perceptron.ipynb

{
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   "cell_type": "markdown",
   "id": "b182d823-dc06-4095-a5aa-1ec9b7195b0e",
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   "source": [
    "# 感知机(Perceptron)\n",
    "\n",
    "感知机（Perceptron）是一种基本的人工神经网络模型，由弗兰克·罗森布拉特（Frank Rosenblatt）于1958年提出。它是机器学习领域的一种线性分类模型，用于解决二分类问题。感知机的核心思想是通过学习找到一个线性分割超平面，将样本划分为两个类别。\n",
    "\n",
    "## 感知机的基本概念\n",
    "\n",
    "1. **输入与权重**\n",
    "感知机接收一个输入向量  $x = (x_1, x_2, \\ldots, x_n) $，每个输入特征对应一个权重  $w = (w_1, w_2, \\ldots, w_n)$ 。感知器的输入向量也可以理解为信号的输入。\n",
    "\n",
    "\n",
    "输入维度  $n$  决定了超平面的维度：\n",
    "\n",
    "*  如果  $n = 2$ ，决策边界是二维平面上的一条直线。\n",
    "*  如果  $n = 3$ ，决策边界是三维空间中的一个平面。\n",
    "*  如果  $n > 3$ ，决策边界是  $n$ -维空间中的一个超平面。\n",
    "\n",
    "\n",
    "2. **加权求和**\n",
    "感知机将输入向量与权重向量相乘并求和，加上一个偏置  $b$ ：\n",
    "\n",
    "    $z = \\sum_{i=1}^n w_i x_i + b$\n",
    "\n",
    "3. **激活函数**\n",
    "使用符号函数（Sign Function）将加权求和的结果转换为分类结果：\n",
    "$$\n",
    "y =\n",
    "\\begin{cases}\n",
    "1 & \\text{if } z \\leq 0 \\\\\n",
    "-1 & \\text{if } z > 0\n",
    "\\end{cases}\n",
    "$$\n",
    "这里  $y$  是感知机的输出，也可以理解为信号的输出。\n",
    "\n",
    "$w = (w_1, w_2, \\ldots, w_n)$是控制输入信号的重要性的参数，而偏置是调整神经元被激活的容易程度（感知器输出为1的程度）。比如，若$b$为-0.1，则只要输入信号的加权总和超过0.1，神经元就会被激活。但是如果$b$为-20，则输入信号的加权总和必须超过20.0，神经元才会被激活。偏置  $b$ 的值决定了神经元被激活的容易程度。\n",
    "\n",
    "在神经网络中，偏置（Bias）是指在神经元计算输出时加上的一个额外的可训练参数，它不依赖于输入特征，而是相当于为神经元的输入加上一个“基准值”或“截距项”（intercept）。偏置的主要作用包括以下几个方面：\n",
    "\n",
    "1. 增加模型的灵活性和表达能力：\n",
    "\n",
    "若没有偏置，神经元的输出将严格受限于输入与权重的线性组合在原点(0,0,…,0)处通过。换句话说，神经网络中的每个激活函数曲线都将只能围绕原点变化，这会严重限制模型拟合数据的能力。\n",
    "添加偏置项后，神经元输出不再被迫通过原点，从而可以灵活地将激活函数向上或向下平移，使网络在表示更复杂的函数时更为灵活。\n",
    "\n",
    "2. 帮助模型更好地拟合数据：\n",
    "\n",
    "偏置项使得网络能适应数据中存在的非零均值分布。如果网络没有偏置，当输入数据的均值不是零时，单纯靠权重与输入的线性组合很难有效捕捉数据的真实分布，加上偏置后，网络能更方便地调整输出值，使之更好地贴合数据特征。\n",
    "\n",
    "3. 促进对称性打破，避免恒为零的梯度或无效权重更新：\n",
    "\n",
    "在训练开始时，如果没有偏置且初始权重对称，网络的多个神经元可能学到完全相同的映射模式，导致冗余和学习效率低下；偏置有助于打破这种对称，使各个神经元能学习到不同的特征，提高网络的判别能力和训练速度。\n",
    "\n",
    "\n",
    "## 使用感知机模拟逻辑门"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f45ce04b-0b42-4ded-a654-27e105aec0c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AND\n",
      "输入\t\t感知机输出\t期望输出\n",
      "[0 0]\t\t0\t\t0\n",
      "[0 1]\t\t0\t\t0\n",
      "[1 0]\t\t0\t\t0\n",
      "[1 1]\t\t1\t\t1\n",
      "-------------------------------------------------\n",
      "OR\n",
      "输入\t\t感知机输出\t期望输出\n",
      "[0 0]\t\t0\t\t0\n",
      "[0 1]\t\t1\t\t1\n",
      "[1 0]\t\t1\t\t1\n",
      "[1 1]\t\t1\t\t1\n",
      "-------------------------------------------------\n",
      "NAND\n",
      "输入\t\t感知机输出\t期望输出\n",
      "[0 0]\t\t1\t\t1\n",
      "[0 1]\t\t1\t\t1\n",
      "[1 0]\t\t1\t\t1\n",
      "[1 1]\t\t0\t\t0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 定义感知机函数\n",
