02-02-neural-network.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 인공신경망(artificial neural network)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 생각해 볼 문제\n",
    "\n",
    "**문제 1)** 다음의 경우에서, $x$가 7일 때, $y$의 값은 얼마입니까?\n",
    "\n",
    "|**$x$**|**$y$**|\n",
    "|---|---|---|\n",
    "|0|2|\n",
    "|1|3|\n",
    "|2|6|\n",
    "|3|11|\n",
    "|4|18|\n",
    "|5|27|\n",
    "|6|38|\n",
    "|7|?|\n",
    "|8|66|\n",
    "\n",
    "**문제 2)** 위의 관계를 선형 회귀식으로 나타낼 수 있습니까?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 코드\n",
    "\n",
    "**코드 1)** \"문제 1\"을 선형 회귀 프로그램으로 풀어봅니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=7 y=? [[ 0.43987903]]\n",
      "------------------------------------\n",
      "W [[ 0.66243857]]\n",
      "b [-0.02382797]\n",
      "loss 0.0375111\n"
     ]
    },
    {
     "data": {
      "image/png": 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LJe5lwOBG28nB25q6BnfPArIg8DF7TZq0CY6drOG5N3fy3Fs7Ka+q5fqxA1g4\nK43RA7pFapciIjEllLhvBtLMbCiBYM8H7jhtzUrggeD5+KnAsbCfbw/B8aoann9zF8vfLKS8qpYv\nX9yfhTNHMmaQoi4ircs54+7utWb2APAagadCPufu283s3uD9y4BXCTwNMp/AUyHvjtzIf668qobn\n39rF8g2FHK+q5Utj+rNwVhoXD+renGOIiMSMkM65u/urBALe+LZljb524P7wjnZu5VU1/HTjLp7d\nsJNjJ2uYdVF/Fs1KY2ySoi4irVvLeYVqIxXVtcGoF3K0soaZo/uxaNZIxiUr6iIi0ALjvvqTffzN\nLz/gSGUN147ux8KZaUwY3CPaY4mIxJQWF/ehfbpwyeAeLJw1kksUdRGRM2qBce/M83dPifYYIiIx\nrU20BxARkfBT3EVE4pDiLiIShxR3EZE4pLiLiMQhxV1EJA4p7iIicUhxFxGJQxZ4z68o7NjsAFB0\nnv95H+BgGMcJl1idC2J3Ns3VNJqraeJxriHu3vdci6IW9wthZjnunh7tOU4Xq3NB7M6muZpGczVN\na55Lp2VEROKQ4i4iEodaatyzoj3AF4jVuSB2Z9NcTaO5mqbVztUiz7mLiMjZtdQjdxEROYuYjruZ\nzTazT80s38x+cIb7zcyeCN6/zcwmxchco83sbTOrNrPvNsdMIc61IPg4fWhmG81sQozMNSc411Yz\nyzGzabEwV6N1l5pZrZnNi4W5zGy6mR0LPl5bzexHsTBXo9m2mtl2M1sXC3OZ2fcaPVYfmVmdmfWK\ngbm6m9n/mNkHwcfr7rAO4O4x+QtIAAqAYUB74ANgzGlrbgD+ABhwGfBOjMzVD7gUeBT4bgw9XlcA\nPYNfXx9Dj1cX/nSKcDzwSSzM1WjdagIfED8vFuYCpgO/a46/V02cqwewA0gJbveLhblOW/9VYHUs\nzAX8H+DHwa/7AoeB9uGaIZaP3KcA+e5e6O6ngJeAOaetmQO86AGbgB5mNjDac7n7fnffDNREeJam\nzrXR3Y8ENzcByTEyV4UH/4YDnYHmuBAUyt8vgAeB3wD7m2GmpszV3EKZ6w7gZXcvhsDPQYzM1djt\nwM9jZC4HupqZETjAOQzUhmuAWI57ElDSaLs0eFtT10Rjrmho6lz3EPhXT6SFNJeZzTWzT4DfA38R\nC3OZWRIwF3i6GeYJea6gK4Knsv5gZhfHyFwjgZ5mttbMtpjZXTEyFwBmlgjMJvA/61iY6yngImA3\n8CGw0N1XRA1gAAACJUlEQVTrwzVAi/sMVblwZjaDQNyb5dx2KNz9t8Bvzexq4BFgVpRHAsgEvu/u\n9YGDq5jxHoFTHxVmdgPwCpAW5Zkg0JPJwEygE/C2mW1y99zojvWZrwJvufvhaA8S9GVgK3AtMBx4\nw8w2uPvxcHzzWD5yLwMGN9pODt7W1DXRmCsaQprLzMYDy4E57n4oVuZq4O7rgWFm1icG5koHXjKz\nXcA8YKmZ3RTtudz9uLtXBL9+FWgXI49XKfCau59w94PAeiDSF+2b8vdrPs1zSgZCm+tuAqex3N3z\ngZ3A6LBNEOkLCxdwQaItUAgM5U8XJC4+bc2NfP6C6ruxMFejtX9H811QDeXxSgHygSti7M9xBH+6\noDqJwA+BRXuu09a/QPNcUA3l8RrQ6PGaAhTHwuNF4BTDquDaROAjYGy05wqu607gnHbnSP8ZNuHx\nehr4u+DX/YN/7/uEa4aYPS3j7rVm9gDwGoErz8+5+3Yzuzd4/zICz2C4gUCwKgn8nzDqc5nZACAH\n6AbUm9kiAlfKw/LPrfOdC/gR0JvAEShArUf4zYtCnOtm4C4zqwFOArd58G98lOdqdiHONQ+4z8xq\nCTxe82Ph8XL3j83sj8A2oB5Y7u4fRXuu4NK5wOvufiKS8zRxrkeAF8zsQwIHqN/3wL94wkKvUBUR\niUOxfM5dRETOk+IuIhKHFHcRkTikuIuIxCHFXUQkDinuIiJxSHEXEYlDiruISBz6/xUaihyUcptZ\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7f0ebd080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "W = tf.Variable(tf.zeros([1, 1]))\n",
    "b = tf.Variable(tf.zeros([1]))\n",
    "\n",
    "x = tf.placeholder(tf.float32, [None, 1])\n",
    "y = tf.placeholder(tf.float32, [None, 1])\n",
    "\n",
    "# 데이터를 정규화(normalize)하는 것이 중요합니다.\n",
    "x_data = [[0.0], \n",
    "          [0.1], \n",
    "          [0.2], \n",
    "          [0.3], \n",
    "          [0.4], \n",
    "          [0.5], \n",
    "          [0.6], \n",
    "          [0.8]]\n",
    "y_data = [[.02], \n",
    "          [.03], \n",
    "          [.06], \n",
    "          [.11], \n",
    "          [.18], \n",
    "          [.27], \n",
    "          [.38], \n",
    "          [.66]]\n",
    "\n",
    "model = tf.matmul(x, W) + b\n",
    "loss = tf.reduce_sum(tf.square(model - y))\n",
    "\n",
    "optimizer = tf.train.GradientDescentOptimizer(0.01)\n",
    "train = optimizer.minimize(loss)\n",
    "\n",
    "sess = tf.Session()\n",
    "init = tf.global_variables_initializer()\n",
    "sess.run(init)\n",
    "\n",
    "for i in range(200):\n",
    "    sess.run(train, feed_dict={x: x_data, y: y_data})\n",
    "\n",
    "print(\"x=7\", \"y=?\",  sess.run(model, feed_dict={x: [[.7]]}))\n",
    "\n",
    "print(\"------------------------------------\")\n",
    "print(\"W\", sess.run(W))\n",
    "print(\"b\", sess.run(b))\n",
    "print(\"loss\", sess.run(loss, feed_dict={x: x_data, y: y_data}))\n",
    "\n",
    "%matplotlib inline\n",
    "y_ = sess.run(model, feed_dict={x: x_data})\n",
    "plt.plot(x_data, y_data, 'ro')\n",
    "plt.plot(x_data, y_)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"**코드 2)** 문제 1\"을 신경망 프로그램으로 풀어봅니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=7 y=? [[ 0.52444577]]\n",
