Untitled9_iter_100.ipynb

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      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib as mpl\n",
        "import seaborn as sns\n",
        "import matplotlib.animation as animation\n",
        "import operator\n",
        "from scipy import stats \n",
        "from mpl_toolkits.mplot3d import Axes3D\n",
        "from sklearn.datasets.samples_generator import make_regression \n",
        "import csv\n",
        "import math\n",
        "from google.colab import files\n",
        "\n",
        "uploaded = files.upload()\n",
        "\n",
        "file_data   = \"mnist.csv\"\n",
        "handle_file = open(file_data, \"r\")\n",
        "data        = handle_file.readlines()\n",
        "handle_file.close()\n",
        "\n",
        "size_row    = 28    # height of the image\n",
        "size_col    = 28    # width of the image\n",
        "\n",
        "num_image   = len(data)\n",
        "count       = 0     # count for the number of images\n",
        "\n",
        "#\n",
        "# normalize the values of the input data to be [0, 1]\n",
        "#\n",
        "def normalize(data):\n",
        "\n",
        "    data_normalized = (data - min(data)) / (max(data) - min(data))\n",
        "\n",
        "    return(data_normalized)\n",
        "\n",
        "#\n",
        "# example of distance function between two vectors x and y\n",
        "#\n",
        "def distance(x, y):\n",
        "\n",
        "    d = (x - y) ** 2\n",
        "    s = np.sum(d)\n",
        "    # r = np.sqrt(s)\n",
        "\n",
        "    return(s)\n",
        "\n",
        "#\n",
        "# make a matrix each column of which represents an images in a vector form\n",
        "#\n",
        "list_image  = np.empty((size_row * size_col, num_image), dtype=float)\n",
        "list_label  = np.empty(num_image, dtype=int)\n",
        "\n",
        "for line in data:\n",
        "\n",
        "    line_data   = line.split(',')\n",
        "    label       = line_data[0]\n",
        "    im_vector   = np.asfarray(line_data[1:])\n",
        "    im_vector   = normalize(im_vector)\n",
        "\n",
        "    list_label[count]       = label\n",
        "    list_image[:, count]    = im_vector\n",
        "\n",
        "    count += 1\n",
        "\n",
        "#\n",
        "# plot first 150 images out of 10,000 with their labels\n",
        "#\n",
        "f1 = plt.figure(1)\n",
        "\n",
        "for i in range(150):\n",
        "\n",
        "    label       = list_label[i]\n",
        "    im_vector   = list_image[:, i]\n",
        "    im_matrix   = im_vector.reshape((size_row, size_col))\n",
        "\n",
        "    plt.subplot(10, 15, i+1)\n",
        "    plt.title(label)\n",
        "    plt.imshow(im_matrix, cmap='Greys', interpolation='None')\n",
        "\n",
        "    frame   = plt.gca()\n",
        "    frame.axes.get_xaxis().set_visible(False)\n",
        "    frame.axes.get_yaxis().set_visible(False)\n",
        "\n",
        "\n",
        "#plt.show()\n",
        "\n",
        "#\n",
        "# plot the average image of all the images for each digit\n",
        "#\n",
        "f2 = plt.figure(2)\n",
        "\n",
        "im_average  = np.zeros((size_row * size_col, 10), dtype=float)\n",
        "im_count    = np.zeros(10, dtype=int)\n",
        "\n",
        "for i in range(num_image):\n",
        "\n",
        "    im_average[:, list_label[i]] += list_image[:, i]\n",
        "    im_count[list_label[i]] += 1\n",
        "\n",