    "def AND(x):\n",
    "    weights = np.array([0.5, 0.5])  # w1 和 w2\n",
    "    bias = -0.7                     # 偏置 b\n",
    "    tmp = np.dot(weights, x) + bias\n",
    "    return 1 if tmp > 0 else 0\n",
    "\n",
    "# 定义逻辑 AND 门的输入和期望输出\n",
    "inputs = np.array([\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [1, 1]\n",
    "])\n",
    "    \n",
    "expected_outputs = np.array([0, 0, 0, 1])  # AND 门的期望输出\n",
    "\n",
    "print(\"AND\")\n",
    "print(\"输入\\t\\t感知机输出\\t期望输出\")\n",
    "for i, input_vector in enumerate(inputs):\n",
    "    output = AND(input_vector)\n",
    "    print(f\"{input_vector}\\t\\t{output}\\t\\t{expected_outputs[i]}\")\n",
    "print(\"-------------------------------------------------\")    \n",
    "\n",
    "\n",
    "# 逻辑或\n",
    "def OR(x):\n",
    "    weights = np.array([1, 1])  \n",
    "    bias = -0.5   \n",
    "    z = np.dot(weights, x) + bias  # z = w1*x1 + w2*x2 + b\n",
    "    return 1 if z >= 0 else 0      # \n",
    "\n",
    "# 定义逻辑 OR 门的输入和期望输出\n",
    "inputs = np.array([\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [1, 1]\n",
    "])\n",
    "\n",
    "expected_outputs = np.array([0, 1, 1, 1])  # OR 门的期望输出\n",
    "\n",
    "print(\"OR\")\n",
    "print(\"输入\\t\\t感知机输出\\t期望输出\")\n",
    "for i, input_vector in enumerate(inputs):\n",
    "    output = OR(input_vector)\n",
    "    print(f\"{input_vector}\\t\\t{output}\\t\\t{expected_outputs[i]}\")\n",
    "\n",
    "# 非门 NOT(AND(x))\n",
    "# 逻辑非门 (NAND)\n",
    "print(\"-------------------------------------------------\")   \n",
    "def NAND(x):\n",
    "    weights = np.array([-1, -1])  \n",
    "    bias = 1.5                   \n",
    "    z = np.dot(weights, x) + bias  \n",
    "    return 1 if z >= 0 else 0      \n",
    "\n",
    "inputs = np.array([\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [1, 1]\n",
    "])\n",
    "\n",
    "expected_outputs = np.array([1, 1, 1, 0])  # NAND 门的期望输出\n",
    "\n",
    "# 测试 NAND 门\n",
    "print(\"NAND\")\n",
    "print(\"输入\\t\\t感知机输出\\t期望输出\")\n",
    "for i, input_vector in enumerate(inputs):\n",
    "    output = NAND(input_vector)\n",
    "    print(f\"{input_vector}\\t\\t{output}\\t\\t{expected_outputs[i]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b3baf2f-ca2d-498f-ac76-b00afa449572",
   "metadata": {},
   "source": [
    "## 感知机的局限性\n",
    "感知机可以实现与门、与非门、或门三种逻辑电路。但不能实现异或门，原因是感知机的局限性只能表示由一条直线分隔的空间，但是无法表示弯曲的曲线所分割的空间。\n",
    "\n",
    "我们在二维空间画出表示**或门**的感知机的直线，这条直线分割开两个空间，其中白色空间输出1，蓝色阴影空间输出0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "de70a6d4-8dde-41e0-b0ec-2b0bb6e09b31",
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# 定义直线的参数：z = -0.5 + x1 + x2\n",
    "def line_x2(x1):\n",
    "    return -x1 + 0.5\n",
    "\n",
