DL2022_HW1_P3.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "run_control": {
          "frozen": true
        },
        "id": "L9soqHyHrjHM"
      },
      "source": [
        "# Deep Learning"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "jI66aEkHrjHO"
      },
      "source": [
        "## HW1- Problem 3 - Regression (100 pts)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "heading_collapsed": true,
        "hidden": true,
        "id": "a_uYZ7vnrjHP"
      },
      "source": [
        "### Please fill this part\n",
        "\n",
        "\n",
        "1.   Full Name: Radmehr Karimian\n",
        "2.   Student Number: 98103556\n",
        "\n",
        "\n",
        "*You are just allowded to change those parts that start with \"TO DO\". Please do not change other parts.*\n",
        "\n",
        "*It is highly recommended to read each codeline carefully and try to understand what it exactly does. Best of luck and have fun!*"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "id": "H-G8sVjPrjHP"
      },
      "outputs": [],
      "source": [
        "# You are not allowed to import other packages.\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "from matplotlib import pyplot as plt\n",
        "from sklearn.metrics import mean_squared_error"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/gdrive')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DAYBDI-g1mYT",
        "outputId": "3bbd0389-e978-4647-c857-9b9d688e6c1d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/gdrive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "cd /content/gdrive/MyDrive/DeepLearning"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DJQiEOkb2CoJ",
        "outputId": "3f9e51a8-ee0b-4f61-c22a-b2e43005be3a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "/content/gdrive/MyDrive/DeepLearning\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "!ls"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F1MGLfqW2evn",
        "outputId": "d624c07e-aad6-4af0-98ff-1ef8f59cb06a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "data\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "B_vgOIl2rjHQ"
      },
      "source": [
        "### Part1:\n",
        "Consider the dataset which has been given to you. Split the dataset into the `training dataset` and `test dataset`. You can use `80%` of the data for training and the rest for testing."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "id": "1MtgnC4UrjHQ"
      },
      "outputs": [],
      "source": [
        "dataset = pd.read_csv(\"./data/data01.csv\")\n",
        "\n",
        "# implement the split part\n",
        "# name them: x_train, x_test, y_train, y_test\n",
        "\n",
        "train_dataset = dataset.sample(frac=0.8, replace=False, random_state=1)\n",
        "test_dataset=dataset.drop(train_dataset.index)\n",
        "train = train_dataset.shape[0]\n",
        "test = test_dataset.shape[0]\n",
        "\n",
        "\n",
        "x_train = np.array(train_dataset.X).reshape(train,1)\n",
        "y_train = np.array(train_dataset.Y).reshape(train,1)\n",
        "\n",
        "x_test = np.array(test_dataset.X).reshape(test,1)\n",
        "y_test = np.array(test_dataset.Y).reshape(test,1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "9ZdToYlSrjHR"
      },
      "source": [
        "### Part2:\n",
        "Assume there is simple linear relationship between X and Y. Train a simple `Linear Regression` on the training dataset and report its accuracy on the training and testing dataset, separately."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "id": "6DyBbSuXrjHR"
      },
      "outputs": [],
      "source": [
        "# here you can implement via sgd or use least square solution. we suggest the second one inv(A^T A) * A^T y.\n",
        "# consider m as the returned line --> m[0] = the slope , m[1] = y intercept, also don't forget to use numpy for calculating m.\n",
        "\n",
        "A = x_train\n",
        "A = np.hstack((A,np.ones((train,1),dtype=np.float64)))\n",
        "Y = np.array(y_train).reshape(train,1)\n",
        "\n",
        "m = np.linalg.inv(A.T @  A)@((A).T @ Y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "22l5FPSurjHR",
        "outputId": "85647da9-9608-48f0-ff90-4de2b9bbbd5d"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE train error: 0.3140290524996677\n",
            "MSE test error: 0.39731482572060345\n"
          ]
        }
      ],
      "source": [
        "predicted_train_y = m[0] * x_train + m[1]\n",
        "predicted_test_y = m[0] * x_test + m[1]\n",
        "\n",
        "train_error = np.sum((y_train-predicted_train_y)**2)/len(y_train)\n",
        "test_error = np.sum((y_test-predicted_test_y)**2)/len(y_test)\n",
        "\n",
        "print(f\"MSE train error: {train_error}\\nMSE test error: {test_error}\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "HWzoRn4TrjHS"
      },
      "source": [
        "### Part3:\n",
        "Draw the line you've found in the last part, on train and test points (each separately)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "ADlKtrzBrjHS",
        "outputId": "4902125c-8ee7-4bc8-af2e-d33bde2cfc89"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Train dataset')"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.scatter(x_train, y_train)\n",
        "plt.scatter(x_train, m[0]*x_train + m[1], s=1)\n",
        "plt.title(\"Train dataset\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "id": "TT_2TeOBrjHS",
        "outputId": "4ef0ee2c-dcdf-4174-8ac7-5192b7b0beeb"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Test dataset')"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.scatter(x_test, y_test)\n",
