MachineLearningMath/classification_logistic_reg_multiclass.ipynb

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            "_model_name": "DropdownModel",
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            "_view_module": "@jupyter-widgets/controls",
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            "_view_module_version": "1.5.0",
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            "_model_module": "@jupyter-widgets/controls",
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        },
        "3d7d6953b3014b82816748bc9d7856b9": {
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          "model_name": "DropdownModel",
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            "_dom_classes": [],
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            "_model_name": "DropdownModel",
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            "_view_module": "@jupyter-widgets/controls",
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            "_model_module": "@jupyter-widgets/controls",
            "layout": "IPY_MODEL_0e3029fc170244319bc9ec1e83fc2cb9"
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        },
        "6b33d4bae0cb41ecb6961df56905f5f6": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "IntSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_view_name": "IntSliderView",
            "style": "IPY_MODEL_48ffb7022925454dadaf994aa6a6ebb9",
            "_dom_classes": [],
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            "_model_name": "IntSliderModel",
            "orientation": "horizontal",
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            "_model_module_version": "1.5.0",
            "value": 1,
            "_view_count": null,
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            "_view_module_version": "1.5.0",
            "min": 1,
            "continuous_update": true,
            "readout_format": "d",
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            "readout": true,
            "_model_module": "@jupyter-widgets/controls",
            "layout": "IPY_MODEL_c345beb76e734ec6a8d34be49444e8c5"
          }
        },
        "3e0f7053760644fa88274f1d0dfad766": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
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          "state": {
            "_view_name": "OutputView",
            "msg_id": "",
            "_dom_classes": [],
            "_model_name": "OutputModel",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "image/png": 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\n",
                  "text/plain": "<Figure size 432x288 with 1 Axes>"
                },
                "metadata": {
                  "needs_background": "light"
                }
              },
              {
                "output_type": "display_data",
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  "cells": [
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      "cell_type": "markdown",
      "metadata": {
        "id": "FxLNUh9U56Oq"
      },
      "source": [
        "# 確率勾配法を用いた多クラスロジスティック回帰の実装\n",
        "\n",
        "2次元データの3クラス分類問題を解く多クラスロジスティック回帰を実装する．\n",
        "ここではサンプルを1つづつ用いる確率勾配法を実装する．\n",
        "\n",
        "# 準備"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OmX4Vxtr56Ot",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 33
        },
        "outputId": "d224a137-c363-4115-b425-fae0f0aa2ece"
      },
      "source": [
        "# load modules\n",
        "\n",
        "import numpy as np\n",
        "\n",
        "# !pip install scikit-image==0.12.3\n",
        "# import skimage.data\n",
        "\n",
        "import matplotlib\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.pyplot import imshow\n",
        "%matplotlib inline\n",
        "# plt.gray();\n",
        "plt.set_cmap(plt.cm.Paired);\n",
        "\n",
        "import sklearn\n",
        "# from sklearn.datasets import fetch_olivetti_faces\n",
        "from sklearn.datasets import make_blobs\n",
        "\n",
        "from ipywidgets import interact, interactive, fixed, RadioButtons\n",
        "import ipywidgets as widgets\n",
        "from IPython.display import display\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
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        },
        "id": "lCETYUKWFrn1",
        "outputId": "58bc2445-64dc-4d91-e27b-800a06a1eb86"
      },
      "source": [
        "!pip install autograd\n",
        "import autograd.numpy as anp # autogradのnumpyの別名をanpにする\n",
        "# from autograd import elementwise_grad as grad\n",
        "from autograd import grad\n",
        "from autograd import jacobian, hessian"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: autograd in /usr/local/lib/python3.7/dist-packages (1.3)\n",
            "Requirement already satisfied: future>=0.15.2 in /usr/local/lib/python3.7/dist-packages (from autograd) (0.16.0)\n",
            "Requirement already satisfied: numpy>=1.12 in /usr/local/lib/python3.7/dist-packages (from autograd) (1.19.5)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WowliG4X56Ov",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "50b3819d-4098-4f51-bddb-7e04db54cfe6"
      },
      "source": [
        "# check versions\n",
        "\n",
        "print(\"sklearn version :\", sklearn.__version__, \" >= 0.18.0\")\n",
        "# print(\"skimage version :\", skimage.__version__, \" >= 0.12.0\")\n",
        "print(\"numpy version :\", np.__version__, \" >= 0.12.0\")\n",
        "print(\"matplotlib version:\", matplotlib.__version__, \">= 2.0.0\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "sklearn version : 0.22.2.post1  >= 0.18.0\n",
            "numpy version : 1.19.5  >= 0.12.0\n",
            "matplotlib version: 3.2.2 >= 2.0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VlwGR6Sy56Ow"
      },
      "source": [
        "# データセットの準備\n",
        "\n",
        "sklearnのmake_blobで2次元データを準備する．\n",
        "返り値は，データXとラベルyである．3クラスの場合，ラベルyは0,1,2で返ってくる．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i71KTWcz56Ow",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "262e9549-2d09-4cd4-bd5d-3297e5b8b37e"
      },
      "source": [
        "X, y = make_blobs(n_samples=20, # 20個生成\n",
        "                  n_features=2, # 2次元\n",
        "                  centers=3,    # クラスタ中心2個\n",