    "# 定义四个点\n",
    "points = np.array([\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [1, 1]\n",
    "])\n",
    "\n",
    "# 绘图\n",
    "x = np.linspace(-0.5, 1.5, 100)  # x1 的范围\n",
    "y = line_x2(x)  # 计算直线上的 x2\n",
    "\n",
    "plt.figure(figsize=(6, 6))\n",
    "\n",
    "# 绘制直线\n",
    "plt.plot(x, y, label=\"-0.5 + x1 + x2 = 0\", color=\"blue\")\n",
    "\n",
    "# 填充直线下方的区域\n",
    "plt.fill_between(x, y, -0.5, color=\"lightblue\", alpha=0.5, label=\"z < 0\")\n",
    "\n",
    "# 绘制点\n",
    "for point in points:\n",
    "    plt.scatter(point[0], point[1], color=\"red\")\n",
    "    plt.text(point[0] + 0.05, point[1] + 0.05, f\"({point[0]}, {point[1]})\", fontsize=9)\n",
    "\n",
    "# 设置坐标轴范围\n",
    "plt.xlim(-0.5, 1.5)\n",
    "plt.ylim(-0.5, 1.5)\n",
    "\n",
    "# 添加网格、标签和图例\n",
    "plt.axhline(0, color=\"black\", linewidth=0.5)\n",
    "plt.axvline(0, color=\"black\", linewidth=0.5)\n",
    "plt.grid(color=\"gray\", linestyle=\"--\", linewidth=0.5)\n",
    "plt.xlabel(\"x1\")\n",
    "plt.ylabel(\"x2\")\n",
    "plt.legend()\n",
    "plt.title(\"Plot of -0.5 + x1 + x2 with Shaded Region\")\n",
    "\n",
    "# 显示图像\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f87031e-80dc-4c3e-a3b2-ecd73135aea2",
   "metadata": {},
   "source": [
    "或门在$(x1,x2)=(0,0)$时输出0，在$(x1,x2)=(0,1), (1,0), (1,1)$时输出为1。如果想利用感知机制作或门，只需使得感知器分割的两个空间，各自包含所有的绿色三角形和所有的红色圆形即可。上图实现了或门，但是对于异或门，不能通过一条直线分割两个平面得到，下图显示了异或门的空间示意图。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "6cfdb0df-c3ee-4492-a46f-59e5f8cc43e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/n7/h8vtfbcn3cn8b86gk1fgql700000gn/T/ipykernel_2177/836208780.py:16: MatplotlibDeprecationWarning: The collections attribute was deprecated in Matplotlib 3.8 and will be removed in 3.10.\n",
      "  paths = contours.collections[0].get_paths()\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义隐式函数\n",
    "def f(x, y):\n",
    "    return (y - x)**2 - (y + x - 1)**2 + 0.1 - 0.3*y\n",
    "\n",
    "# 创建网格，用于绘制隐式曲线\n",
    "x = np.linspace(-1, 2, 800)  # Range from -1 to 2\n",
    "y = np.linspace(-1, 2, 800)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z = f(X, Y)\n",
    "\n",
    "# 绘制等值线 f(x,y)=0 (分割平面的曲线)\n",
    "contours = plt.contour(X, Y, Z, levels=[0], colors='blue', linewidths=2)\n",
    "paths = contours.collections[0].get_paths()\n",
    "\n",
    "# 从可能的多条等高线中选择一条最长的作为主分支曲线\n",
    "max_len = 0\n",
    "main_path = None\n",
    "for path in paths:\n",
    "    v = path.vertices\n",
    "    length = np.sum(np.sqrt(np.sum(np.diff(v, axis=0)**2, axis=1)))\n",
    "    if length > max_len:\n",
    "        max_len = length\n",
    "        main_path = v\n",
    "\n",
    "plt.clf()  # Clear the current figure and redraw\n",
    "\n",
    "# 绘制填充区域，f<0用浅蓝色，f>0用浅红色\n",