        "for i in range(10):\n",
        "\n",
        "    im_average[:, i] /= im_count[i]\n",
        "\n",
        "    plt.subplot(2, 5, i+1)\n",
        "    plt.title(i)\n",
        "    plt.imshow(im_average[:,i].reshape((size_row, size_col)), cmap='Greys', interpolation='None')\n",
        "\n",
        "    frame   = plt.gca()\n",
        "    frame.axes.get_xaxis().set_visible(False)\n",
        "    frame.axes.get_yaxis().set_visible(False)\n",
        "\n",
        "plt.show()\n",
        "\n"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/utils/deprecation.py:144: FutureWarning: The sklearn.datasets.samples_generator module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
            "  warnings.warn(message, FutureWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-d125ea3b-873a-4059-9310-262a33f795fb\" name=\"files[]\" multiple disabled />\n",
              "     <output id=\"result-d125ea3b-873a-4059-9310-262a33f795fb\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Saving mnist.csv to mnist.csv\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 150 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 10 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b_YcDHFWIRFP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "theta = np.random.normal(size=(size_row*size_col))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DemnhlAQP0XJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sigmoid(z): \n",
        "  g = 1 / (1 + np.exp(-z)) \n",
        "  \n",
        "  return g "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DRugdPmoP2G5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "c841b03a-e8eb-46e5-a47e-07173e332f6f"
      },
      "source": [
        "z_list = []\n",
        "for i in range(0, 10):\n",
        "  z_list.append(0.0)\n",
        "\n",
        "print(z_list)"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xtbUZT3IP28F",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "for i in range(0, num_image):\n",
        "  label       = list_label[i]\n",
        "  im_vector   = list_image[:, i]\n",
        "  im_matrix   = im_vector.reshape((size_row, size_col))\n",
        "  y = 0\n",
        "  for ny in range(0, size_row):\n",
        "      for nz in range(0, size_col):\n",
        "        y = y + theta[size_col*ny + nz]*im_matrix[ny][nz]\n",
        "  # print(y)\n",
        "  z_list[label] = z_list[label] + sigmoid(y)\n",
        "  # print(sigmoid(y))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OWQYa_g6P4H2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#평균내기\n",
        "\n",
        "# for i in range(0, 10):\n",
        "  # z_list[i] = z_list[i] / label_list[i]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WUWOjwQQTDdR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#first hidden layer로 가기 위한 초기 fully connected u 생성\n",
        "w_tmp = np.ones(shape=(6000, 197, 785))\n",
        "v_tmp = np.ones(shape=(6000, 50, 197))\n",
        "u_tmp = np.ones(shape=(6000, 10, 50))\n",
        "\n",
        "matrix_u = np.zeros((197, 785))  #197줄\n",
        "matrix_u[0][0] = 1               #y레이어의 bias를 위한 값 1\n",
        "\n",
        "for i in range(1, 197):\n",
        "  for j in range(0, 785):\n",
        "    matrix_u[i][j] = np.random.normal()\n",
        "\n",
        "\n",
        "# matrix_u[196][0] = 0            #줄, 칸\n",
        "##############################################\n",
        "matrix_v = np.zeros((50, 197))  #50줄\n",
        "matrix_v[0][0] = 1               #y레이어의 bias를 위한 값 1\n",