        "plt.scatter(x_test, m[0]*x_test + m[1], s=1)\n",
        "plt.title(\"Test dataset\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "eU5ScxcirjHT"
      },
      "source": [
        "### Part4:\n",
        "Were the reported accuracies acceptable?\n",
        "\n",
        "What about the line you drew in the last part?\n",
        "\n",
        "Was it appropriate for the dataset?\n",
        "<br><br/>\n",
        "Explain what are the main problems here."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "hidden": true,
        "id": "QSoJzwG-rjHT"
      },
      "source": [
        "they were not good, this model predicted this dataset well as linear regression but our data isn't linear i think that third-digree is much better answer"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "WhjgsDCyrjHT"
      },
      "source": [
        "### Part5:\n",
        "Now, consider the `Locally Weighted Linear Regression` approach for this problem. Do expect it performs better than simple `Linear Regression` for this dataset?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "hidden": true,
        "id": "Iedals7_rjHT"
      },
      "source": [
        "yes it would be better because as you can see you can break our data in forms that as liner in several parts, so this is why Locally Weighted Linear Regression would be better option than Linear Regression."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "RgjkZZFGrjHT"
      },
      "source": [
        "### Part6:\n",
        "Here, we want to implement the `suggested model`. You can implement any weight function you want, the below implementation is just a sample:\n",
        "<br><br/>\n",
        "\\begin{equation*}\n",
        "    w^{(i)}=exp\\left(-\\frac{(\\mathbf x^{(i)}-\\mathbf x)^\\top(\\mathbf x^{(i)}-\\mathbf x)}{2\\tau^2}\\right)\n",
        "\\end{equation*}"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "id": "VPYqkgcMrjHU"
      },
      "outputs": [],
      "source": [
        "def get_weight_matrix(the_query_point, train_dataset, hyperparameter):\n",
        "    l = train_dataset.shape[0]\n",
        "    W = np.mat(np.eye(l))\n",
        "    for i, xi in enumerate(train_dataset):\n",
        "      q = np.array([np.sum(the_query_point[0,0]),1])\n",
        "      W[i, i] = np.exp(-(np.transpose(xi-q) @ (xi-q))/(2*hyperparameter**2))\n",
        "    return W"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "N18FCgLKrjHU"
      },
      "source": [
        "Now implement the `closed form solution` based on the following formula:\n",
        "<br><br/>\n",
        "\\begin{equation*}\n",
        "    \\boldsymbol\\theta=(X^\\top WX)^{-1}(X^\\top WY)\n",
        "\\end{equation*}\n",
        "<br><br/>\n",
        "Of course if you use another form, implement your own."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "id": "JhCZUp84rjHU"
      },
      "outputs": [],
      "source": [
        "def predict(train_X, train_Y, query_x, hyperparameter):\n",
        "    l = train_dataset.shape[0]\n",
        "    X = np.hstack((train_X, np.ones((l, 1))))\n",
        "    qx = np.mat([query_x, 1])\n",
        "    W = get_weight_matrix(qx, X, hyperparameter)\n",
        "\n",
        "    theta = np.linalg.inv(np.transpose(X) @ W @ X)@(np.transpose(X) @ W @ train_Y)\n",
        "\n",
        "    return np.sum(np.dot(qx, theta))[0]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "qO4X-egKrjHU"
      },
      "source": [
        "### Part7:\n",
        "Report accuracy of this model on the test dataset. Also, draw a plot that contains (x_test, y_test) pairs and (x_test, predicted_y) pairs that differ in color."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DJiKAu5CrjHU",
        "outputId": "0c45e1e5-0704-4c02-8bca-ebe6af70fee7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/numpy/matrixlib/defmatrix.py:145: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  arr = N.array(data, dtype=dtype, copy=copy)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE test error: 0.11280268817178454\n"
          ]
        }
      ],
      "source": [
        "hyperparameter=0.1\n",
        "predicted_test = [predict(x_train, y_train, query, hyperparameter) for query in x_test]\n",
        "error = np.sum((y_test-predicted_test)**2)\n",
        "error = error/len(y_test)\n",
        "print(f\"MSE test error: {error}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "5Ra7e_1XrjHU",
        "outputId": "d2bc0a2a-baac-453e-e48b-b718ad8f55d8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f60e7f17d90>"
            ]
          },
          "metadata": {},
          "execution_count": 49
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.scatter(x_test, y_test, c=\"blue\")\n",
        "plt.scatter(x_test, predicted_test, c=\"yellow\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "vMurodkyrjHU"
      },
      "source": [
        "### Part8:\n",
        "Is the performance of the new model better than the previous one? `Explain`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "hidden": true,
        "id": "x6m4wdm1rjHV"
      },
      "source": [
        "according to better fit and less MSE it's better"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "BzYsC5SprjHV"
      },
      "source": [
        "### Part9:\n",
        "Now, we want to consider the `KNN` approach for this problem; Do you think it will perform well?"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "hidden": true,
        "id": "DcC5KupOrjHV"
      },
      "source": [
        "I think because it's non linear it will works better"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "heading_collapsed": true,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "-v5omwzlrjHV"