        "                  cluster_std = 2 # クラスタの大きさ（標準偏差）\n",
        "                 )\n",
        "\n",
        "X = np.hstack((X, np.ones((X.shape[0], 1)))) # 同次座標\n",
        "\n",
        "# データの正規化\n",
        "X[:, 0] -= X[:, 0].mean()\n",
        "X[:, 1] -= X[:, 1].mean()\n",
        "X[:, 0] /= X[:, 0].std()\n",
        "X[:, 1] /= X[:, 1].std()\n",
        "\n",
        "\n",
        "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, edgecolors='k');\n",
        "plt.gca().set_aspect('equal');\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L0so-NsG56Ow"
      },
      "source": [
        "0,1,2のラベルyをone-hotエンコードに変更する．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gGvaaVlR56Ox",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ed22ba66-d805-4c0a-c3d0-3e0d2f1f8adc"
      },
      "source": [
        "y # これは0,12"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 1, 1, 2, 2, 0, 1, 0, 2, 1, 2, 1, 0, 2, 2, 0, 1, 0, 0])"
            ]
          },
          "metadata": {},
          "execution_count": 85
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uVCD6_YZ56Ox"
      },
      "source": [
        "from sklearn.preprocessing import OneHotEncoder"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AbTaILKE56Oy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "83600b3d-870e-48fa-c7db-5514275c3c35"
      },
      "source": [
        "Y = OneHotEncoder(categories='auto').fit_transform(y.reshape(-1,1)).toarray()\n",
        "Y # これでone-hotになっている"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0., 0.],\n",
              "       [0., 1., 0.],\n",
              "       [0., 1., 0.],\n",
              "       [0., 1., 0.],\n",
              "       [0., 0., 1.],\n",
              "       [0., 0., 1.],\n",
              "       [1., 0., 0.],\n",
              "       [0., 1., 0.],\n",
              "       [1., 0., 0.],\n",
              "       [0., 0., 1.],\n",
              "       [0., 1., 0.],\n",
              "       [0., 0., 1.],\n",
              "       [0., 1., 0.],\n",
              "       [1., 0., 0.],\n",
              "       [0., 0., 1.],\n",
              "       [0., 0., 1.],\n",
              "       [1., 0., 0.],\n",
              "       [0., 1., 0.],\n",
              "       [1., 0., 0.],\n",
              "       [1., 0., 0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 87
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-pGZTXI056Oy"
      },
      "source": [
        "識別境界を直線で描くヘルパー関数の準備．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b26Eu9sy56Oz"
      },
      "source": [
        "# 境界線を引く関数の定義\n",
        "\n",
        "def plotBoundary(X, net, w, mesh=True, n_neighbors=1):\n",
        "\n",
        "    # plot range\n",
        "    x_min = min(X[:,0])\n",
        "    x_max = max(X[:,0])\n",
        "    y_min = min(X[:,1])\n",
        "    y_max = max(X[:,1])\n",
        "\n",
        "    # visualizing decision function\n",
        "    XX, YY = np.mgrid[x_min:x_max:200j, y_min:y_max:200j] # make a grid\n",
        "    Z = np.zeros((XX.size, X.shape[1]))\n",
        "    for i,xi in enumerate(np.c_[XX.ravel(), YY.ravel(), np.ones(XX.size)]):\n",
        "        Z[i] = net(w, xi)\n",
        "    Z = np.argmax(Z, axis=1) # --> 0,1,2\n",
        "    Z = Z.reshape(XX.shape) # just reshape\n",
        "\n",
        "    if mesh:\n",
        "        plt.pcolormesh(XX, YY, Z, zorder=-10) # paint in 2 colors, if Z > 0 or not\n",
        "\n",
        "    plt.xlim(x_min, x_max)\n",
        "    plt.ylim(y_min, y_max)\n",
        "    "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9IoFkjX89z2p"
      },
      "source": [
        "# 多クラスロジスティック回帰の実装\n",
        "\n",
        "では多クラスロジスティック回帰（multinominal logistric regression, softmax regression）を実装する．\n",
        "\n",
        "実装が正しいかどうかを確認するために，autogradでも実装しておく．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SZpVXgwiEW0d"
      },
      "source": [
        "W0 = np.random.rand(3, 3)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y-cCJOWTFuLR"
      },
      "source": [
        "# autogradによる実装．関数名に'a_'をつけておく．\n",
        "\n",
        "def a_softmax(a):\n",
        "    d = anp.exp(a).sum()\n",
        "    return anp.exp(a) / d\n",
        "\n",
        "def a_mlr(W, xi):\n",
        "    \"\"\"Multinominal Logistic Regression\"\"\"\n",
        "    return a_softmax(W.T @ xi)\n",
        "\n",
        "def g_a_mlr(W, xi, yi):\n",
        "    \"\"\"gradient of Multinominal Logistic Regression\"\"\"\n",
        "    return anp.dot(xi.reshape(-1, 1), (a_softmax(anp.dot(W.T, xi)) - yi).reshape(1, -1))\n",
        "\n",
        "def a_loss(W, xi, yi):\n",
        "    fi = a_mlr(W, xi)\n",
        "    loss = - yi[0] * anp.log(fi[0]) - yi[1] * anp.log(fi[1]) - yi[2] * anp.log(fi[2]) # cross entropy\n",
        "    return loss"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "710cFLLO9zmI"
      },
      "source": [
        "# numpyによる実装\n",
        "\n",
        "def softmax(a):\n",
        "    d = np.exp(a).sum()\n",
        "    return np.exp(a) / d\n",
        "\n",
        "def mlr(W, xi):\n",
        "    \"\"\"Multinominal Logistic Regression\"\"\"\n",
        "    return softmax(W.T @ xi)\n",
        "\n",
        "def g_mlr(W, xi, yi):\n",
        "    \"\"\"gradient of Multinominal Logistic Regression\"\"\"\n",
        "    return xi.reshape(-1, 1) @ (softmax(W.T @ xi) - yi).reshape(1, -1)\n",
        "\n",
        "def loss(w, xi, yi):\n",
        "    fi = mlr(w, xi)\n",
        "    loss = - yi[0] * np.log(fi[0]) - yi[1] * np.log(fi[1]) - yi[2] * np.log(fi[2]) # cross entropy\n",
        "    return loss\n",
        "\n",
        "def loss01(w, xi, yi):\n",
        "    \"\"\"0-1 loss\"\"\"\n",
        "    fi = mlr(w, xi)\n",
        "    predicted_class = np.argmax(fi)\n",
        "    loss = 1 - yi[predicted_class]\n",
        "    return loss"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qfpIux6U56O0"
      },
      "source": [
        "ネットワークの出力と勾配の出力を確かめる（デバッグ）．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X2pg5PrD56O0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "47e6382e-1174-4bf3-c4f3-8e2561eaab9e"
      },
      "source": [
        "i = np.random.randint(len(y))\n",
        "print(i)\n",
        "X[i], Y[i]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "10\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([-0.68207743,  1.11594753,  1.        ]), array([0., 1., 0.]))"