        "\n",
        "for i in range(1, 50):\n",
        "  for j in range(0, 197):\n",
        "    matrix_v[i][j] = np.random.normal()\n",
        "\n",
        "\n",
        "# matrix_v[196][0] = 0            #줄, 칸\n",
        "##############################################\n",
        "matrix_w = np.zeros((10, 50))  #10줄\n",
        "# matrix_w[0][0] = 1               #y레이어의 bias를 위한 값 1\n",
        "\n",
        "for i in range(0, 10):\n",
        "  for j in range(0, 50):\n",
        "    matrix_w[i][j] = np.random.normal()\n",
        "\n",
        "w_tmp = matrix_w\n",
        "v_tmp = matrix_v\n",
        "u_tmp = matrix_u\n",
        "\n",
        "# matrix_w[196][0] = 0            #줄, 칸\n",
        "\n",
        "# print(matrix)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "idHIKSRGY0p9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import operator\n",
        "\n",
        "y_ = np.ones((197, 1))\n",
        "\n",
        "x_list = np.ones(shape=(6000, 785, 1))\n",
        "\n",
        "y__list = np.ones(shape=(6000, 197, 1))\n",
        "z__list = np.ones(shape=(6000, 50, 1))\n",
        "h__list = np.ones(shape=(6000, 10, 1))\n",
        "\n",
        "y_list = np.ones(shape=(6000, 197, 1))\n",
        "z_list = np.ones(shape=(6000, 50, 1))\n",
        "h_list = np.ones(shape=(6000, 10, 1))\n",
        "l_list = np.zeros(shape=(6000, 10, 1))\n",
        "\n",
        "y_list_tmp = np.ones(shape=(6000, 197, 1))\n",
        "z_list_tmp = np.ones(shape=(6000, 50, 1))\n",
        "h_list_tmp = np.ones(shape=(6000, 10, 1))\n",
        "y__list_tmp = np.ones(shape=(6000, 197, 1))\n",
        "z__list_tmp = np.ones(shape=(6000, 50, 1))\n",
        "h__list_tmp = np.ones(shape=(6000, 10, 1))\n",
        "\n",
        "# w_tmp = np.ones(shape=(6000, 197, 785))\n",
        "# v_tmp = np.ones(shape=(6000, 50, 197))\n",
        "# u_tmp = np.ones(shape=(6000, 10, 50))\n",
        "\n",
        "# matrix_u = np.zeros((197, 785))  #197줄\n",
        "# matrix_u[0][0] = 1               #y레이어의 bias를 위한 값 1\n",
        "\n",
        "\n",
        "#training set 6000개에 대해서\n",
        "for i in range(0, 6000):\n",
        "  # print(i)\n",
        "  label       = list_label[i]\n",
        "  bias   = [1]       #bias 1\n",
        "  im_vector = np.concatenate((bias, list_image[:, i]), axis = None)\n",
        "\n",
        "  # print(type(list_image[: , i]))\n",
        "  # print(list_image[:, i])\n",
        "  # print(im_vector)\n",
        "  im_matrix   = im_vector.reshape((size_row*size_col + 1, 1))\n",
        "  \n",
        "  x_list[i] = im_matrix\n",
        "\n",
        "  y_ = np.dot(matrix_u, im_matrix)  #x와 가중치 u를 곱해서 y_를 만듦\n",
        "  y__list[i] = y_\n",
        "  \n",
        "  y_vector = np.ones((197,1)) #bias\n",
        "  for j in range (1, 197):\n",
        "    y_vector[j][0] = 1 / (1 + math.exp(-y_[j][0]))\n",
        "    # sigmoid(y_[j][0])  #sigmoid 함수를 적용해서 y_에서 y를 만듦\n",
        "\n",
        "  y   = y_vector.reshape((197, 1))\n",
        "  y_list[i] = y\n",
        "\n",
        "  z_  = np.dot(matrix_v, y)  #y와 가중치 v를 곱해서 z_를 만듦\n",
        "  z__list[i] = z_\n",
        "  z_vector = np.ones((50,1)) #bias\n",
        "  for j in range (1, 50):\n",
        "    z_vector[j][0] = 1 / (1 + math.exp(-z_[j][0]))  #sigmoid 함수를 적용해서 y_에서 y를 만듦\n",
        "\n",
        "  z   = z_vector.reshape((50, 1))\n",
        "  z_list[i] = z\n",
        "  \n",
        "  # print(z)\n",
        "\n",
        "  h_  = np.dot(matrix_w, z)  #z와 가중치 w를 곱해서 h_를 만듦\n",
