ4eTICsbECDzwQ2DYRERG1RAEPKq+88goefPBB3HfffejSpQv++c9/IiwsDP/5z38C3bQG2XtU7B56yIaIiMC0hYiIqCXTBXLlVVVV2L59O2bMmOG4TaPRYOjQodi8eXO95U0mE0wmk2O+uLgYAGA2m2E2m/3f4GoGgwJ76fR6Kx56yASzmft9fGH/u6n597scsc7qYJ3VwTqrx1+19ub5AhpUzp49C6vViuTkZKfbk5OTsW/fvnrLz507F7Nnz653+6pVqxBWt5vDjyoqtLjiiqtw8mQ4br31EHbvPoDdu1VbfYuUk5MT6CZcFlhndbDO6mCd1dPctS539au+DQhoUPHWjBkz8HitX/srLi5Geno6hg8fjqioKFXbMm6cTIQ5OQcwbNgw6DmS1ieyhjmsoZ+xzupgndXBOqvHX7W27xHxRECDSkJCArRaLU6fPu10++nTp5GSklJveaPRCKPRWO92vV4f0DdroNffErCG6mCd1cE6q4N1Vk9z19qb5wroYFqDwYC+fftizZo1jttsNhvWrFmD7OzsALaMiIiIgkHAd/08/vjjmDhxIvr164crr7wSr732GsrKynDfffcFumlEREQUYAEPKuPHj8eZM2cwc+ZMnDp1Cr169cLKlSvrDbAlIiKiy0/AgwoATJkyBVOmTAl0M4iIiCjIBPyEb0REREQNYVAhIiKioMWgQkREREGLQYWIiIiCFoMKERERBS0GFSIiIgpaDCpEREQUtBhUiIiIKGgxqBAREVHQCooz0/pKCAHAu5+Lbk5msxnl5eUoLi7mL3j6iDVUB+usDtZZHayzevxVa/t2274db8wlHVRKSkoAAOnp6QFuCREREXmrpKQE0dHRjS6jCE/iTJCy2Ww4efIkIiMjoSiK6usvLi5Geno68vPzERUVpfr6WwLWUB2sszpYZ3WwzurxV62FECgpKUFaWho0msZHoVzSPSoajQatW7cOdDMQFRXFf5YmYg3VwTqrg3VWB+usHn/U2l1Pih0H0xIREVHQYlAhIiKioMWg0gRGoxHPPPMMjEZjoJtyyWIN1cE6q4N1VgfrrJ5gqPUlPZiWiIiIWjb2qBAREVHQYlAhIiKioMWgQkREREGLQYWIiIiCFoOKGxs2bMDo0aORlpYGRVHwxRdfON0vhMDMmTORmpqK0NBQDB06FAcPHgxMY4NEc9Ts/PnzmDBhAqKiohATE4P7778fpaWlKr6K4Dd37lz0798fkZGRSEpKwq233or9+/c7LVNZWYnJkycjPj4eERERGDduHE6fPu20TF5eHm666SaEhYUhKSkJTz75JCwWi5ovJai988476NGjh+OEV9nZ2VixYoXjftbYP+bNmwdFUfDYY485bmOtm8esWbOgKIrT1KlTJ8f9wVZnBhU3ysrK0LNnT/zjH/9wef8LL7yAN954A//85z/xww8/IDw8HCNGjEBlZaXKLQ0ezVGzCRMm4JdffkFOTg6+/vprbNiwAQ899JBaL+GSsH79ekyePBlbtmxBTk4OzGYzhg8fjrKyMscy06ZNw1dffYVPP/0U69evx8mTJ3Hbbbc57rdarbjppptQVVWFTZs24cMPP8QHH3yAmTNnBuIlBaXWrVtj3rx52L59O7Zt24brr78eY8aMwS+//AKANfaHrVu34t1330WPHj2cbmetm0/Xrl1RUFDgmDZu3Oi4L+jqLMhjAMTSpUsd8zabTaSkpIgXX3zRcdvFixeF0WgUn3zySQBaGHx8qdnevXsFALF161bHMitWrBCKoogTJ06o1vZLTWFhoQAg1q9fL4SQddXr9eLTTz91LPPrr78KAGLz5s1CCCGWL18uNBqNOHXqlGOZd955R0RFRQmTyaTuC7iExMbGivfff5819oOSkhKRlZUlcnJyxLXXXiseffRRIQTfz83pmWeeET179nR5XzDWmT0qTXDkyBGcOnUKQ4cOddwWHR2NAQMGYPPmzQFsWfDypGabN29GTEwM+vXr51hm6NCh0Gg0+OGHH1Rv86WiqKgIABAXFwcA2L59O8xms1OtO3XqhDZt2jjVunv37khOTnYsM2LECBQXFzt6DKiG1WrFwoULUVZWhuzsbNbYDyZPnoybbrrJqaYA38/N7eDBg0hLS0O7du0wYcIE5OXlAQjOOl/SP0oYaKdOnQIApz+Wfd5+HznzpGanTp1CUlKS0/06nQ5xcXGsawNsNhsee+wxDB48GN26dQMg62gwGBATE+O0bN1au/pb2O8jaffu3cjOzkZlZSUiIiKwdOlSdOnSBTt37mSNm9HChQvx008/YevWrfXu4/u5+QwYMAAffPABOnbsiIKCAsyePRtXX3019uzZE5R1ZlAhagEmT56MPXv2OO1npubTsWNH7Ny5E0VFRfjss88wceJErF+/PtDNalHy8/Px6KOPIicnByEhIYFuTot24403Oq736NEDAwYMQEZGBhYvXozQ0NAAtsw17vppgpSUFACoNxr69OnTjvvImSc1S0lJQWFhodP9FosF58+fZ11dmDJlCr7++musXbsWrVu3dtyekpKCqqoqXLx40Wn5urV29bew30eSwWBA+/bt0bdvX8ydOxc9e/bE66+/zho3o+3bt6OwsBB9+vSBTqeDTqfD+vXr8cYbb0Cn0yE5OZm19pOYmBh06NABhw4dCsr3NINKE7Rt2xYpKSlYs2aN47bi4mL88MMPyM7ODmDLgpcnNcvOzsbFixexfft2xzLfffcdbDYbBgwYoHqbg5UQAlOmTMHSpUvx3XffoW3btk739+3bF3q93qnW+/fvR15enlOtd+/e7RQMc3JyEBUVhS5duqjzQi5BNpsNJpOJNW5GN9xwA3bv3o2dO3c6pn79+mHChAmO66y1f5SWliI3NxepqanB+Z5u9uG5LUxJSYnYsWOH2LFjhwAgXnnlFbFjxw5x7NgxIYQQ8+bNEzExMeLLL78Uu3btEmPGjBFt27YVFRUVAW554DRHzUaOHCl69+4tfvjhB7Fx40aRlZUl7rrrrkC9pKD0yCOPiOjoaLFu3TpRUFDgmMrLyx3LPPzww6JNmzbiu+++E9u2bRPZ2dkiOzvbcb/FYhHdunUTw4cPFzt37hQrV64UiYmJYsaMGYF4SUHp6aefFuvXrxdHjhwRu3btEk8//bRQFEWsWrVKCMEa+1Pto36EYK2byxNPPCHWrVsnjhw5Ir7//nsxdOhQkZCQIAoLC4UQwVdnBhU31q5dKwDUmyZOnCiEkIfb/vWvfxXJycnCaDSKG264Qezfvz+wjQ6w5qjZuXPnxF133SUiIiJEVFSUuO+++0RJSUkAXk3wclVjAGL+/PmOZSoqKsTvf/97ERsbK8LCwsTYsWNFQUGB0/McPXpU3HjjjSI0NFQkJCSIJ554QpjNZpVfTfD67W9/KzIyMoTBYBCJiYnihhtucIQUIVhjf6obVFjr5jF+/HiRmpoqDAaDaNWqlRg/frw4dOiQ4/5gq7MihBDN309DRERE1HQco0JERERBi0GFiIiIghaDChEREQUtBhUiIiIKWgwqREREFLQYVIiIiChoMagQERFR0GJQISIioqDFoEJEqsrMzMRrr73m13UcPXoUiqJg586dfl0PEfkfgwoRuaQoSqPTrFmzfHrerVu34qGHHmpS244cOYK7774baWlpCAkJQevWrTFmzBjs27cPAJCeno6CggJ069atSeshosDTBboBRBScCgoKHNcXLVqEmTNnYv/+/Y7bIiIiHNeFELBardDp3H+kJCYmNqldZrMZw4YNQ8eOHbFkyRKkpqbi+PHjWLFiheOn6bVarV9+bp6I1MceFSJyKSUlxTFFR0dDURTH/L59+xAZGYkVK1agb9++MBqN2LhxI3JzczFmzBgkJycjIiIC/fv3x+rVq52et+6uH0VR8P7772Ps2LEICwtDVlYWli1b1mC7fvnlF+Tm5uLtt9/GwIEDkZGRgcGDB2POnDkYOHAggPq7fiZNmuSyV2jdunUAAJPJhOnTp6NVq1YIDw/HgAEDHPcRUWAxqBCRz55++mnMmzcPv/76K3r06IHS0lKMGjUKa9aswY4dOzBy5EiMHj0aeXl5jT7P7Nmzceedd2LXrl0YNWoUJkyYgPPnz7tcNjExERqNBp999hmsVqtH7Xz99ddRUFDgmB599FEkJSWhU6dOAIApU6Zg8+bNWLhwIXbt2oU77rgDI0eOxMGDB70rCBE1P7/8JjMRtSjz588X0dHRjvm1a9cKAOKLL75w+9iuXbuKN9980zGfkZEhXn31Vcc8APGXv/zFMV9aWioAiBUrVjT4nG+99ZYICwsTkZGR4rrrrhN/+9vfRG5uruP+I0eOCABix44d9R77+eefi5CQELFx40YhhBDHjh0TWq1WnDhxwmm5G264QcyYMcPt6yMi/2KPChH5rF+/fk7zpaWlmD59Ojp37oyYmBhERETg119/dduj0qNHD8f18PBwREVFobCwsMHlJ0+ejFOnTuHjjz9GdnY2Pv30U3Tt2hU5OTmNrmfHjh34zW9+g7feeguDBw8GAOzevRtWqxUdOnRARESEY1q/fj1yc3PdlYCI/IyDaYnIZ+Hh4U7z06dPR05ODl566SW0b98eoaGhuP3221FVVdXo8+j1eqd5RVFgs9kafUxkZCRGjx6N0aNHY86cORgxYgTmzJmDYcOGuVz+1KlTuOWWW/DAAw/g/vvvd9xeWloKrVaL7du3Q6vVOj2m9oBhIgoMBhUiajbff/89Jk2ahLFjxwKQIeDo0aN+X6+iKOjUqRM2bdrk8v7KykqMGTMGnTp1wiuvvOJ0X+/evWG1WlFYWIirr77a720lIu8wqBBRs8nKysKSJUswevRoKIqCv/71r257Rry1c+dOPPPMM/jNb36DLl26wGAwYP369fjPf/6DP/7xjy4f87vf/Q75+flYs2YNzpw547g9Li4OHTp0wIQJE3Dvvffi5ZdfRu/evXHmzBmsWbMGPXr0wE033dSs7Sci7zCoEFGzeeWVV/Db3/4WgwYNQkJCAv74xz+iuLi4WdfRunVrZGZmYvbs2Y7DkO3z06ZNc/mY9evXo6CgAF26dHG6fe3atRgyZAjmz5+POXPm4IknnsCJEyeQkJCAgQMH4uabb27WthOR9xQhhAh0I4iIiIhc4VE/REREFLQYVIiIiChoMagQERFR0GJQISIioqDFoEJERERBi0GFiIiIghaDChEREQUtBhUiIiIKWgwqREREFLQYVIiIiChoMagQERFR0Pr/nSuBpgCIYFAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# exercice 4\n",
    "\n",
    "train_sizes = np.arange(10, 501, 10)\n",
    "new_train_rmse = dict()\n",
    "new_test_rmse = dict()\n",
    "\n",
    "x_test_poly = make_polynomial_phi(x_test, 9)\n",
    "for train_size in train_sizes:\n",
    "    # Prepare the data\n",
    "    new_x = np.linspace(0, 10, train_size)\n",
    "    noise = np.random.normal(loc=0, scale=0.5, size=train_size)\n",
    "    new_y = 4*np.sin(new_x) + noise\n",
    "\n",
    "    x_train_poly = make_polynomial_phi(new_x, 9)\n",
    "    # Train the model\n",
    "    w_pi = linear_regression_PI(x_train_poly, new_y)\n",
    "    # make our predictions\n",
    "    y_pred_train = x_train_poly @ w_pi\n",
    "    y_pred_test = x_test_poly @ w_pi\n",
    "    \n",
    "    # save the bases and associate rmse\n",
    "    rmse_train[train_size] = my_rmse(new_y, y_pred_train)\n",
    "    rmse_test[train_size] = my_rmse(y_test, y_pred_test)\n",
    "\n",
    "plt.plot(rmse_train.keys(), rmse_train.values(), color=\"blue\", label=\"Train Results\")\n",
    "plt.plot(rmse_test.keys(), rmse_test.values(), color=\"orange\", label=\"Test Results\")\n",