    "plt.contourf(X, Y, Z, levels=[-np.inf, 0, np.inf], colors=['lightblue','lightcoral'], alpha=0.5)\n",
    "\n",
    "# 绘制主分支曲线\n",
    "plt.plot(main_path[:,0], main_path[:,1], 'b-', label='Separating Curve')\n",
    "\n",
    "# 绘制四个特殊点，并标注它们所在区域\n",
    "plt.plot(0, 0, 'co', label='(0,0) in blue region (f<0)')\n",
    "plt.plot(1, 1, 'c^', label='(1,1) in blue region (f<0)')\n",
    "plt.plot(0, 1, 'mo', label='(0,1) in red region (f>0)')\n",
    "plt.plot(1, 0, 'm^', label='(1,0) in red region (f>0)')\n",
    "\n",
    "# 调整图例位置，不遮挡关键点。\n",
    "# 将图例放在右侧空白区域（例如使用 bbox_to_anchor 将图例放在绘图外部）\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0.)\n",
    "\n",
    "plt.title('XOR')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.grid(True)\n",
    "\n",
    "# 扩大显示范围，避免图例和坐标点重叠\n",
    "plt.xlim(-1, 2)\n",
    "plt.ylim(-1, 2)\n",
    "\n",
    "plt.tight_layout()  # Optimize layout for legend placement outside the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36269967-2668-4290-a997-01943f5cd84c",
   "metadata": {},
   "source": [
    "## 多层感知机\n",
    "单层感知机只能解决线性可分问题，对于线性不可分问题无法解决。但是感知机的绝妙之处在于其可以进行叠加，即多层感知机（MLP，Multi-Layer Perceptron），引入了隐藏层和非线性激活函数，从而能够处理非线性问题。\n",
    "\n",
    "使用之前的AND函数、NAND函数、OR函数进行XOR函数的实现。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "c5c1a432-fa32-4ed9-8884-0639282776ed",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XOR\n",
      "输入\t\t感知机输出\t期望输出\n",
      "[0 0]\t\t0\t\t0\n",
      "[0 1]\t\t1\t\t1\n",
      "[1 0]\t\t1\t\t1\n",
      "[1 1]\t\t0\t\t0\n"
     ]
    }
   ],
   "source": [
    "# Re-import necessary libraries after environment reset\n",
    "import numpy as np\n",
    "\n",
    "# 定义 XOR 函数\n",
    "def XOR(x):\n",
    "    s1 = NAND(x)  # Step 1: Calculate NAND\n",
    "    s2 = OR(x)    # Step 2: Calculate OR\n",
    "    y = AND([s1, s2])  # Step 3: Combine results with AND\n",
    "    return y\n",
    "\n",
    "# # 定义 NAND 函数\n",
    "# def NAND(x):\n",
    "#     weights = np.array([-1, -1])  \n",
    "#     bias = 1.5                   \n",
    "#     z = np.dot(weights, x) + bias  \n",
    "#     return 1 if z >= 0 else 0      \n",
    "\n",
    "# # 定义 OR 函数\n",
    "# def OR(x):\n",
    "#     weights = np.array([1, 1])  \n",
    "#     bias = -0.5   \n",
    "#     z = np.dot(weights, x) + bias  \n",
    "#     return 1 if z >= 0 else 0      \n",
    "\n",
    "# # 定义 AND 函数\n",
    "# def AND(x):\n",
    "#     weights = np.array([0.5, 0.5])  \n",
    "#     bias = -0.7                     \n",
    "#     z = np.dot(weights, x) + bias\n",
    "#     return 1 if z > 0 else 0\n",
    "\n",
    "# 测试 XOR 函数\n",
    "inputs = np.array([\n",
    "    [0, 0],\n",
    "    [0, 1],\n",
    "    [1, 0],\n",
    "    [1, 1]\n",
    "])\n",
    "\n",
    "expected_outputs = np.array([0, 1, 1, 0])  # XOR 门的期望输出\n",