        "  h__list[i] = h_\n",
        "  \n",
        "  h_vector = np.ones((10,1)) #bias\n",
        "  for j in range (0, 10):\n",
        "    h_vector[j][0] = 1 / (1 + math.exp(-h_[j][0]))  #sigmoid 함수를 적용해서 h_에서 h를 만듦\n",
        "\n",
        "  h   = h_vector.reshape((10, 1))\n",
        "  # tmp = h.ravel()\n",
        "  # max_value = max(tmp)\n",
        "  # print(max_value)\n",
        "  # max_index = tmp.index(max_value)\n",
        "  index, value = max(enumerate(h), key=operator.itemgetter(1))\n",
        "  h_list[i] = h\n",
        "  l_list[i][index] = 1\n",
        "  # print(l_list[i])\n",
        "  # print(h)\n",
        "\n",
        "  y_list_tmp[i] = y_list[i]\n",
        "  z_list_tmp[i] = z_list[i]\n",
        "  h_list_tmp[i] = h_list[i]\n",
        "  y__list_tmp[i] = y__list[i]\n",
        "  z__list_tmp[i] = z__list[i]\n",
        "  h__list_tmp[i] = h__list[i]\n",
        "\n",
        "# print(l_list)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i1AbB1lMv1yY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def objective_function(size, label_List, h_List):\n",
        "  result = 0.0\n",
        "  for i in range(0, size):\n",
        "    for k in range(0, 10):\n",
        "      result = result + ((-1)*label_List[i][k]*math.log(h_List[i][k][0]) - (1-label_List[i][k])*math.log(1-h_List[i][k][0]))\n",
        "  result = result / size\n",
        "\n",
        "  return result"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z7uMF29V6ZAh",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def w_gredient_descent(learning_rate, k_value, n_value, size, label_List):\n",
        "  result = 0.0\n",
        "  for i in range(0, size):\n",
        "    result = result + (z_list_tmp[i][n_value][0]*(sigmoid(h_list_tmp[i][k_value][0]) - label_List[i][k_value][0]))\n",
        "  result = result / size\n",
        "  result = result * learning_rate\n",
        "  final = w_tmp[k_value][n_value] - result\n",
        "\n",
        "  return final"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FQMnniqxLxzl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def v_gredient_descent(learning_rate, k_value, n_value, size, label_List):\n",
        "  result = 0.0\n",
        "  for i in range(0, size):\n",
        "    result = result + (y_list_tmp[i][n_value][0]*w_tmp[0][k_value]*(sigmoid(h_list_tmp[i][0][0]) - label_List[i][0][0])*(sigmoid(z__list_tmp[i][k_value][0])*(1 - sigmoid(z__list_tmp[i][k_value][0]))))\n",
        "  result = result / size\n",
        "  result = result * learning_rate\n",
        "  final = v_tmp[k_value][n_value] - result\n",
        "\n",
        "  return final"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UabSYhhIO6JU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def u_gredient_descent(learning_rate, k_value, n_value, size, label_List):\n",
        "  result = 0.0\n",
        "  for i in range(0, size):\n",
        "    result = result + (x_list[i][n_value][0]*w_tmp[0][1]*(sigmoid(h_list_tmp[i][0][0]) - label_List[i][0][0])*(sigmoid(z__list_tmp[i][1][0])*(1 - sigmoid(z__list_tmp[i][1][0])))*(sigmoid(y__list_tmp[i][k_value][0])*(1 - sigmoid(y__list_tmp[i][k_value][0]))))\n",
        "  result = result / size\n",
        "  result = result * learning_rate\n",
        "  final = u_tmp[k_value][n_value] - result\n",
        "\n",
        "  return final"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0vn3FkYXStur",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "7742ad64-45ba-4157-e197-0ae54c1710e9"