            ]
          },
          "metadata": {},
          "execution_count": 92
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qb0_sLyt56O1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fb039ba3-da16-48dc-af6d-ef7bfd285ba5"
      },
      "source": [
        "xi = X[i]\n",
        "print(mlr(W0, xi))\n",
        "print(a_mlr(W0, xi))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.48113965 0.33741857 0.18144177]\n",
            "[0.48113965 0.33741857 0.18144177]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KJvGt0IW56O1"
      },
      "source": [
        "yi = Y[i]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k8OOVWQ556O2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6f104a2d-2b5f-4882-d3be-e8170d69ef69"
      },
      "source": [
        "print(g_mlr(W0, xi, yi))\n",
        "print(g_a_mlr(W0, xi, yi))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.3281745   0.45193184 -0.12375734]\n",
            " [ 0.53692661 -0.73940611  0.2024795 ]\n",
            " [ 0.48113965 -0.66258143  0.18144177]]\n",
            "[[-0.3281745   0.45193184 -0.12375734]\n",
            " [ 0.53692661 -0.73940611  0.2024795 ]\n",
            " [ 0.48113965 -0.66258143  0.18144177]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vu_0lb9eKa2b",
        "outputId": "176b514b-2a8e-43b1-ebfc-3455334a1345"
      },
      "source": [
        "print(loss(W0, xi, yi))\n",
        "print(a_loss(W0, xi, yi))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.0864310661053076\n",
            "1.0864310661053076\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kVNRfkgk56O2"
      },
      "source": [
        "以下では，サンプルを先頭から順番に一つずつ用いて，SGDの更新則を適用する．\n",
        "サンプルは3色のクラスに分かれている．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NFnWROvHEYWr"
      },
      "source": [
        "W = W0.copy()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "js1olq_156O2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297,
          "referenced_widgets": [
            "6e8db37a9384487baf68f0e7ea8e03ae",
            "90e65b0ab25144e9a9cdec97df209295",
            "87d19e20ba704d69b42213ac05ce26e5",
            "05784935e2e84fefa1d582ff58eb3891",
            "e8679ece228140b68dc88241ce5633bf",
            "a867af62624e4e618b4b6a790c02b04a",
            "7c3154aac16341699d2c264b8b5f051d"
          ]
        },
        "outputId": "4661c06f-eb44-4168-e416-515dc0de6a9f"
      },
      "source": [
        "val_start = 0 # スライドバーの最小値\n",
        "val_end   = len(y)-1 # スライドバーの最大値\n",
        "val_step  = 1 # スライドバーはこの値ずつ増える\n",
        "val_default = 0 # スライドバーの初期値\n",
        "\n",
        "\n",
        "@interact(sample=(val_start, val_end, val_step)) # この行が関数の直前に必要\n",
        "def g(sample=val_default): # この関数を毎回呼び出す    \n",
        "    \n",
        "    global W\n",
        "    \n",
        "    if sample > len(y)-1:\n",
        "        return\n",
        "\n",
        "    plt.scatter(X[:, 0], X[:, 1], marker='o', s=50, c=y, edgecolors='k')\n",
        "    plt.scatter(X[sample, 0], X[sample, 1], marker='o', s=90, facecolors='none',  edgecolors='k')\n",
        "   \n",
        "    plotBoundary(X, mlr, W)\n",
        "    \n",
        "    xi = X[sample]\n",
        "    yi = Y[sample]\n",
        "\n",
        "   \n",
        "    plt.gca().set_aspect('equal');\n",
        "    plt.show()\n",
        "\n",
        "    # 更新則\n",
        "    alpha = 0.01\n",
        "    W = W - alpha * g_mlr(W, xi, yi)\n",
        "\n",
        "    "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "6e8db37a9384487baf68f0e7ea8e03ae",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(IntSlider(value=0, description='sample', max=19), Output()), _dom_classes=('widget-inter…"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tNlTbH7756O3"
      },
      "source": [
        "- 以下ではステップサイズalphaに加えて，慣性項betaを変更する．\n",
        "- また01-損失も計算し，最小化している目的関数である交差エントロピー損失と比較する．\n",
        "- 更に，エポックを設定し，スライドバーを延々と動かし続けられるようにする．\n",
        "- またミニバッチ学習のbatch_sizeを設定する（1ならSGD）．実装では，勾配を蓄積してbatch_size回だけ溜まったら更新することにしている"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AIwpOvum56O3"
      },
      "source": [
        "W = W0.copy()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": false,
        "id": "G_NBbvbH56O3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 655,
          "referenced_widgets": [
            "38876ce13bf44da480778fbcf46746f2",
            "fe51b6838d884e3f8f0a8176c07cf85f",
            "cc4bcd605ce14d8cbcacc67b5931158e",
            "e23a97150c034a59b5fff1eb5816a190",
            "3d7d6953b3014b82816748bc9d7856b9",
            "6b33d4bae0cb41ecb6961df56905f5f6",
            "3e0f7053760644fa88274f1d0dfad766",
            "e79ae907a960441aa407fe1a4446ef2f",
