3.multi-class_classification_and_neural_network/ex3.neural_network.ipynb

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   "cell_type": "markdown",
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   "source": [
    "# Neural Network 神经网络\n",
    "此Notebook是配合Andrew Ng \"Machine Leanring\"中[神经网络](https://github.com/loveunk/machine-learning-deep-learning-notes/blob/master/machine-learning/neural-networks.md)部分学习使用。\n",
    "\n",
    "测试用python版本为3.6\n",
    "* 机器学习路径：https://github.com/loveunk/machine-learning-deep-learning-notes/\n",
    "* 内容正文综合参考网络资源，使用中如果有疑问请联络：www.kaikai.ai"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 加载训练集并预处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
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   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy.io as sio\n",
    "import matplotlib\n",
    "import scipy.optimize as opt\n",
    "from sklearn.metrics import classification_report # 这个包是评价报告"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "RoXVSf57S8Ls"
   },
   "outputs": [],
   "source": [
    "# 加载数据的函数\n",
    "def load_data(path, transpose=True):\n",
    "    data = sio.loadmat(path)\n",
    "    y = data.get('y')  # shape为二位数组 (5000,1)\n",
    "    y = y.reshape(y.shape[0])  # reshape 为 column vector\n",
    "\n",
    "    X = data.get('X')  # shape为二位数组 (5000,400)\n",
    "\n",
    "    if transpose:\n",
    "        # 对于这个数据集，需要把每一组数据（图像）转置（因此这里先reshape为20*20，然后再转置）\n",
    "        X = np.array([im.reshape((20, 20)).T for im in X])\n",
    "\n",
    "        # 把每一个sample reshape为vector\n",
    "        X = np.array([im.reshape(400) for im in X])\n",
    "\n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "LXPmv8w_S8Ng"
   },
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ousaFkXCS8Pe"
   },
   "source": [
    "# 神经网络模型图示\n",
    "<img style=\"float: center;\" src=\"./img/nn_model.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "M4VZSJjwS8Pg"
   },
   "outputs": [],
   "source": [
    "def load_weight(path):\n",
    "    data = sio.loadmat(path)\n",
    "    return data['Theta1'], data['Theta2']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "vLw-N-5KS8Pj",
    "outputId": "6f633547-cfe5-4c17-d5d4-33bfc62b320b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((25, 401), (10, 26))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta1, theta2 = load_weight('ex3weights.mat')\n",
    "\n",
    "theta1.shape, theta2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "skKWOY7dS8Po"
   },
   "source": [
    "### 加载数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZCP4dmIfS8Pp",
    "outputId": "f06d14ec-b00b-4388-c6b2-968b7b922c52"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((5000, 401), (5000,))"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X, y = load_data('ex3data1.mat',transpose=False)\n",
    "\n",
    "X = np.insert(X, 0, values=np.ones(X.shape[0]), axis=1)  # intercept\n",
    "\n",
    "X.shape, y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BiTm_vuhS8Pt"
   },
   "source": [
    "# Feed Forward Prediction（前馈预测）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "19n-ZftsS8Pv"
   },
   "outputs": [],
   "source": [
    "a1 = X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "7hIzICohS8Py",
    "outputId": "2f6beec8-e8a9-48ff-d1f1-2c85cb454611"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 25)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z2 = a1 @ theta1.T # (5000, 401) @ (25,401).T = (5000, 25)\n",
    "z2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "epsZNwONS8P2"
   },
   "outputs": [],
   "source": [
    "z2 = np.insert(z2, 0, values=np.ones(z2.shape[0]), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "6AHM7j15S8P5",
    "outputId": "98e2ecd6-c813-476b-cffd-3131ec59c767"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 26)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2 = sigmoid(z2)\n",
    "a2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "oNcsvnVdS8QV",
    "outputId": "65937b14-c299-4565-8413-004b02fe4d0c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 10)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z3 = a2 @ theta2.T\n",
    "z3.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sX9maZviS8Qp",
    "outputId": "7bc8de1a-457a-450f-d51c-1b3ca0c2daaf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.38245045e-04, 2.05540079e-03, 3.04012453e-03, ...,\n",
       "        4.91017499e-04, 7.74325818e-03, 9.96229459e-01],\n",
       "       [5.87756717e-04, 2.85026516e-03, 4.14687943e-03, ...,\n",
       "        2.92311247e-03, 2.35616705e-03, 9.96196668e-01],\n",
       "       [1.08683616e-04, 3.82659802e-03, 3.05855129e-02, ...,\n",
       "        7.51453949e-02, 6.57039547e-03, 9.35862781e-01],\n",
       "       ...,\n",
       "       [6.27824726e-02, 4.50406476e-03, 3.54510925e-02, ...,\n",
       "        2.63669734e-03, 6.89448164e-01, 2.74369466e-05],\n",
       "       [1.01908736e-03, 7.34360211e-04, 3.78558700e-04, ...,\n",
       "        1.45616578e-02, 9.75989758e-01, 2.33374461e-04],\n",
       "       [5.90807037e-05, 5.41717668e-04, 2.58968308e-05, ...,\n",
       "        7.00508308e-03, 7.32814653e-01, 9.16696059e-02]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a3 = sigmoid(z3)\n",
    "a3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0_NmJUTaS8Q3",
    "outputId": "94fe50f4-fde0-45b5-96e9-1108a115e4ff"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000,)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = np.argmax(a3, axis=1) + 1  # numpy is 0 base index, +1 for matlab convention，返回沿轴axis最大值的索引，axis=1代表行\n",
    "y_pred.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WeeqKlzyS8Q-"
   },
   "source": [
    "# 准确率\n",
    " \n",
    "虽然人工神经网络是非常强大的模型，但训练数据的准确性并不能完美预测实际数据，在这里很容易过拟合。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "rGxDoBPjS8Q_",
    "outputId": "9bb22765-2902-4db8-801f-93a73091bd82"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           1       0.97      0.98      0.97       500\n",
      "           2       0.98      0.97      0.97       500\n",
      "           3       0.98      0.96      0.97       500\n",
      "           4       0.97      0.97      0.97       500\n",
      "           5       0.98      0.98      0.98       500\n",
      "           6       0.97      0.99      0.98       500\n",
      "           7       0.98      0.97      0.97       500\n",
      "           8       0.98      0.98      0.98       500\n",
      "           9       0.97      0.96      0.96       500\n",
      "          10       0.98      0.99      0.99       500\n",
      "\n",
      "   micro avg       0.98      0.98      0.98      5000\n",
      "   macro avg       0.98      0.98      0.98      5000\n",
      "weighted avg       0.98      0.98      0.98      5000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(classification_report(y, y_pred))"
   ]
  }
 ],
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