      },
      "source": [
        "#이제 여기에다가\n",
        "\n",
        "#iteration에 따라\n",
        "#cost function 값을 배열에 저장하고\n",
        "#세타값을 업데이트 시키고(위의 세개 함수 호출)\n",
        "#업데이트 시킨값을 다시 cost함수에 넣고\n",
        "#업데이트 시키고\n",
        "#이것을 반복하는 함수를 짠다.\n",
        "\n",
        "#아직 해야하는 것 : h값에 따라 가장 큰값의 index로 L값정하는거 위에 추가해야함.\n",
        "\n",
        "iteration = 100\n",
        "l_r = 0.01\n",
        "\n",
        "cost_history = np.zeros(iteration)\n",
        "\n",
        "total_number_of_predictions = 6000\n",
        "accuracy_history = np.zeros(iteration)\n",
        "\n",
        "for t in range(0, iteration):\n",
        "  number_of_correct_predictions = 0\n",
        "  \n",
        "  print(t)\n",
        "\n",
        "  # cost_history[t] = objective_function(6000, l_list, h_list_tmp)\n",
        "  result = 0.0\n",
        "  for i in range(0, 6000):\n",
        "    for k in range(0, 10):\n",
        "      result = result + ((-1)*l_list[i][k]*math.log(h_list_tmp[i][k][0]) - (1-l_list[i][k])*math.log(1-h_list_tmp[i][k][0]))\n",
        "  result = result / 6000\n",
        "  cost_history[t] = result\n",
        "\n",
        "# (1 / (1 + math.exp(-y__list_tmp[i][m][0])))\n",
        "\n",
        "  for m in range(0, 10):\n",
        "    # print(m)\n",
        "    for n in range(0, 50):\n",
        "      # matrix_w[m][n] = w_gredient_descent(l_r, m, n, 6000, l_list)\n",
        "      result = 0.0\n",
        "      for i in range(0, 60):\n",
        "        result = result + (z_list_tmp[i][n][0]*((1 / (1 + math.exp(-h_list_tmp[i][m][0]))) - l_list[i][m][0]))\n",
        "      result = result / 60\n",
        "      result = result * l_r\n",
        "      final = w_tmp[m][n] - result\n",
        "      matrix_w[m][n] = final\n",
        "\n",
        "  for m in range(0, 50):\n",
        "    # print(m)\n",
        "    for n in range(0, 197):\n",
        "      # matrix_v[m][n] = v_gredient_descent(l_r, m, n, 6000, l_list)\n",
        "      result = 0.0\n",
        "      for i in range(0, 60):\n",
        "        result = result + (y_list_tmp[i][n][0]*w_tmp[0][m]*((1 / (1 + math.exp(-h_list_tmp[i][0][0]))) - l_list[i][0][0])*((1 / (1 + math.exp(-z__list_tmp[i][m][0])))*(1 - (1 / (1 + math.exp(-z__list_tmp[i][m][0]))))))\n",
        "      result = result / 60\n",
        "      result = result * l_r\n",
        "      final = v_tmp[m][n] - result\n",
        "\n",
        "  for m in range(0, 197):\n",
        "    # print(m)\n",
        "    for n in range(0, 785):\n",
        "      # matrix_u[m][n] = u_gredient_descent(l_r, m, n, 6000, l_list)\n",
        "      result = 0.0\n",
        "      for i in range(0, 60):\n",
        "        result = result + (x_list[i][n][0]*w_tmp[0][1]*((1 / (1 + math.exp(-h_list_tmp[i][0][0]))) - l_list[i][0][0])*((1 / (1 + math.exp(-z__list_tmp[i][1][0])))*(1 - (1 / (1 + math.exp(-z__list_tmp[i][1][0])))))*((1 / (1 + math.exp(-y__list_tmp[i][m][0])))*(1 - (1 / (1 + math.exp(-y__list_tmp[i][m][0]))))))\n",
        "      result = result / 60\n",
        "      result = result * l_r\n",
        "      final = u_tmp[m][n] - result\n",
        "\n",
        "####################################################################\n",
        "\n",
        "  for k in range(0, 6000):\n",
        "  # print(i)\n",
        "    label       = list_label[k]\n",
        "    bias   = [1]       #bias 1\n",
        "    im_vector = np.concatenate((bias, list_image[:, k]), axis = None)\n",
        "\n",