      "------------------------------------\n",
      "W1 [[ 0.5375073   0.55929071 -0.84682059  0.7096402  -0.95135283  0.30052352\n",
      "  -0.21535921 -0.29589343  0.54455209  0.08900868]]\n",
      "W2 [[ 0.36884078]\n",
      " [ 0.32978484]\n",
      " [-0.77960706]\n",
      " [ 1.17369366]\n",
      " [-0.38263774]\n",
      " [-0.33719748]\n",
      " [ 0.39680076]\n",
      " [-0.82311153]\n",
      " [-0.47004855]\n",
      " [-0.51503998]]\n",
      "b1 [-0.03867738 -0.04682932  0.         -0.26978603  0.         -0.24149601\n",
      "  0.          0.         -0.43742236 -0.07845309]\n",
      "b2 [ 0.019881]\n",
      "loss 0.00132997\n"
     ]
    },
    {
     "data": {
      "image/png": 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U9owclMyItM707KgbikTkWGa22DmXfrJxmrk3oIOHq3l3XSkLCnfwxpoSyg5V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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7d839a5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 신경망에서는 가중치를 '0'이 아니라 난수로 초기화해야만 학습이 가능합니다.\n",
    "W1 = tf.Variable(tf.random_uniform([1, 10], -1, 1))\n",
    "b1 = tf.Variable(tf.zeros([10]))\n",
    "W2 = tf.Variable(tf.random_uniform([10, 1], -1, 1))\n",
    "b2 = tf.Variable(tf.zeros([1]))\n",
    "\n",
    "x = tf.placeholder(tf.float32, [None, 1])\n",
    "y = tf.placeholder(tf.float32, [None, 1])\n",
    "\n",
    "x_data = [[0.0], \n",
    "          [0.1], \n",
    "          [0.2], \n",
    "          [0.3], \n",
    "          [0.4], \n",
    "          [0.5], \n",
    "          [0.6], \n",
    "          [0.8]]\n",
    "y_data = [[.02], \n",
    "          [.03], \n",
    "          [.06], \n",
    "          [.11], \n",
    "          [.18], \n",
    "          [.27], \n",
    "          [.38], \n",
    "          [.66]]\n",
    "\n",
    "L1 = tf.nn.relu(tf.matmul(x, W1) + b1)\n",
    "\n",
    "model = tf.matmul(L1, W2) + b2\n",
    "loss = tf.reduce_sum(tf.square(model - y))\n",
    "\n",
    "optimizer = tf.train.GradientDescentOptimizer(0.01)\n",
    "train = optimizer.minimize(loss)\n",
    "\n",
    "sess = tf.Session()\n",
    "init = tf.global_variables_initializer()\n",
    "sess.run(init)\n",
    "\n",
    "for i in range(10000):\n",
    "    sess.run(train, feed_dict={x: x_data, y: y_data})\n",
    "\n",
    "print(\"x=7\", \"y=?\",  sess.run(model, feed_dict={x: [[.7]]}))\n",