            "2ecea7e314104a81be80aaea3f453eb8",
            "b10c1930d90341dd928012319d789bcc",
            "3833b613241849a3b45fe248dec9f8cd",
            "a7303907c6624a87957cba36c03848e2",
            "0e3029fc170244319bc9ec1e83fc2cb9",
            "48ffb7022925454dadaf994aa6a6ebb9",
            "c345beb76e734ec6a8d34be49444e8c5",
            "00e03c62c6634e6b89b6fbbaca557996"
          ]
        },
        "outputId": "28794b41-bb08-4de9-9104-43197c65892d"
      },
      "source": [
        "N = len(y)\n",
        "epochs = 100\n",
        "max_iter = N * epochs - 1\n",
        "\n",
        "val_start = 0 # スライドバーの最小値\n",
        "val_end   = max_iter # スライドバーの最大値\n",
        "val_step  = 1 # スライドバーはこの値ずつ増える\n",
        "val_default = 0 # スライドバーの初期値\n",
        "\n",
        "loss_val = []\n",
        "loss01_val = []\n",
        "\n",
        "d = np.zeros_like(W)\n",
        "grad = np.zeros_like(W)\n",
        "batch_size = 2\n",
        "batch_index = 0\n",
        "\n",
        "@interact(sample=(val_start, val_end, val_step),\n",
        "          alpha=[1.0, 0.1, 0.05, 0.01, 0.001],\n",
        "          beta=[0, 0.5, 0.9, 0.99],\n",
        "          batch_size=(1, N),\n",
        "          )\n",
        "def g(sample=val_default, alpha=0.1, beta=0.9, batch_size=1):\n",
        "    \n",
        "    global W, d, grad, batch_index\n",
        "\n",
        "    xi = X[sample % N]\n",
        "    yi = Y[sample % N]\n",
        "\n",
        "    grad += g_mlr(W, xi, yi)\n",
        "\n",
        "    batch_index += 1\n",
        "    if batch_index >= batch_size:    \n",
        "\n",
        "        # 更新則\n",
        "        d = beta * d + (1 - beta) * grad  # beta=0なら慣性項を使わない\n",
        "        W = W - alpha * grad\n",
        "\n",
        "        grad *= 0  # zero_grad\n",
        "        batch_index = 0\n",
        "\n",
        "        plt.scatter(X[:, 0], X[:, 1], marker='o', s=50, c=y, edgecolors='k')\n",
        "        plt.scatter(X[sample % N, 0], X[sample % N, 1], \n",
        "                    marker='o', s=90, facecolors='none',  edgecolors='k')\n",
        "        plotBoundary(X, mlr, W)\n",
        "        plt.gca().set_aspect('equal');\n",
        "        plt.show()\n",
        "\n",
        "        loss_val.append(sum([loss(W, xi, yi) for xi, yi in zip(X, Y)])) # loss for all samples\n",
        "        loss01_val.append(sum([loss01(W, xi, yi) for xi, yi in zip(X, Y)])) # loss for all samples\n",
        "        plt.plot(loss_val, label='loss')\n",
        "        plt.plot(loss01_val, label='01-loss')\n",
        "        plt.ylabel('loss')\n",
        "        plt.xlabel('iterations')\n",
        "        plt.legend()\n",
        "        plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "38876ce13bf44da480778fbcf46746f2",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(IntSlider(value=0, description='sample', max=1999), Dropdown(description='alpha', index=…"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8IC0w4cg56O4"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BawULno_e7s4"
      },
      "source": [
        "# 顔画像の識別\n",
        "\n",
        "\n",
        "ここではsklearnのデータセットとして準備されているOlivetti facesデータセットを用いる．\n",
        "詳しくは[sklearnのマニュアル](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.fetch_olivetti_faces.html)を参照．\n",
        "\n",
        "このデータセットには400枚の顔画像があり，それぞれが4096次元のベクトルである（64x64画像を表す）．\n",
        "人物は40人であり，各人物の画像が10枚ずつある．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MF7Vd7xce8-b"
      },
      "source": [
        "import sklearn\n",
        "from sklearn.datasets import fetch_olivetti_faces\n",
        "\n",
        "\n",
        "# load the face dataset\n",
        "\n",
        "dataset = fetch_olivetti_faces(shuffle=False)\n",
        "X = dataset.data\n",
        "y = dataset.target"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wxwUzK1JvkMG"
      },
      "source": [
        "ラベル'y'は人物番号になっているので，one-hotエンコーディングに変更する．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xw6OXg-LfRJr",
        "outputId": "33eac796-b214-4061-f3d4-038e0baf427b"
      },
      "source": [
        "from sklearn.preprocessing import OneHotEncoder\n",
        "Y = OneHotEncoder(categories='auto').fit_transform(y.reshape(-1,1)).toarray()\n",
        "Y # これでone-hotになっている"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0., 0., ..., 0., 0., 0.],\n",
              "       [1., 0., 0., ..., 0., 0., 0.],\n",
              "       [1., 0., 0., ..., 0., 0., 0.],\n",
              "       ...,\n",
              "       [0., 0., 0., ..., 0., 0., 1.],\n",
              "       [0., 0., 0., ..., 0., 0., 1.],\n",