    "plt.xlabel(\"Train Size\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.xticks([10, 100, 200, 300, 400, 500])\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6315547-1273-42ae-973a-0825c2312804",
   "metadata": {},
   "source": [
    "# Classification with KNN\n",
    "In this exercise you will implement the K-nearest neighbours (K-NN) algorithm for multi-class classification and use it to classify the Wine dataset. You will also need to determine the optimal value of $K$ using the accuracy on a validation set and report the test set performance based on the accuracy.\n",
    "\n",
    "Dataset: The Wine dataset contains the results of a chemical analysis of wines grown in the same region in Italy but derived from three different cultivars. The analysis determined the quantities of 13 constituents found in each of the three types of wines. The dataset contains 178 observations, with 13 attributes each. There are three different classes of wines.\n",
    "\n",
    "Specifically:\n",
    "1. 1.\tLoad the Wine dataset and split it into a training set ($70\\%$), a validation set ($15\\%$), and a testing set ($15\\%$).\n",
    "    \n",
    "2. You will write code that implements the K-NN algorithm for multi-class classification. Use Euclidean distance as the distance metric.\n",
    "    - _Obs: it is better if you take only odd values of K, considering you are predicting the class based on the majority of the neighbours._\n",
    "\n",
    "\n",
    "3. Use the K-NN algorithm on the training set for a range of values of $K$ and evaluate its performance on the validation set using the accuracy. Plot the accuracy on the validation set against the range of values that were tried for $K$. Your plot should look like Figure 3. \n",
    "    - *Observation: it is better if you take only odd values of K, considering you are predicting the class based on the majority of the neighbours.*\n",
    "    - **You will also have to implement the accuracy-score from scratch.**\n",
    "\n",
    "\n",
    "4. \tChoose the value of $K$ that gives the best accuracy score in point 3 and report the accuracy of the K-NN algorithm on the test set using the selected value of $K$.\n",
    "\t- *Observation: when obtaining the predictions for the testing set, remember to include the validation set in your training set.*\n",
    "\n",
    "\n",
    "\n",
    "* __Note:__ You are not allowed to use any Python libraries such as scikit-learn to implement the K-NN algorithm or to calculate distances or the accuracy score. You may use numpy or other basic libraries for matrix operations.\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a08168d9-c8d3-496c-b24e-3c6aa92cc406",
   "metadata": {},
   "source": [
    "### Preparing the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3644c7b-3b33-4595-b49c-29b9a53ca088",
   "metadata": {},
   "source": [
    "Load the dataset and generate the training, validation and testing sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "836ed810-8ac1-4781-b4b7-ac9d46762ab6",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "X_wine = pd.read_csv('X_wine.csv')\n",
    "y_wine = pd.read_csv('y_wine.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0aec99a-7224-4d05-a4f3-23259d621b88",