    "\n",
    "print(\"------------------------------------\")\n",
    "print(\"W1\", sess.run(W1))\n",
    "print(\"W2\", sess.run(W2))\n",
    "print(\"b1\", sess.run(b1))\n",
    "print(\"b2\", sess.run(b2))\n",
    "print(\"loss\", sess.run(loss, feed_dict={x: x_data, y: y_data}))\n",
    "\n",
    "%matplotlib inline\n",
    "y_ = sess.run(model, feed_dict={x: x_data})\n",
    "plt.plot(x_data, y_data, 'ro')\n",
    "plt.plot(x_data, y_)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**신경망을 통해서 비선형의 문제를 풀 수 있습니다.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\"**코드 3)** 문제 1\"을 다층 신경망 프로그램으로 풀어봅니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=7 y=? [[ 0.52002245]]\n",
      "------------------------------------\n",
      "W1 [[-0.07586861 -0.4049499   0.45395193  0.9920547  -0.91539931  0.77438051\n",
      "   0.60203791 -0.14035439 -0.27673721  1.0105778 ]]\n",
      "W2 [[ 0.35578322 -0.56802201 -0.09509635 -0.0987792  -0.38431835  0.74238276\n",
      "  -0.70493937  0.46592617  0.22398949 -0.85181737]\n",
      " [ 0.30016255  0.3586421  -0.40471935 -0.31304264 -0.44059229 -0.1701057\n",
      "   0.12751222 -0.14494371 -0.51701784 -0.26338601]\n",
      " [-0.77599692 -0.73140311  0.47941309  0.98313236  0.05861426  0.56292576\n",
      "  -0.80430323  0.10536575  0.78865772 -0.34722877]\n",
      " [-0.92458844  0.06487604 -0.27961889 -0.64384389  0.60167342  1.01069856\n",
      "   0.69319147  0.35933554 -0.64002275 -0.70548749]\n",
      " [-0.48266554  0.11959291 -0.43488359  0.93410158  0.25272298 -0.70943737\n",
      "  -0.37772965 -0.54861355  0.43795609 -0.09187484]\n",
      " [ 0.8479259  -0.46652427  0.01416314 -0.16250961  0.27409267  0.66534984\n",
      "   0.92366552 -0.49259511  0.52642715  0.66605616]\n",
      " [-0.8423171  -0.83650476  0.34100148 -0.94465357 -0.68674415 -0.76230216\n",
      "   0.43956661 -0.43146941  0.52443898  0.61005282]\n",
      " [ 0.77867341 -0.31664991 -0.04404306  0.20365453 -0.11573172  0.12653637\n",
      "  -0.69063258  0.14566898 -0.42562914 -0.83469915]\n",
      " [ 0.46201563 -0.58767843 -0.45545912 -0.79403996 -0.23714805  0.07196641\n",
      "   0.72191572 -0.06461263 -0.64614511 -0.53380609]\n",
      " [-0.79189205 -0.11228715  0.69219029  0.74874717  0.39846852 -0.21446019\n",
      "  -0.75514019  0.94154102  0.154139   -0.59338331]]\n",
