homework/Day_075_HW.ipynb

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    "# 作業目標:\n",
    "\n",
    "    通過建立多層的神經網路, 了解權值矩陣更新"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "# 作業重點: \n",
    "\n",
    "3  層神經網路\n",
    "\n",
    "通過增加更多的中間層，以對更多關係的組合進行建模\n",
    "\n",
    "syn1 權值矩陣將隱層的組合輸出映射到最終結果，\n",
    "\n",
    "而在更新 syn1 的同時，還需要更新 syn0 權值矩陣，\n",
    "\n",
    "以從輸入資料中更好地產生這些組合"
   ]
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   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
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   "source": [
    "# Sigmoid 函數可以將任何值都映射到一個位於 0 到  1 範圍內的值。通過它，我們可以將實數轉化為概率值\n",
    "def nonlin(x,deriv = False):\n",
    "    if(deriv == True):\n",
    "        return x * (1 - x)\n",
    "    return 1 / (1 + np.exp(-x))"
   ]
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   "source": [
    "X = np.array([[0, 0, 1],\n",
    "                [0, 1, 1],\n",
    "                [1, 0, 1],\n",
    "                [1, 1, 1] ])  \n",
    "        \n",
    "# define y for output dataset            \n",
    "y = np.array([[0, 0, 1, 1]]).T"
   ]
  },
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   "cell_type": "code",
   "execution_count": 10,
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   "source": [
    "# seed random numbers to make calculation\n",
    "# deterministic (just a good practice)\n",
    "np.random.seed(1)\n",
    "#亂數設定產生種子得到的權重初始化集仍是隨機分佈的，\n",
    "#但每次開始訓練時，得到的權重初始集分佈都是完全一致的。\n",
    " \n",
    "# initialize weights randomly with mean 0\n",
    "syn0 = 2 * np.random.random((3, 4)) - 1\n",
    "\n",
    "# define syn1\n",
    "syn1 = 2 * np.random.random((4, 1)) - 1\n",
    "\n",
    "iter = 0\n",
    "#該神經網路權重矩陣的初始化操作。\n",
    "#用 “syn0” 來代指 (即“輸入層-第一層隱層”間權重矩陣）\n",
    "#用 “syn1” 來代指 (即“輸入層-第二層隱層”間權重矩陣）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "神經網路訓練\n",
    "for 迴圈反覆運算式地多次執行訓練代碼，使得我們的網路能更好地擬合訓練集"
   ]
  },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Output After Training:\n",
      "[[0.98897842 0.00859283 0.99329464 0.020559  ]\n",
      " [0.99239926 0.00578644 0.9953692  0.01356081]\n",
      " [0.0028465  0.99783855 0.00174085 0.99500462]\n",
      " [0.00413653 0.99678458 0.00252402 0.99239262]]\n",
      "\n",
      "\n",
      "\n",
      "[[0.18094473]\n",
      " [0.17968971]\n",
      " [0.74847665]\n",
      " [0.74787556]]\n"
     ]
    }
   ],
   "source": [
    "for iter in range(10000):\n",
    "    # forward propagation\n",
    "    l0 = X\n",
    "    l1 = nonlin(np.dot(l0, syn0))\n",
    "    l2 = nonlin(np.dot(l1, syn1))\n",
    "    \n",
    "    '''\n",
    "    新增\n",
    "    l2_error 該值說明了神經網路預測時“丟失”的數目。\n",
    "    l2_delta 該值為經確信度加權後的神經網路的誤差，除了確信誤差很小時，它近似等於預測誤差。\n",
    "    '''\n",
    " \n",
    "    l2_error = y - l2\n",
    "    l2_delta = l2_error * nonlin(l2, True)\n",
    "\n",
    "    # how much did we miss?\n",
    "    l1_error = l2_delta.dot(syn1.T)\n",
    " \n",
    "    # multiply how much we missed by the \n",
    "    # slope of the sigmoid at the values in l1\n",
    "    l1_delta = l1_error * nonlin(l1, True)\n",
    "\n",
    "\n",
    "    \n",
    "    # update weights\n",
    "    syn0 += np.dot(l0.T, l1_delta)\n",
    "    # syn1 update weights\n",
    "    syn1 +- np.dot(l1.T, l2_delta)\n",
    "    \n",
    "print(\"Output After Training:\")\n",
    "print(l1)\n",
    "print(\"\\n\\n\")\n",
    "print(l2)"
   ]
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