   "metadata": {},
   "source": [
    "Let's inspect the dataset. There are 13 features and one target column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "ec8beb33-b369-4fd7-a8f9-2eaa9e2ba92f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Alcohol</th>\n",
       "      <th>Malicacid</th>\n",
       "      <th>Ash</th>\n",
       "      <th>Alcalinity_of_ash</th>\n",
       "      <th>Magnesium</th>\n",
       "      <th>Total_phenols</th>\n",
       "      <th>Flavanoids</th>\n",
       "      <th>Nonflavanoid_phenols</th>\n",
       "      <th>Proanthocyanins</th>\n",
       "      <th>Color_intensity</th>\n",
       "      <th>Hue</th>\n",
       "      <th>0D280_0D315_of_diluted_wines</th>\n",
       "      <th>Proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Alcohol  Malicacid   Ash  Alcalinity_of_ash  Magnesium  Total_phenols  \\\n",
       "0    14.23       1.71  2.43               15.6        127           2.80   \n",
       "1    13.20       1.78  2.14               11.2        100           2.65   \n",
       "2    13.16       2.36  2.67               18.6        101           2.80   \n",
       "3    14.37       1.95  2.50               16.8        113           3.85   \n",
       "4    13.24       2.59  2.87               21.0        118           2.80   \n",
       "\n",
       "   Flavanoids  Nonflavanoid_phenols  Proanthocyanins  Color_intensity   Hue  \\\n",
       "0        3.06                  0.28             2.29             5.64  1.04   \n",
       "1        2.76                  0.26             1.28             4.38  1.05   \n",
       "2        3.24                  0.30             2.81             5.68  1.03   \n",
       "3        3.49                  0.24             2.18             7.80  0.86   \n",
       "4        2.69                  0.39             1.82             4.32  1.04   \n",
       "\n",
       "   0D280_0D315_of_diluted_wines  Proline  \n",
       "0                          3.92     1065  \n",
       "1                          3.40     1050  \n",
       "2                          3.17     1185  \n",
       "3                          3.45     1480  \n",
       "4                          2.93      735  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_wine.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "780db93b-1cb3-4b48-8c3a-4980acb0d403",
   "metadata": {},
   "source": [
    "We can inspect the class distribution by using `value_counts()` on the target variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d45c38ad-e30c-4f0a-823e-aa8f89eec215",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "class\n",
       "2        71\n",
       "1        59\n",
       "3        48\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_wine.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5268baac-164d-4c23-92d2-fa5eeffca5bb",
   "metadata": {},
   "source": [
    "Now you will write code to split the data into training ($70\\%$), validation ($15\\%$), and testing ($15\\%$). \n",
    "\n",
    "You can use `train_test_split()` but make sure to calculate the right proportions and remember that this only returns 2 different sets, not 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "92a12994-bbac-4ba3-b115-0de949b87231",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# set the random_state for reproducibilty of your results\n",