    "\n",
    "print(\"XOR\")\n",
    "print(\"输入\\t\\t感知机输出\\t期望输出\")\n",
    "for i, input_vector in enumerate(inputs):\n",
    "    output = XOR(input_vector)\n",
    "    print(f\"{input_vector}\\t\\t{output}\\t\\t{expected_outputs[i]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4787987-b2e6-4df9-ad03-469a3daf1399",
   "metadata": {},
   "source": [
    "异或门是一种多层结构的神经网络，可以用下图来表示，下图是一个简单的两层神经网络示意图："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "ffffa912-bde9-4289-9828-af95dd55cd53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_neural_network_adjusted():\n",
    "    fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "    # 定义节点位置\n",
    "    layer_0 = [(0, 0.7), (0, 0.3)]  # x1, x2\n",
    "    layer_1 = [(2, 0.8), (2, 0.2)]  # s1, s2\n",
    "    layer_2 = [(4, 0.5)]  # y\n",
    "\n",
    "    # 绘制第0层 (输入层 x)\n",
    "    for i, (x, y) in enumerate(layer_0):\n",
    "        ax.scatter(x, y, s=600, color='lightblue', edgecolor='black', zorder=5)\n",
    "        ax.text(x - 0.2, y, f\"x{i+1}\", fontsize=12, ha='center')\n",
    "\n",
    "    # 绘制第1层 (隐藏层 s)\n",
    "    for i, (x, y) in enumerate(layer_1):\n",
    "        ax.scatter(x, y, s=600, color='lightgreen', edgecolor='black', zorder=5)\n",
    "        ax.text(x - 0.3, y, f\"s{i+1}\", fontsize=12, ha='center')\n",
    "\n",
    "    # 绘制第2层 (输出层 y)\n",
    "    for x, y in layer_2:\n",
    "        ax.scatter(x, y, s=600, color='lightcoral', edgecolor='black', zorder=5)\n",
    "        ax.text(x + 0.3, y, \"y\", fontsize=12, ha='center')\n",
    "\n",
    "    # 连接第0层与第1层\n",
    "    for x1, y1 in layer_0:\n",
    "        for x2, y2 in layer_1:\n",
    "            ax.plot([x1, x2], [y1, y2], color='gray', linestyle='-', zorder=1)\n",
    "\n",
    "    # 连接第1层与第2层\n",
    "    for x1, y1 in layer_1:\n",
    "        for x2, y2 in layer_2:\n",
    "            ax.plot([x1, x2], [y1, y2], color='gray', linestyle='-', zorder=1)\n",
    "\n",
    "    # 设置坐标范围\n",
    "    ax.set_xlim(-1, 5)\n",
    "    ax.set_ylim(-0.2, 1.2)\n",
    "\n",
    "    # 去除坐标轴\n",
    "    ax.axis('off')\n",
    "    plt.title(\"Two-Layer Neural Network (Adjusted)\", fontsize=16)\n",
    "    plt.show()\n",
    "\n",
    "# 调用绘图函数\n",
    "draw_neural_network_adjusted()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "232bdc4d-9cdd-49c5-882e-fd42a8a557f9",
   "metadata": {},
   "source": [
    "* 第0层 (输入层)：包含两个节点，分别表示  $x_1$  和  $x_2$ 。\n",
    "* 第1层 (隐藏层)：包含两个个节点，分别表示  $s_1$, $s_2$ 。\n",
    "* 第2层 (输出层)：包含一个节点，表示输出  $y$ 。\n",
    "\n",
    "1. 第0层的两个神经元接收输入信号，并将信号发送至第1层的神经元。\n",
    "2. 第1层的神经元将信号发送至第2层的神经元，第2层的神经元输出$y$。\n",
    "\n",
    "这种2层感知机的运行过程可以比作流水线的组装作业。第1段（第1层）的工人对传送过来的零件进行加工，完成后再传送给第2段（第2层）的工人。第2层的工人对第1层的工人传过来的零件进行加工，完成这个零件后出货 （输出）。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}