              "       [0., 0., 0., ..., 0., 0., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 114
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YD01BItWvzon"
      },
      "source": [
        "このデータを学習用と検証用に8:2に分割する．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XpaiOuaifBk6"
      },
      "source": [
        "from sklearn.model_selection import StratifiedShuffleSplit\n",
        "ss = StratifiedShuffleSplit(n_splits=1, \n",
        "                            train_size=0.8,  # training\n",
        "                            test_size=0.2,  # validation\n",
        "                            random_state=0)\n",
        "\n",
        "train_index, val_index = next(ss.split(X, Y))\n",
        "\n",
        "X_train, X_val = X[train_index], X[val_index]\n",
        "Y_train, Y_val = Y[train_index], Y[val_index]  # one-hot encoding\n",
        "y_train, y_val = y[train_index], y[val_index]  # label"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mBPQT6_FwRdx"
      },
      "source": [
        "stratifiedサンプリングにより，各クラスを学習用と検証用に分けている．インデックスを見て確認する．"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1XNhiLTpwHTQ",
        "outputId": "a11ddcc8-36fe-4def-cf22-d761988e0cd1"
      },
      "source": [
        "np.sort(y_train), np.sort(y_val)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([ 0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1,  1,  1,  1,  1,  1,  2,\n",
              "         2,  2,  2,  2,  2,  2,  2,  3,  3,  3,  3,  3,  3,  3,  3,  4,  4,\n",
              "         4,  4,  4,  4,  4,  4,  5,  5,  5,  5,  5,  5,  5,  5,  6,  6,  6,\n",
              "         6,  6,  6,  6,  6,  7,  7,  7,  7,  7,  7,  7,  7,  8,  8,  8,  8,\n",
              "         8,  8,  8,  8,  9,  9,  9,  9,  9,  9,  9,  9, 10, 10, 10, 10, 10,\n",
              "        10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12,\n",
              "        12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14,\n",
              "        14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16,\n",
              "        17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19,\n",
              "        19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21,\n",
              "        21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23,\n",
              "        23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 24, 24, 24, 25, 25, 25, 25,\n",
              "        25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27,\n",
              "        27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29,\n",
              "        29, 29, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31,\n",
              "        31, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33, 33,\n",
              "        34, 34, 34, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 35, 35, 35, 36,\n",
              "        36, 36, 36, 36, 36, 36, 36, 37, 37, 37, 37, 37, 37, 37, 37, 38, 38,\n",
              "        38, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 39, 39, 39]),\n",
              " array([ 0,  0,  1,  1,  2,  2,  3,  3,  4,  4,  5,  5,  6,  6,  7,  7,  8,\n",
              "         8,  9,  9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16,\n",
              "        17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25,\n",
              "        25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33,\n",
              "        34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39]))"
            ]
          },
          "metadata": {},
          "execution_count": 119
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VtEbB1YWg46w",
        "outputId": "031e740c-6680-4bda-c897-68cef557a04b"
      },
      "source": [
        "X_train.shape, Y_train.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((320, 4096), (320, 40))"
            ]
          },
          "metadata": {},
          "execution_count": 112
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Ag7cDlQzmWX"
      },
      "source": [
        "では学習ループを回す．\n",
        "- バッチサイズ8\n",
        "- 学習率（ステップサイズ）alpha 0.01\n",
        "- 慣性項 beta 0.99\n",
        "- 20エポック\n",
        "- 5エポックごとにalphaを半分にする\n",
        "- バッチで更新した時点の損失を計算\n",
        "- エポック毎に認識率を計算"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 76,
          "referenced_widgets": [
            "3b52fcc6143848e58d0bff0d5064f2d6",
            "9aea75e485a24ec49bdb8d4a6c07d0b2",
            "11f7bbfd47094b1f9e1201d93b68dc7e",
            "a4e0b0ec620e4b5f9e0e2fea68be4f7f",
            "f230c681d76247439ffca92da7ef4478",
            "8f9f7be3530c44b58c38174bd799a5f5",
            "a25c46608b364a0ea9d0b108ebb6bb8a",
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        },
        "id": "WZv92eXKflqJ",