    "random_state = 113"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "40f9fff4-e811-41a0-940b-1539a002c3d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# your code goes here:\n",
    "X_train, X_val_test, y_train, y_val_test = train_test_split(X_wine, y_wine, test_size=0.3, random_state=random_state)\n",
    "\n",
    "X_val, X_test, y_val, y_test = train_test_split(X_val_test, y_val_test, test_size=0.5, random_state=random_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c36e0e12-6f05-415e-9736-e980667818c3",
   "metadata": {},
   "source": [
    "### Here you will implement the KNN algorithm using the euclidean distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "87585ca3-a5f7-4155-822d-bafcc3be3d5c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def euclidean_dist(x1:np.ndarray, x2:np.ndarray) -> float:\n",
    "    \"\"\"Get the euclidean distance between 2 points in a space\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    x1 : np.ndarray\n",
    "        First point\n",
    "    x2 : np.ndarray\n",
    "        Second point\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    float\n",
    "        Distance between the points\n",
    "    \"\"\"\n",
    "    # your code goes here:\n",
    "    # First we calculate the squared difference\n",
    "    squared_diff = (x1- x2) ** 2\n",
    "    # Then the distance\n",
    "    dist = np.sqrt(np.sum(squared_diff))\n",
    "    return dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f56f6ba5-944e-4109-b423-7dec4890036a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def knn_predict(X_data:np.ndarray, y_data:np.ndarray, X_pred:np.ndarray, k:float) -> np.ndarray:\n",
    "    \"\"\"Perform predictions using the KNN (k-nearest neighbors) algorithm.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    X_data : np.ndarray\n",
    "        Training dataset.\n",
    "    y_data : np.ndarray\n",
    "        Labels from training dataset.\n",
    "    X_pred : np.ndarray\n",
    "        Prediction dataset.\n",
    "    k : int\n",
    "        Number of nearest neighbors for classification.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    np.ndarray\n",
    "        Predictions for the prediction dataset.\n",
    "    \"\"\"\n",
    "    # your code goes here:\n",
    "    # The list where we save our results\n",
    "    y_predict = list()\n",
    "\n",
    "    # Choose an line on our prediction data to check the knn\n",
    "    for i_pred in range(len(X_pred)):\n",
    "        distances = list()\n",
    "        x_i_pred = X_pred[i_pred, :].T\n",
    "        # Let's compare with every point in our data and append the distances\n",
    "        for i_data in range(len(X_data)):\n",
    "            x_i_data = X_data[i_data, :].T\n",
    "            distances.append(euclidean_dist(x_i_pred, x_i_data))\n",
    "        # Get the k-nearsts points and save it's labels\n",
    "        k_index = np.argsort(distances)[:k]\n",
    "        k_labels = y_data[k_index]\n",
    "        # So get the most common class to our classification\n",