      "W3 [[ 0.54389238]\n",
      " [-0.94896996]\n",
      " [ 0.51825577]\n",
      " [ 0.80355018]\n",
      " [-0.22505569]\n",
      " [ 0.73278052]\n",
      " [-0.49879065]\n",
      " [ 0.84162313]\n",
      " [-0.75698841]\n",
      " [-0.29192543]]\n",
      "b1 [ 0.          0.         -0.25146294  0.09013545  0.         -0.13660713\n",
      " -0.01161614  0.          0.         -0.15941314]\n",
      "b2 [ 0.         -0.00350189 -0.08687837 -0.04919521  0.00079805 -0.016861\n",
      " -0.03423407 -0.0156937  -0.15391803  0.        ]\n",
      "b3 [-0.0197454]\n",
      "loss 1.41836e-05\n"
     ]
    },
    {
     "data": {
      "image/png": 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lXsPKKnys2baPhZvy/GWevYecPQcAiImqxymdmnHN4C4kdfFPsbRv/iN75SIi\nR6ByD4ZDThSqOvWxq7Ck8h0s/iJflrOX4jL/Xnm7Zg0Y0CWOMUP8UyyndGpGg/pRXv5NRCRCqNyP\nV5UThcqtHmsORLH4yTdYtDmWRVEt2LTbfzCzfj2jd6fmjExJ8B/47BJHx+YNdZq/iISEyv0InHPs\nL60gr7CUvKJS8vaXsLuwlLz9/o/d+0vZ88Fmdg9/gLxGzdnZJI7iaP80SuttBQxIbsrVKQkkdYmj\nT6fmNIzWXrmI1IzaVe5HmP4IhM/nKCguY/d/y/lgUZf4i7qysKuWd2nlgc1DxUTVo2XjGFrWj6VV\nUT5d9mynzf499NmeSdLWNcQX7MR8h/9aEZFQqz3lXmX6A4BNmyi/cTx5ZUbe0J+TV/j9Yv6uoEsO\nfr6nqIwKnzvst28cE0XLJjG0bNyAds0a0rNDM395V360OvhnA+IaR9OkQX3/lEriONi06YffsEuX\nED4ZIiJHVnvKfcIEKCri024DeODcVPIaNSO/UVNYA6yZ/4PhLWKjD5ZyYqvGDOgSV1nUDQ4WddWP\nY54ymTjx+z90QCcKiYjnak+5Z2cD0OLAPnrtWE+rogJaHsj3/znjOeIaR9OqcQNaNo4hLjaa+lE1\ndO0UnSgkImHInDv8NEWoJScnu4yMjMC/IDHxx6c/Nm4MViwRkbBmZgudc8nVjQto99bMhprZWjPL\nNLO7D3O/mdkTlfcvM7OkYwl9RBMn+qc7qtL0h4jIYVVb7mYWBTwNXAj0AkaaWa9Dhl0IdK/8SAWe\nDXJO/zTH5Mn+PXUz/5+TJ2v6Q0TkMAKZc08BMp1zWQBmNhMYBqyqMmYY8ILzz/F8bWYtzKyDc25b\nUNPqOikiIgEJZFqmE7C5ynZO5W1HO0ZERGpIjS7HY2apZpZhZhm5ubk1+dAiInVKIOW+BehcZTu+\n8rajHYNzbrJzLtk5l9ymTZujzSoiIgEKpNzTge5m1tXMYoARwOxDxswGRle+a2YwkB/0+XYREQlY\ntQdUnXPlZnYrMBeIAqY551aa2fjK+ycB7wEXAZlAETA2dJFFRKQ6np3EZGa5wGHOSgpIa2BXEOME\nS7jmgvDNplxHR7mOTiTm6uKcq3Ze27NyPx5mlhHIGVo1LVxzQfhmU66jo1xHpy7nqtF3y4iISM1Q\nuYuIRKDaWu6TvQ7wI8I1F4RvNuU6Osp1dOpsrlo55y4iIkdWW/fcRUTkCMK63MPiUsPHlquHmX1l\nZiVmdmfkie5uAAADpElEQVRNZAow16jK52m5mX1pZv3CJNewylxLKi9PcUY45KoybqCZlZvZ5eGQ\ny8zONrP8yudriZndFw65qmRbYmYrzWxeOOQys99Xea5WmFmFmbUMg1zNzexfZra08vkK7vlBzrmw\n/MB/wtR6oBsQAywFeh0y5iLgfcCAwcA3YZKrLTAQmAjcGUbP1xAgrvLzC8Po+WrCd1OEfYE14ZCr\nyrhP8J+od3k45ALOBt6tidfVUeZqgf9qsQmV223DIdch4y8BPgmHXMAfgL9Wft4GyANigpUhnPfc\nD15q2DlXCvz3UsNVHbzUsHPua6CFmXXwOpdzbqdzLh0oC3GWo831pXNuT+Xm1/