        "outputId": "d6cd304a-f359-4c8f-bba6-5b02a44dae62"
      },
      "source": [
        "from tqdm.notebook import tqdm\n",
        "\n",
        "N = len(X_train)\n",
        "n_epochs = 20\n",
        "\n",
        "loss_train = []\n",
        "loss_val = []\n",
        "acc_train = []\n",
        "acc_val = []\n",
        "\n",
        "W = np.random.rand(X_train.shape[1], Y_train.shape[1]) / 10000\n",
        "\n",
        "d = np.zeros_like(W)\n",
        "grad = np.zeros_like(W)\n",
        "batch_size = 8\n",
        "\n",
        "alpha = 0.01\n",
        "beta = 0.99\n",
        "\n",
        "with tqdm(range(n_epochs)) as pbar_epoch:\n",
        "    for epoch in pbar_epoch:\n",
        "        pbar_epoch.set_description(\"[Epoch %d]\" % (epoch))\n",
        "\n",
        "        batch_index = 0\n",
        "\n",
        "        with tqdm(enumerate(zip(X_train, Y_train)),\n",
        "                  total=N,\n",
        "                  leave=False) as pbar_loss:\n",
        "            for bi, (xi, yi) in pbar_loss:\n",
        "\n",
        "                grad += g_mlr(W, xi, yi)\n",
        "\n",
        "                batch_index += 1\n",
        "                if batch_index >= batch_size:    \n",
        "\n",
        "                    # 更新則\n",
        "                    d = beta * d + (1 - beta) * grad  # beta=0なら慣性項を使わない\n",
        "                    W = W - alpha * grad\n",
        "\n",
        "                    grad *= 0  # zero_grad\n",
        "                    batch_index = 0\n",
        "\n",
        "                    loss_train.append(sum([loss(W, xi, yi) for xi, yi in zip(X_train, Y_train)]) / len(y_train))\n",
        "                    loss_val.append(sum([loss(W, xi, yi) for xi, yi in zip(X_val, Y_val)]) / len(y_val))\n",
        "                \n",
        "                if len(loss_train) > 0:\n",
        "                    pbar_loss.set_postfix_str(\"loss train={:.4f} val={:.4f}\".format(loss_train[-1], loss_val[-1]))\n",
        "\n",
        "\n",
        "        # validation\n",
        "        acc_train.append(sum(np.argmax(X_train @ W, axis=1) == y_train) / len(y_train))\n",
        "        acc_val.append(sum(np.argmax(X_val @ W, axis=1) == y_val) / len(y_val))\n",
        "        pbar_epoch.set_postfix_str(\"acc train={:.4f} val={:.4f}\".format(acc_train[-1], acc_val[-1]))\n",
        "\n",
        "        if epoch % 5 == 0:\n",
        "            alpha *= 0.5"
      ],
      "execution_count": null,
      "outputs": [
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    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 541
        },
        "id": "x6-CkLDcqrJg",
        "outputId": "02c23254-10db-4a17-a8fa-6021623876b8"
      },
      "source": [
        "plt.plot(loss_train, label='train')\n",
        "plt.plot(loss_val, label='val')\n",
        "plt.ylabel('loss')\n",
        "plt.xlabel('iterations')\n",
        "plt.legend()\n",
        "plt.show()\n",
        "\n",
        "plt.plot(acc_train, label='train')\n",
        "plt.plot(acc_val, label='val')\n",
        "plt.ylabel('accuracy')\n",
        "plt.xlabel('epochs')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MYAawzjm3AcDMngbOBNomAgcMDN0fBPRgQ7D0FYWBIIcnlUF9Alz0DMRFwWxhIv2In4lgFLC5zeMC4Ih229wCvG5m1wDpgIZijEGFgSB5CaWQMlpJQKQPinQVzIXAI8650cApwONmtltMZjbLzJaY2ZJYH08o1jjnKAwEGd6yHTL3i3Q4ItIBPxNBIZDb5vHo0LK2rgRmAzjnPgBSgJz2O3LO3e+cy3fO5Q8ZEkXVqUJJdQMNTS0MbtzqjcEvIn2On4lgMTDBzMaaWRJwATCn3TZfAscDmNlkvESgr/wxpCgQJJkG0hpKdEYg0kf5lgicc03A1cA8YDVe76CVZnarmZ0R2uwG4CozWwY8BVzuonn2FdlNYSDIaAvldp0RiPRJvtYRhGoC5rZbdlOb+6uAI/2MQSKrKBBktJV4D7J0RiDSF0X6YrHEuILyIOMTS70HOiMQ6ZOUCMRXhYEgBySXQ3wSDBge6XBEpAMaa0h8VRQIkpdQAgNyNWa/SB+l/0zxVWEgyAi2q1lIpA9TIhDf1NQ3EahtJLtxmxKBSB+mRCC+KQoESaWOtMYyJQKRPkyJQHxTEAgyakfX0byIxiIinVMiEN8UqZhMJCooEYhvCsuD7BcXOiNQIhDps5QIxDdFgSCTUsogPhnSh0Y6HBHphOoIxDeFgSDjEkohfYxqCET6MP13im+KAnWMpFjNQiJ9nBKB+KKpuYWtlXXkNKmGQKSvUyIQX2ytrCO5JUhaU0CJQKSPUyIQXxQF6nZ2HdXw0yJ9mhKB+KIwUNumhkCJQKQvUyIQX+xyRqCmIZE+TYlAfFFQHmRiUhkkpEL6kEiHIyJ7oEQgvigKBBmXWOqdDZhFOhwR2QMlAvFFYSDIKNUQiEQFJQLpcc45CsuDDGlWDYFINFAikB4XqG0kvrGKtOZKJQKRKKBEID2uMBBk9I55CNR1VKSvUyKQHleoeQhEoooSgfS4wvKgislEoogSgfS4wkCQsfEluMR0SMuOdDgishdKBNLjigJBxieVYqohEIkKSgTS4woDQXKtRNcHRKKEEoH0uKJAkKGqIRCJGkoE0qPqGptpqC4ntaVaXUdFooQSgfSoInUdFYk6SgTSo1RDIBJ9fE0EZnaSmX1uZuvM7MZOtjnPzFaZ2Uoze9LPeMR/heVBclVDIBJVEvzasZnFA3cBJwAFwGIzm+OcW9VmmwnAz4EjnXPlZjbUr3ikd7Q2DbmkDCw1K9LhiEgYwjojMLMXzOxUM+vKGcQMYJ1zboNzrgF4Gjiz3TZXAXc558oBnHPbu7B/6YMKAkH2TypTDYFIFAn3wH43cBGw1sxuM7NJYTxnFLC5zeOC0LK2JgITzew9M1tkZid1tCMzm2VmS8xsSXFxcZghSyQUBYLkxqmGQCSahJUInHNvOucuBg4FNgJvmtn7ZnaFmSV24/UTgAnAccCFwN/NLLOD17/fOZfvnMsfMkTTHvZlheW1DG9RDYFINAm7qcfMsoHLge8CHwN/wUsMb3TylEIgt83j0aFlbRUAc5xzjc65L4A1eIlBolBziyNYWUpKS61qCESiSLjXCF4E3gHSgNOdc2c4555xzl0DDOjkaYuBCWY21sySgAuAOe22eQnvbAAzy8FrKtrQ5d9C+oTiqnqGtYQu8+iMQCRqhNtr6K/OuQUdrXDO5XeyvMnMrgbmAfHAQ865lWZ2K7DEOTcntO5EM1sFNAM/c86Vdvm3kD6hMFCrGgKRKBRuIphiZh875wIAZpYFXOicu3tPT3LOzQXmtlt2U5v7DvhJ6CZRrjBQ16aGQIlAJFqEe43gqtYkABDq7nmVPyFJtGqdkMYlDwTVEIhEjXATQbzZzk7hoWKxJH9CkmhVFAgyNqEUU0WxSFQJt2noNeAZM7sv9Ph7oWUiOxQGguwXVwKZ0yIdioh0QbiJ4L/xDv4/CD1+A3jAl4gkahWW1TLcbYPMUyIdioh0QViJwDnXAtwTuol0qLZiOylWpxoCkSgTViIIDQ73v8AUIKV1uXNunE9xSZSpCDaS2bAVklGPIZEoE+7F4ofxzgaagK8BjwH/8CsoiT6akEYkeoWbCFKdc/MBc85tcs7dApzqX1gSbbx5CFRVLBKNwr1YXB8agnptqFq4kM6HlpB+qKgiyGgroSUlk7iUQZEOR0S6INwzguvwxhm6FjgMuAS4zK+gJPoUlgcZE1fizUMgIlFlr2cEoeKx851zPwWqgSt8j0qiTkEgSF5CCZZ5cKRDEZEu2usZgXOuGTiqF2KRKFZUXstwtx2y8iIdioh0UbjXCD42sznAs0BN60Ln3Au+RCVRp7Z8GymuXheKRaJQuIkgBSgFvt5mmQOUCIT6pmZSagpUQyASpcKtLNZ1AenU1oo6RluJ90CJQCTqhFtZ/DDeGcAunHPf6fGIJOoUBlRDIBLNwm0a+leb+ynAt4Cing9HolHrPATNKVnEJ2dEOhwR6aJwm4aeb/vYzJ4C3vUlIok6hYEg0+NKMA02JxKVwi0oa28CMLQnA5HoVRSahyBOzUIiUSncawRV7HqNYCveHAUiFJbXMpJiDT8tEqXCbRpSw690Kli+lWQaQFNUikSlsJqGzOxbZjaozeNMMzvLv7AkWrS0OOIrN3sP1DQkEpXCvUZws3OuovWBcy4A3OxPSBJNSmrqGdGyzXugRCASlcJNBB1tF27XU4lhRYE6TUgjEuXCTQRLzOwOMxsfut0BLPUzMIkOrTUETSnZkJQe6XBEZB+EmwiuARqAZ4CngTrgR34FJdFjxxSVWTobEIlW4fYaqgFu9DkWiUKFgSAnxJWQkHVEpEMRkX0Ubq+hN8wss83jLDOb519YEi2KymsYaaohEIlm4TYN5YR6CgHgnCtHlcUC1JYVkUSTLhSLRLFwE0GLme34TzezPDoYjVT6n7iK1hoCnRGIRKtwu4D+AnjXzBYCBhwNzPItKokK1fVNZDUUQRJKBCJRLNyLxa+ZWT7ewf9j4CUg6Gdg0vd5PYZaJ6TJjWwwIrLPwr1Y/F1gPnAD8FPgceCWMJ53kpl9bmbrzKzTXkdmdo6ZuVCykShRGOo62piaA4mpkQ5HRPZRuNcIrgMOBzY5574GHAIE9vQEM4sH7gJOBqYAF5rZlA62ywjt/z9diFv6gNZiMjdIF4pFolm4iaDOOVcHYGbJzrnPgEl7ec4MYJ1zboNzrgGvEO3MDrb7NXA7XpGaRJGiQJAxccUkZo+NdCgi0g3hJoKCUB3BS8AbZvYysGkvzxkFbG67j9CyHczsUCDXOffKnnZkZrPMbImZLSkuLg4zZPFbUXk1I60UU1WxSFQL92Lxt0J3bzGzBcAg4LXuvLCZxQF3AJeH8fr3A/cD5Ofnq9tqH1FbWkiiaghEol6XRxB1zi0Mc9NCoG1XktGhZa0ygGnAW2YGMByYY2ZnOOeWdDUu6X07awiUCESi2b7OWRyOxcAEMxtrZknABcCc1pXOuQrnXI5zLs85lwcsApQEokRjcwtptQXeg8y8iMYiIt3jWyJwzjUBVwPzgNXAbOfcSjO71czO8Ot1pXdsq6xjFKHrNYNGRzYYEekWXyeXcc7NBea2W3ZTJ9se52cs0rO8rqMl1KcOJTkxJdLhiEg3+Nk0JDGstZjMDVJFsUi0UyKQfVIUCJJr21VDIBIDlAhkn2wpr2JkXBnxgzXYnEi0UyKQfVJbWkQCzeo6KhIDlAhkn7jyUGG5EoFI1FMikC5zzpFS01pDoKYhkWinRCBdVl7byLDmbThMNQQiMUCJQLqsdfjp+tShkJAc6XBEpJuUCKTLCkMzkzUPVA2BSCxQIpAuKwwEyY3bToJqCERigq9DTEhs2lJexXDKiM/WhWKRWKBEIF0WLN5MgrVAlhKBSCxQ05B0mQu01hAoEYjEAiUC6bKkKk1IIxJLlAikS4INzWQ1bqWFOBg4au9PEJE+T4lAuqSowqshqEsdCglJkQ5HRHqAEoF0SWsxWdNANQuJxAolAumSotCENBp+WiR2qPuodMmWskqGU4blqJhMJFYoEUiX1BR/Sbw50BmBSMxQ05B0iSvf6N1RDYFIzFAikC5JqGqdh0AXi0VihRKBhK25xZFRV0QL8aohEIkhSgQStu1VdYykmNrUYRCvy0sisUKJQMJWFAiSa9tpzNA8BCKxRIlAwlZQ7k1IE69RR0Viis7vJWxbyioYRjlNQ1RDIBJLdEYgYast3kScOZJy8iIdioj0ICUCCVtz6UbvjmoIRGKKEoGELVE1BCIxSYlAwuKcI622kGbiIWNEpMMRkR6kRBAlNpbUcNeCddQ3NUfk9Svrmhjaso2alOGqIRCJMb4mAjM7ycw+N7N1ZnZjB+t/YmarzOxTM5tvZmp87sDWijoufuA//H7e5/z6X6siEkNheZBcK6ZBNQQiMce3RGBm8cBdwMnAFOBCM5vSbrOPgXzn3EHAc8Dv/IonWlUEG7n84Q8J1DZw+sEj+ceiL3l2yeZej2NjaQ2jrRjL0vUBkVjj5zn+DGCdc24DgJk9DZwJ7PhK65xb0Gb7RcAlPsYTdeoam7nqsSWsL67m4ctnMHPcYEqr6/nFSyuYPGIg00YN6pU4tlQEuW3OJ7xtARqGj++V1xSR3uNn09AooO1X14LQss5cCbza0Qozm2VmS8xsSXFxcQ+G2Hc1tzh+/MwnfPhFGX88bzpHTcghIT6OOy88hJz0JL73+FLKaxp8j6OqrpErHl5MRsNWAJKyVUwmEmv6xMViM7sEyAd+39F659z9zrl851z+kCFDeje4CHDOccuclby6Yiu/PG0KZxw8cse67AHJ3HPJYRRX1XPt0x/T3OJ8i6OxuYUfPfkx67ZXc/vXM7yF6joqEnP8TASFQNsri6NDy3ZhZt8AfgGc4Zyr9zGeqHHXgnU8vmgT3ztmHFcetfs38INzM7n1zKm8s7aEP77+uS8xOOf45UsreHtNMb87bT+mrfozJA2AIZN8eT0RiRw/E8FiYIKZjTWzJOACYE7bDczsEOA+vCSw3cdYosbsxZv5w+trOPuQUfz3SQd0ut0FM8Zw4Yxc7n5rPa+t2Nrjcdz91nqeXryZ644dw9lrb4Ti1XDeY5A2uMdfS0Qiy7dE4JxrAq4G5gGrgdnOuZVmdquZnRHa7PfAAOBZM/vEzOZ0srt+Yf7qbfz8xeUcM3EIt597EHFx5q1oaYb5v4Y/HwibF+/Y/pYzpnJwbiY/fXYZ67ZX91gcL39SyO/nfc5ZBw/n+uo/whdvw5l3w/7H99hriEjfYc7518bsh/z8fLdkyZJIh9Hjlm4q5+IHFjFxWAZPXTWT9ORQh65gOTz/XVj3JiQPgpYmuOgZGHs04M0RcPqd75KZlsjLVx/FgOTudQT7z4ZSLn3wQw7JHcQTuS+SsPh+OOHXcOS13f0VRSSCzGypcy6/o3V94mJxf7duexVXPrqY4QNTeOjyw3cmga0r4P7jYMNCOO1PcPWHkJkLT5wLa14HYGRmKndedAhflNTws2eX0Z3Evr64mlmPLyV3cCqPTPrASwJfuVpJQCTGKRFE2NaKOi57aDEJcXE89p0jyBmQ7K1Y/hw8eAI01sEVcyH/O5AxHC6f612wffoiWPUyAF8dn8PPT57Mqyu2ct/bG/YpjpLqei5/+EMS443ZMzeSuvBWOPDb3tmAiMQ0JYIIqgg2ctlDH1IRbOSRKw5nTHYaNDfBvF/A81fC8IPgewshd8bOJ6Vnw2X/hFGHwrOXwydPAfDdo8dy6kEj+N1rn/HeupIuxRFsaOa7jy6huKqeZ75eTfabP4Fxx3nXBeL0ERGJdfovD9eqOXDv0bD4Ae9beje1Vg1vKKnm3ksO86qEa0rg8bPgg7/BjFneAT9j+O5PThkEl74IeUfDS9+HxQ9gZvzunIMYP2QAVz/5EQXltWHF0dziuP6Zj1lWEOCRE+MZv+CHMHwanP8PSEjq9u8pIn2fEkE4Al/Cy1dD2QZ45Qb4y0Hw3l+gvmqfdtdR1TBFH8N9x8LmD+Gse+CU3+/5QJyUDhfNhoknezG991fSkxO479LDaGp2/OAfH1HXuPeRSn87dzXzVm7j98elM/OD78OAoXDxc5CcsU+/m4hEHyWCvWlphhd/AK4FfvAeXPYvGDoF3rgJ/jQNFrQ146gAAA31SURBVPwWasvC3l2HVcMfPwEPfhPM4Mp5MP2i8HaWmALnPw5Tz4Y3fgkL/pdxOen88byDWV5YwU0vr9jjxeNH3vuCB9/9gmtmDODc1deAxcElL3jJQET6DQ0svzcf/A02veu1l2flebexR0PhUnjnDlh4O7z/N8i/Ar7yIxg4co+726VqeOYo79v84gdg7DFw7sOQntO1+OIT4ZwHIDENFt4GDdWceOJvuObr+3Pnv9cxPTeLi47YfViI11du5Vf/WsWZB6Tzk23/F2pK4YpXIFuDyon0N0oEe7J1uVfINfn03b+ljzoMLngCtn8G7/4JFt0DH94PB18IR17X4QH1mcVf7qwaPjITHj0dNi+Cr14Dx9+y7xO+xMXDGXd6zUUf/A0aarj+lD+yrKCCm+esYPKIDA4Zk7Vj82WbA1z79MccOjKNO9wfsOLPvGamkYfs2+uLSFRTQVlnGuu8PvzBMvjBB15vnT0p3wjv3wkfPQ4tjV5zzdE/gWFTaW5xPPbBRn7zymqO3D+Hh77eTMJzl0N9JZz5N5h2Ts/E7BzMvxXevQMOOp/AiX/m9LsX0djk+Oc1RzEkI5nNZbV86+73SE0w3hjzGClrXoaz/w4HndczMYhIn7SngjIlgs689nNYdDdc8jzs/43wn1e1DRbdBYsfhIZqqvb7Br+pPIVntgzn2Ak53D/lU5Lf+DkMGu2dUQyb2vOxv/0H+Pev4YDTWPnVP3H2/Us5ZEwmd110KOffv4jtlUHePvA1Mpc/DCf+xjsjEZGYpkTQVesXeN04Z8zyeu/sg7rKUpY8eztTv3yCLKumOGcGOSP2w5Y/C/ufAOf8HVKz9r6jfbXoXnjtv2H/b/DyxNu47oU1ZKUlUl3fxPwjPmbMR7/zqoa/+f/8i0FE+gwNMdEVtWXw0g8hZyJ841f7tIv315dw8v3LuWTtsfxu8nPUfO3XDKnf7CWBY37mjRXkZxIAmPl9OONvsG4+Z668nqtm5FBe28jTM77wkoCqhkUkRGcEbTkHz30HVs+B786HkdO79PRAbQO/nbua2UsKGDM4jd9+60CvRgCgqR4qCnq/V87y5+CFWbiR0yk/8EoGz7vG66F00WwVjIn0I3s6I1CvobaWPwsrX4Djb+pSEnDO8c9Pt3DrP1dSXtvI948dz3XHTyA1KX7nRgnJkemaeeC5kJiKPXs5gwt/CCMO9moPlAREJESJoFXgS69P/5ivwJHXh/20gvJafvnSChZ8XszBowfx2HeOYMrIgT4Gug8OOBUufhaWPgIn/05VwyKyCyUCaFM97OBb93r98veiucXx8Htf8MfX12AGN502hcu+mkd862Qyfc2447ybiEg7SgSwe/XwXqwsquDnLyzn04IKvjZpCL8+axqjs9L8j1NExAdKBHuqHm4n2NDMn+ev4YF3viArLZE7LzyE0w4agVkfPQsQEQlD/04EjXXw/FWQlg2n/cUb9K0T768v4cbnl/NlWS0XHJ7LjScfQGaaLriKSPTr34lg/q+geLVXPdzJEBK1DU3c/upnPPrBJsbmpPPUVTP5yvi9DDchIhJF+m8iWL/AG0JixqxOh5BYvLGMnz67jE2ltVxxZB7/9c0Ddu0SKiISA/pnIthL9XBdYzN/mPc5D773BaOzUnl61kxmjtNZgIjEpv6XCJyDV34CNdvhwqcgadfePh9/Wc4Nzy5jQ3ENl8wcw89Pnkx6cv97m0Sk/+h/R7hPZ8PKF3erHq5vaubPb67lvoXrGTEolX9cecTO4SFERGJY/0oEgS9h7k93qx5eXlDBDc9+wppt1VxweC6/OHUyGSmJEQxURKT39J9E0EH1cENTC39bsI67FqwjZ0ASD19xOF+bpPl6RaR/6T+JYNHdu1QPr95SyQ2zl7FqSyVnHzqKm0+byqA0nQWISP/TfxLBpFOgrpKmAy/g3n+v5S/z1zIoNYn7Lz2ME6cOj3R0IiIR038SQfZ41k27lhvu/YBlBRWcfvBIfnXGVAanqzpYRPq3fpMInl2ymV+8tIIByQncddGhnHrQiEiHJCLSJ/SbRDA2J53jDxjKrWdOY0hGcqTDERHpM3yds9jMTjKzz81snZnd2MH6ZDN7JrT+P2aW51cs+XmDueeSw5QERETa8S0RmFk8cBdwMjAFuNDMprTb7Eqg3Dm3P/An4Ha/4hERkY75eUYwA1jnnNvgnGsAngbObLfNmcCjofvPAcebBvcXEelVfiaCUcDmNo8LQss63MY51wRUALuN7mZms8xsiZktKS4u9ilcEZH+yddrBD3FOXe/cy7fOZc/ZMiQSIcjIhJT/EwEhUBum8ejQ8s63MbMEoBBQKmPMYmISDt+JoLFwAQzG2tmScAFwJx228wBLgvdPxf4t3PO+RiTiIi041sdgXOuycyuBuYB8cBDzrmVZnYrsMQ5Nwd4EHjczNYBZXjJQkREepGvBWXOubnA3HbLbmpzvw74tp8xiIjInlm0tcSYWTGwaR+fngOU9GA4PU3xdY/i676+HqPi23f7Oec67G0TdYmgO8xsiXMuP9JxdEbxdY/i676+HqPi80dUdB8VERH/KBGIiPRz/S0R3B/pAPZC8XWP4uu+vh6j4vNBv7pGICIiu+tvZwQiItKOEoGISD8Xk4mgL02I08Fr55rZAjNbZWYrzey6DrY5zswqzOyT0O2mjvblY4wbzWx56LWXdLDezOyvoffvUzM7tBdjm9TmffnEzCrN7Pp22/T6+2dmD5nZdjNb0WbZYDN7w8zWhn5mdfLcy0LbrDWzyzraxofYfm9mn4X+fi+aWWYnz93jZ8HnGG8xs8I2f8dTOnnuHv/ffYzvmTaxbTSzTzp5bq+8h93inIupG95wFuuBcUASsAyY0m6bHwL3hu5fADzTi/GNAA4N3c8A1nQQ33HAvyL4Hm4Ecvaw/hTgVcCAmcB/Ivi33opXKBPR9w84BjgUWNFm2e+AG0P3bwRu7+B5g4ENoZ9ZoftZvRDbiUBC6P7tHcUWzmfB5xhvAX4axmdgj//vfsXXbv0fgZsi+R525xaLZwR9ekIc59wW59xHoftVwGp2n6ehrzsTeMx5FgGZZjYiAnEcD6x3zu1rpXmPcc69jTdeVlttP2ePAmd18NRvAm8458qcc+XAG8BJfsfmnHvdeXOAACzCGx04Yjp5/8IRzv97t+0pvtCx4zzgqZ5+3d4Si4mgxybE8VuoSeoQ4D8drP6KmS0zs1fNbGqvBgYOeN3MlprZrA7Wh/Me94YL6PyfL5LvX6thzrktoftbgWEdbNMX3svv4J3hdWRvnwW/XR1qvnqok6a1vvD+HQ1sc86t7WR9pN/DvYrFRBAVzGwA8DxwvXOust3qj/CaOw4G7gRe6uXwjnLOHYo33/SPzOyYXn79vQoNbX4G8GwHqyP9/u3GeW0Efa6vtpn9AmgCnuhkk0h+Fu4BxgPTgS14zS990YXs+Wygz/8/xWIi6PMT4phZIl4SeMI590L79c65Sudcdej+XCDRzHJ6Kz7nXGHo53bgRbzT77bCeY/9djLwkXNuW/sVkX7/2tjW2mQW+rm9g20i9l6a2eXAacDFoUS1mzA+C75xzm1zzjU751qAv3fy2hH9LIaOH2cDz3S2TSTfw3DFYiLo0xPihNoTHwRWO+fu6GSb4a3XLMxsBt7fqVcSlZmlm1lG6328i4or2m02B/g/od5DM4GKNk0gvaXTb2GRfP/aafs5uwx4uYNt5gEnmllWqOnjxNAyX5nZScB/AWc452o72Sacz4KfMba97vStTl47nP93P30D+Mw5V9DRyki/h2GL9NVqP254vVrW4PUm+EVo2a14H3qAFLwmhXXAh8C4XoztKLwmgk+BT0K3U4DvA98PbXM1sBKvB8Qi4Ku9GN+40OsuC8XQ+v61jc+Au0Lv73Igv5f/vul4B/ZBbZZF9P3DS0pbgEa8duor8a47zQfWAm8Cg0Pb5gMPtHnud0KfxXXAFb0U2zq8tvXWz2BrL7qRwNw9fRZ68f17PPT5+hTv4D6ifYyhx7v9v/dGfKHlj7R+7tpsG5H3sDs3DTEhItLPxWLTkIiIdIESgYhIP6dEICLSzykRiIj0c0oEIiL9nBKBiM9Co6H+K9JxiHRGiUBEpJ9TIhAJMbNLzOzD0Ljx95lZvJlVm9mfzJs7Yr6ZDQltO93MFrUZzz8rtHx/M3szNODdR2Y2PrT7AWb2XGgOgCfaVD7fZt7cFJ+a2R8i9KtLP6dEIAKY2WTgfOBI59x0oBm4GK+KeYlzbiqwELg59JTHgP92zh2EV/3auvwJ4C7nDXj3VbxqVPBGmb0emIJXbXqkmWXjDZ0wNbSf3/j7W4p0TIlAxHM8cBiwODTT1PF4B+wWdg4o9g/gKDMbBGQ65xaGlj8KHBMaU2aUc+5FAOdcnds5js+HzrkC5w2g9gmQhzf8eR3woJmdDXQ45o+I35QIRDwGPOqcmx66TXLO3dLBdvs6Jkt9m/vNeLODNeGNRPkc3iigr+3jvkW6RYlAxDMfONfMhsKO+Yb3w/sfOTe0zUXAu865CqDczI4OLb8UWOi8GecKzOys0D6SzSytsxcMzUkxyHlDZf8YONiPX0xkbxIiHYBIX+CcW2Vm/4M3k1Qc3iiTPwJqgBmhddvxriOAN6z0vaED/QbgitDyS4H7zOzW0D6+vYeXzQBeNrMUvDOSn/TwryUSFo0+KrIHZlbtnBsQ6ThE/KSmIRGRfk5nBCIi/ZzOCERE+jklAhGRfk6JQESkn1MiEBHp55QIRET6uf8PRuAGSM40WhMAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eva_MJw-sr1h"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}