      },
      "source": [
        "### Part10:\n",
        "Implementing the `KNN model`."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "id": "Bwdce5QkrjHV"
      },
      "outputs": [],
      "source": [
        "class KNN:\n",
        "    def __init__(self, number_neighbours, X, Y):\n",
        "        self.k = number_neighbours\n",
        "        self.X = X\n",
        "        self.Y = Y\n",
        "\n",
        "    def distance(self, x1, x2):\n",
        "        distance = np.abs(x2-x1) # implement the distance function\n",
        "        return distance\n",
        "\n",
        "    def return_nn_ids(self, x):\n",
        "        indices = []\n",
        "        dis = []\n",
        "        for point in self.X:\n",
        "          dis.append(self.distance(point,x))\n",
        "        for i in range(self.k):\n",
        "          door = np.inf\n",
        "          indexx = 0\n",
        "          for j,d in enumerate(dis):\n",
        "            if door>d :\n",
        "              indexx = j\n",
        "              door = d\n",
        "              dis[j]=np.inf\n",
        "          indices.append([self.Y[indexx,0]])\n",
        "        return indices\n",
        "\n",
        "    def predict(self, x):\n",
        "        neareest_indices = self.return_nn_ids(x)\n",
        "        predicted_y = np.sum(neareest_indices)/np.size(neareest_indices)\n",
        "        return predicted_y"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "id": "pYmvCRwBrjHV"
      },
      "outputs": [],
      "source": [
        "def evaluation(k, x_train, y_train, x_test, y_test):\n",
        "    model = KNN(k, x_train, y_train)\n",
        "    predicted_y = np.array([model.predict(x) for x in x_test]).reshape(test,1)\n",
        "    error = np.sum((y_test-predicted_y)**2)/len(y_test)\n",
        "    return error, predicted_y"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dAUwhgu0rjHV",
        "outputId": "6ce33e94-4ebc-431a-ca5b-8621d7d25036"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MSE error of KNN for test dataset: 0.11235554485342879\n"
          ]
        }
      ],
      "source": [
        "k = 3\n",
        "error_knn, predicted_y = evaluation(k, x_train, y_train, x_test, y_test)\n",
        "print(f\"MSE error of KNN for test dataset: {error_knn}\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "hidden": true,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "eTLV_FaxrjHV",
        "outputId": "e111dfd4-04af-4c7a-e604-748db88197f7"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f60e7eb0dd0>"
            ]
          },
          "metadata": {},
          "execution_count": 53
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.scatter(x_test, y_test, c=\"blue\")\n",
        "plt.scatter(x_test, predicted_y, c=\"yellow\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "deletable": false,
        "editable": false,
        "hidden": true,
        "run_control": {
          "frozen": true
        },
        "id": "Fo8auuGqrjHV"
      },
      "source": [
        "To find best K for this algorithm we suggest to use cross-validation.\n",
        "<br><br/>\n",
        "Did this model perform well (due to the plot and test accuracy)?\n",
        "it performs better that last solution but not perfect"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "accuracies = []\n",
        "ks = range(1, 100)\n",
        "max_error = 1\n",
        "for k in ks:\n",
        "    error_knn, predicted_y = evaluation(k, x_train, y_train, x_test, y_test)\n",
        "    accuracy = 1 - error_knn\n",
        "    if (error_knn<max_error):\n",
        "      k_min = k\n",
        "      best_acc = 1 - error_knn\n",
        "      max_error = error_knn\n",
        "    accuracies.append(accuracy)\n",
        "fig, ax = plt.subplots()\n",
        "ax.plot(ks, accuracies)\n",
        "ax.set(xlabel=\"k\",\n",
        "       ylabel=\"Accuracy\",\n",
        "       title=\"Performance of knn\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "rP-L1Pc4DkSS",
        "outputId": "6bc18159-0cac-4a8d-bf47-e149b666273e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(f\"the best accuracy is for k = {k_min} with {best_acc}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tV_ETK1uFbec",
        "outputId": "fbaed6bb-7815-4045-aebb-0493b26122e5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "the best accuracy is for k = 5 with 0.894718175588322\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "k = 5\n",
        "error_knn, predicted_y = evaluation(k, x_train, y_train, x_test, y_test)\n",
        "plt.scatter(x_test, y_test, c=\"blue\")\n",
        "plt.scatter(x_test, predicted_y, c=\"yellow\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "_lbhdbQqIvux",
        "outputId": "ea411fab-6ebb-48ab-f796-92f8d7d2292c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f60e563e550>"
            ]
          },
          "metadata": {},
          "execution_count": 62
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "hidden": true,
        "id": "gqorKU6jrjHV"
      },
      "source": [
        "As you saw we found best K "
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3.7.4 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": "3.7.4"
    },
    "toc": {
      "base_numbering": 1,
      "nav_menu": {},
      "number_sections": true,
      "sideBar": true,
      "skip_h1_title": false,
      "title_cell": "Table of Contents",
      "title_sidebar": "Contents",
      "toc_cell": false,
      "toc_position": {},
      "toc_section_display": true,
      "toc_window_display": false
    },
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