ivARQOuQpd5Ssc\naAzUxIGgQF5fALcBbwI7ayDT0eSqaYHkuhp4yzmXDf7/B2GSq6qRwCthkssBTc3M8O/g5AHlwQoQ\nzuUerpcaDtfLGx9trnH4f+sJtYBymdllZrYGmANcFw65zKwTcBmhWHzmOHJVGlI5lfW+mfUOk1wn\nAXFm9pmZLTSz0WGSCwAziwWG4v9hHQ65ngJ6AluB5cDtzjlfsALUngWyJWjM7Bz85V4jc9uBcM7N\nAmaZ2U+AB4HzPI4E8Dhwl3PO59+5ChuL8E99FJrZRcDb+FdB81p9YABwLtAI+MrMvnbOrfM21kGX\nAP9xzuV5HaTSBcAS4KfACcC/zWy+c64gGN88nPfcg3apYQ9yeSGgXGbWF5gCDHPO7Q6XXP/lnPsc\n6GZmrcMgVzIw08w2ApcDz5jZpV7ncs4VOOcKKz9/D4gOk+crB5jrnNvvnNsFfA6E+qD90by+RlAz\nUzIQWK6x+KexnHMuE9gA9AhaglAfWDiOAxL1gSygK98dkOh9yJiL+f4B1QXhkKvK2PupuQOqgTxf\nCfiv3DkkzP4dT+S7A6pJ+P8TmNe5Dhk/g5o5oBrI89W+yvOVAmSHw/OFf4rh48qxscAK4BSvc1WO\na45/TrtxqP8Nj+L5eha4v/LzdpWv+9bByhC20zIuTC81HEguM2sPZADNAJ+Z3YH/SHlQft061lzA\nfUAr/HugAOUuxBcvCjDXcPzrAZQBB4CrXOUr3uNcNS7AXJcDN5lZOf7na0Q4PF/OudVm9gGwDPAB\nU5xzK7zOVTn0MuBD59z+UOY5ylwPAjPMbDn+HdS7nP83nqDQGaoiIhEonOfcRUTkGKncRUQikMpd\nRCQCqdxFRCKQyl1EJAKp3EVEIpDKXUQkAqncRUQi0P8DtJGkouYDkGwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7d16774e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD4AAAD8CAYAAAAv4Rf7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7d1729048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD4AAAD8CAYAAAAv4Rf7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nN7Jxb2Tj3nBr/P/S9ST19XVaqQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7d13f6518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAABECAYAAACIyeKpAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAiAiolIJgIiISiUAIiIq9V99TCdFC+AspwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7d8e78160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7f12adeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAADkAAAD8CAYAAADNPQyCAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAB1xJREFUeJztnW+MXFUZh5+f+8f+Wai71LRlW4QPiCkNBtNsoBpCCioU\nY/0ARomK+oGQgKKSmBoSiR81asRYjQQ1NRIMVqJNLQqIBE0QKbWFltJQSqG7bWmBWtha2m19/TB3\nzTDsds7OnoO777xPMpm7c889+3ty7ty9e+edc2VmeOcd/+8Abwch6YWQ9EJIeiEkvdBZotOe3m7r\n65+Rtc9Xh95g+NBxtbJtEcm+/hnc8puBrH1+75p/tLxtW+yuIemFkPRCSI4i6QpJOyTtlLSqdKjc\nNJWU1AGsBq4EFgOflrS4dLCcpIzkALDTzHaZ2XHg18DKsrHykiLZD+yp+3mweu1NSLpe0kZJG4df\nHcmVLwvZDjxmdoeZLTWzpT19Xbm6zUKK5BCwqO7nhdVr04YUyceBcyWdI6kb+BSwrmysvDT9L8TM\nTki6CfgT0AH83My2FU+WkaR/tcxsA7ChcJZixBmPF0LSC20hWeRC1r+2dbL+/N68fVrrUdtiJEPS\nCyHphZD0Qkh6ISS9EJJeCEkvhKQXQtILIemFIlfrTl98kuX3HMna5/ZPnmx527YYyZD0Qkh6ISQB\nJC2S9BdJT0vaJunmtyNYTlL+Tp4AbjGzTZJOA56Q9ICZPV04WzaajqSZ7TOzTdXy68B2xqjImspM\n6D0p6WzgQuCxEmFKkSwpqQf4LfAVM3ttjPX/q607cuh4zoyTJrXetYua4F1mdu9Ybepr62b3dufM\nOGlSjq4CfgZsN7Pvl4+Un5SR/CDwWWC5pM3VY0XhXFlJqa37G9DS14emCnHG44WQ9EJbSBa5kPXu\nzqPc2PtU1j7v6Tza8rZtMZIh6YWQ9EJIeiEkvRCSXghJL4SkF0LSCyHphZD0QpGrdc8cmMdFP/pa\n1j6fP9D6B2ptMZIh6YWQ9EJIemEidTwdkv4paX3JQCWYyEjeTK3kbNqRWqy0ELgKuLNsnDKkjuQP\ngK8D/xmvQX3Z2Yl/5/0mwWRJqcj6GHDAzJ44Vbv6srPOWbOzBcxBakXWxyXtpjb74HJJvyqaKjMp\n9a7fMLOFZnY2tencHjKzzxRPlpG2+Ds5of8nzexh4OEiSQrSFiMZkl4ISS+oxC2nllzQbWv/MDdr\nn1df9TJbn2ztBgxtMZIh6YWQ9EJIeiEkvRCSXghJL4SkF0LSCyHphZD0QpGrdT29i+z9y/NO27Pl\nodsZPrQnrtaNR0h6ISS9EJKjSHqXpLWSnpG0XdLFpYPlJLVm4Hbgj2Z2dXVTv1kFM2WnqaSkOcAl\nwOcBqruJTq2ZvpqQsrueAxwEflFVSd4paWqVXDUhRbIT+ADwEzO7EDgCvOUOv/W1dSPHhjPHnBwp\nkoPAoJmNTsi3lpr0m6ivret6Z0/OjJMmpexsP7BH0nnVS5cB02YeSUg/un4JuKs6su4CvlAuUn5S\n7yS6GVhaOEsx4ozHCyHphZD0QpFvwr7vrIP8dfVPs/Y58NGDLW/bFiMZkl4ISS+EpBdC0gsh6YWQ\n9EJIeiEkvRCSXmgLySJlZ3NmzLeL33Nd1j4ffWENh9/YH2Vn4xGSXghJL4SkF1Jr675a3Sp1q6S7\nJc0oHSwnKXNk9QNfBpaa2RKgg9oMS9OG1N21E5gpqZNa8eDecpHyk1KsNAR8F3gR2AccNrP7G9vV\nl50dP9n6PbBKkLK79gIrqRUSngnMlvSWicDqy866O2bmTzoJUnbXy4HnzeygmY0A9wLLysbKS4rk\ni8BFkmZVt069jGk2p2TKe/IxapWRm4Cnqm3uKJwrK6m1dbcBtxXOUow44/FCSHqhLSSLlJ2NzOli\n75Xz8/Z5d1fL27bFSIakF0LSCyHphZD0Qkh6ISS9EJJeCEkvhKQXQtILRWrrJL0O7EhoOhd4ObHb\n88zstFbyFLkkCewws6aTL0jamNJutG2rYdpidw3JSZD6Ie1EPsxt+YPfIgeeqUbsrilI6pP0gKRn\nq+feMdpcIWlE0jFJexuPlKrxQ0k7Je2StLtaHmuaqkslHZa0uXp8s2lIM5vUA/gOsKpaXgV8u2F9\nB/ActWmoFgBbgMUNbVYA91VtB4HNQPc4bS8F1k8kY47ddSWwplpeA3yiYf0AsBM4AYxQu73jyjH6\n+GXVdhswEzhjnLYTJofkPDPbVy3vB+Y1rO8H9gAGPAhcD3xknDajz4PV8uhzI8skPSnpPknnNwuY\ndMYj6UFgrE9Vb63/wcxM0niH6w+Z2ZCkG4FvSbrEzB5J+f0NbALOMrNhSSuA3wHnnmqD1Dqey8db\nJ+klSQvMbJ+kBcCBhiZDwKKqEBHgdGrvuQHgkfo2wO7qeWH12oer5/osr9Utb5D0Y0lzzWzcc+Ac\nu+s6YPSbLtcBv29Y/zjwXklLqtnSrqX2ftva0MfnqrZLgKPAK9TqatfVdyZpflX+hqSByuGVUybM\ncHQ9A/gz8Cy191xf9fqZwIZq+YvAserxErXd/Abghmq9gNXUjsK7gReq5Vur9fVtb6J2cNoC/B1Y\n1ixjnPF4ISS9EJJeCEkvtIXkfwFK27nsGXe/nQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff7d89b5da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "W1 = tf.Variable(tf.random_uniform([1, 10], -1, 1))\n",
    "b1 = tf.Variable(tf.zeros([10]))\n",
    "W2 = tf.Variable(tf.random_uniform([10, 10], -1, 1))\n",
    "b2 = tf.Variable(tf.zeros([10]))\n",
    "W3 = tf.Variable(tf.random_uniform([10, 1], -1, 1))\n",
    "b3 = tf.Variable(tf.zeros([1]))\n",
    "\n",
    "x = tf.placeholder(tf.float32, [None, 1])\n",