        "    # print(type(list_image[: , k]))\n",
        "    # print(list_image[:, k])\n",
        "    # print(im_vector)\n",
        "    im_matrix   = im_vector.reshape((size_row*size_col + 1, 1))\n",
        "\n",
        "    y_ = np.dot(matrix_u, im_matrix)  #x와 가중치 u를 곱해서 y_를 만듦\n",
        "    y__list[k] = y_\n",
        "    \n",
        "    y_vector = np.ones((197,1)) #bias\n",
        "    for j in range (1, 197):\n",
        "      y_vector[j][0] = 1 / (1 + math.exp(-y_[j][0]))  #sigmoid 함수를 적용해서 y_에서 y를 만듦\n",
        "\n",
        "    y   = y_vector.reshape((197, 1))\n",
        "    y_list[k] = y\n",
        "\n",
        "    z_  = np.dot(matrix_v, y)  #y와 가중치 v를 곱해서 z_를 만듦\n",
        "    z__list[k] = z_\n",
        "    z_vector = np.ones((50,1)) #bias\n",
        "    for j in range (1, 50):\n",
        "      z_vector[j][0] = 1 / (1 + math.exp(-z_[j][0]))  #sigmoid 함수를 적용해서 y_에서 y를 만듦\n",
        "\n",
        "    z   = z_vector.reshape((50, 1))\n",
        "    z_list[k] = z\n",
        "    \n",
        "    # print(z)\n",
        "\n",
        "    h_  = np.dot(matrix_w, z)  #z와 가중치 w를 곱해서 h_를 만듦\n",
        "    h__list[k] = h_\n",
        "    \n",
        "    h_vector = np.ones((10,1)) #bias\n",
        "    for j in range (0, 10):\n",
        "      h_vector[j][0] = 1 / (1 + math.exp(-h_[j][0]))  #sigmoid 함수를 적용해서 h_에서 h를 만듦\n",
        "\n",
        "    h   = h_vector.reshape((10, 1))\n",
        "    # tmp = h.ravel()\n",
        "    # max_value = max(tmp)\n",
        "    # print(max_value)\n",
        "    # max_index = tmp.index(max_value)\n",
        "    index, value = max(enumerate(h), key=operator.itemgetter(1))\n",
        "    h_list[k] = h\n",
        "    l_list[k][index] = 1\n",
        "    # print(l_list[i])\n",
        "    # print(h)\n",
        "    if index == label:\n",
        "      number_of_correct_predictions = number_of_correct_predictions + 1\n",
        "\n",
        "    y_list_tmp[k] = y_list[k]\n",
        "    z_list_tmp[k] = z_list[k]\n",
        "    h_list_tmp[k] = h_list[k]\n",
        "    y__list_tmp[k] = y__list[k]\n",
        "    z__list_tmp[k] = z__list[k]\n",
        "    h__list_tmp[k] = h__list[k]\n",
        "\n",
        "  accuracy_history[t] = number_of_correct_predictions/total_number_of_predictions\n",
        "  t = t + 1"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "stream",
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          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DcsYGj-cTUkN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "outputId": "8fde5ca7-81eb-478f-8fae-f2859b589cee"
      },
      "source": [
        "#그 코드를 바탕으로 training loss plotting 하기.\n",
        "fig,ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "# print(cost_history[1])\n",
        "\n",
        "ax.set_ylabel('J(Theta)')\n",
        "ax.set_xlabel('Iterations')\n",
        "_=ax.plot(range(iteration),cost_history,'b.', color = 'red')"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2m0mvxqZUvHl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 498
        },
        "outputId": "ad984fdb-978f-4741-9d7f-d1414c4d4cd0"
      },
      "source": [
        "#그 코드를 바탕으로 training loss plotting 하기.\n",
        "fig,ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "# print(cost_history[1])\n",
        "\n",
        "ax.set_ylabel('accuracy')\n",
        "ax.set_xlabel('Iterations')\n",
        "_=ax.plot(range(iteration),accuracy_history,'b.', color = 'red')"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}