    "        classes, count = np.unique(k_labels, return_counts=True)\n",
    "        y_predict.append(classes[np.argmax(count)])\n",
    "    \n",
    "    return np.array(y_predict)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1443e168-3fec-40a9-84e5-a5bb3e03352d",
   "metadata": {},
   "source": [
    "### Select the optimal $K$ by plotting the accuracy score in the validation set at different values of $K$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17ec49e0-84eb-41e5-a6d3-b124520f2aa6",
   "metadata": {},
   "source": [
    "First create a function that calculates the accuracy score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6179ed96-a064-4c7b-8f6b-aa11425da940",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_acc_score(X_data:np.ndarray, y_data:np.ndarray, X_pred:np.ndarray, y_true:np.ndarray, k_values):\n",
    "    # your code goes here:\n",
    "    k_accuracy = dict()\n",
    "    # For every k we check it's precision\n",
    "    for k in k_values:\n",
    "        y_predict = knn_predict(X_data=X_data, y_data=y_data, X_pred=X_pred, k=k)\n",
    "        y_predict = y_predict.reshape(-1, 1)\n",
    "        # Calculate the accuracy\n",
    "        correct = np.sum((y_true == y_predict).astype(int))\n",
    "        accuracy = correct/len(y_true)\n",
    "        # Save the accuracy for every k\n",
    "        k_accuracy[k] = accuracy\n",
    "\n",
    "    return k_accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6df1af4-5361-4cb3-baaa-23ae6470c0e2",
   "metadata": {},
   "source": [
    "Generate the plot and select the optimal $K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "41ae15c8-b904-4383-92a1-616bd0f3b4bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# your code goes here:\n",
    "# Get the accurarys for 1:31:2 and plot the results\n",
    "k_values = np.arange(1, 32, 2)\n",
    "accuracies = calculate_acc_score(X_train.values, y_train.values, X_val.values, y_val.values, k_values)\n",
    "\n",
    "plt.subplots(figsize=(12,5))\n",
    "plt.plot(accuracies.keys(), accuracies.values(), marker=\"o\", label=\"validation\")\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"Accuracy\")\n",
    "plt.xticks(k_values)\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08575674-1b72-4c31-90c2-8e3891af6762",
   "metadata": {},
   "source": [
    "Calculate the test set performance using the optimal $K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ff7c6e2a-84a0-42ea-9b7f-b343072355cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy for K = 3: 0.5925925925925926\n"
     ]
    }
   ],
   "source": [
    "# your code goes here:\n",
    "# By the plot, we choose k=3 as our optimal K\n",
    "best_k = max(accuracies, key=accuracies.get)\n",
    "# So we concatenate our train and validate data\n",
    "X_train_val = np.concatenate((X_train, X_val))\n",
    "y_train_val = np.concatenate((y_train, y_val))\n",
    "\n",
    "# Finally get the accuracy for the best k in the test data\n",
    "performance = calculate_acc_score(X_train_val, y_train_val, X_test.values, y_test.values, [best_k])\n",
    "print(f\"Accuracy for K = {best_k}:\", performance[best_k])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}