    "y = tf.placeholder(tf.float32, [None, 1])\n",
    "\n",
    "x_data = [[0.0], \n",
    "          [0.1], \n",
    "          [0.2], \n",
    "          [0.3], \n",
    "          [0.4], \n",
    "          [0.5], \n",
    "          [0.6], \n",
    "          [0.8]]\n",
    "y_data = [[.02], \n",
    "          [.03], \n",
    "          [.06], \n",
    "          [.11], \n",
    "          [.18], \n",
    "          [.27], \n",
    "          [.38], \n",
    "          [.66]]\n",
    "\n",
    "L1 = tf.nn.relu(tf.matmul(x, W1) + b1)\n",
    "L2 = tf.nn.relu(tf.matmul(L1, W2) + b2)\n",
    "\n",
    "model = tf.matmul(L2, W3) + b3\n",
    "loss = tf.reduce_sum(tf.square(model - y))\n",
    "\n",
    "optimizer = tf.train.GradientDescentOptimizer(0.01)\n",
    "train = optimizer.minimize(loss)\n",
    "\n",
    "sess = tf.Session()\n",
    "init = tf.global_variables_initializer()\n",
    "sess.run(init)\n",
    "\n",
    "for i in range(10000):\n",
    "    sess.run(train, feed_dict={x: x_data, y: y_data})\n",
    "\n",
    "print(\"x=7\", \"y=?\",  sess.run(model, feed_dict={x: [[.7]]}))\n",
    "\n",
    "print(\"------------------------------------\")\n",
    "print(\"W1\", sess.run(W1))\n",
    "print(\"W2\", sess.run(W2))\n",
    "print(\"W3\", sess.run(W3))\n",
    "print(\"b1\", sess.run(b1))\n",
    "print(\"b2\", sess.run(b2))\n",
    "print(\"b3\", sess.run(b3))\n",
    "print(\"loss\", sess.run(loss, feed_dict={x: x_data, y: y_data}))\n",
    "\n",
    "%matplotlib inline\n",
    "y_ = sess.run(model, feed_dict={x: x_data})\n",
    "plt.plot(x_data, y_data, 'ro')\n",
    "plt.plot(x_data, y_)\n",
    "plt.show()\n",
    "\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "plt.imshow(x_data)\n",
    "plt.show()\n",
    "\n",
    "%matplotlib inline\n",
    "plt.imshow(y_data)\n",
    "plt.show()\n",
    "\n",
    "%matplotlib inline\n",
    "plt.imshow(sess.run(W1))\n",
    "plt.show()\n",
    "\n",
    "%matplotlib inline\n",
    "plt.imshow(sess.run(W2))\n",
    "plt.show()\n",
    "\n",
    "%matplotlib inline\n",
    "plt.imshow(sess.run(W3))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**보다 좋은 결과를 만들기 위하여, 신경망을 여러 층으로 만들 수 있습니다.**"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.1"
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 "nbformat": 4,
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