PGL2_deepwalk.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 图游走类模型\n",
    "\n",
    "## 课堂内容概览\n",
    "![](https://ai-studio-static-online.cdn.bcebos.com/801d3a2ab83847b6990c47bccbca29f9c8745f4b664c407c9fd159e85208ceee)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 课堂实践：生成单条 DeepWalk 游走序列"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Looking in indexes: https://mirror.baidu.com/pypi/simple/\n",
      "Requirement already satisfied: pgl in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (1.2.1)\n",
      "Requirement already satisfied: redis-py-cluster in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pgl) (2.1.0)\n",
      "Requirement already satisfied: visualdl>=2.0.0b; python_version >= \"3\" in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pgl) (2.0.3)\n",
      "Requirement already satisfied: cython>=0.25.2 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pgl) (0.29)\n",
      "Requirement already satisfied: numpy>=1.16.4 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pgl) (1.16.4)\n",
      "Requirement already satisfied: redis<4.0.0,>=3.0.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from redis-py-cluster->pgl) (3.5.3)\n",
      "Requirement already satisfied: Pillow>=7.0.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from visualdl>=2.0.0b; python_version >= \"3\"->pgl) (7.1.2)\n",
      "Requirement already satisfied: Flask-Babel>=1.0.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.0.0)\n",
      "Requirement already satisfied: flask>=1.1.1 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.1.1)\n",
      "Requirement already satisfied: flake8>=3.7.9 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from visualdl>=2.0.0b; python_version >= \"3\"->pgl) (3.8.2)\n",
      "Requirement already satisfied: requests in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2.22.0)\n",
      "Requirement already satisfied: protobuf>=3.11.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from visualdl>=2.0.0b; python_version >= \"3\"->pgl) (3.12.2)\n",
      "Requirement already satisfied: six>=1.14.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.15.0)\n",
      "Requirement already satisfied: pre-commit in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.21.0)\n",
      "Requirement already satisfied: pytz in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from Flask-Babel>=1.0.0->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2019.3)\n",
      "Requirement already satisfied: Babel>=2.3 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from Flask-Babel>=1.0.0->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2.8.0)\n",
      "Requirement already satisfied: Jinja2>=2.5 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from Flask-Babel>=1.0.0->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2.10.3)\n",
      "Requirement already satisfied: itsdangerous>=0.24 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from flask>=1.1.1->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.1.0)\n",
      "Requirement already satisfied: click>=5.1 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from flask>=1.1.1->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (7.0)\n",
      "Requirement already satisfied: Werkzeug>=0.15 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from flask>=1.1.1->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (0.16.0)\n",
      "Requirement already satisfied: mccabe<0.7.0,>=0.6.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from flake8>=3.7.9->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (0.6.1)\n",
      "Requirement already satisfied: pycodestyle<2.7.0,>=2.6.0a1 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from flake8>=3.7.9->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2.6.0)\n",
      "Requirement already satisfied: pyflakes<2.3.0,>=2.2.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from flake8>=3.7.9->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2.2.0)\n",
      "Requirement already satisfied: importlib-metadata; python_version < \"3.8\" in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from flake8>=3.7.9->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (0.23)\n",
      "Requirement already satisfied: chardet<3.1.0,>=3.0.2 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from requests->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (3.0.4)\n",
      "Requirement already satisfied: urllib3!=1.25.0,!=1.25.1,<1.26,>=1.21.1 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from requests->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.25.6)\n",
      "Requirement already satisfied: idna<2.9,>=2.5 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from requests->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2.8)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from requests->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2019.9.11)\n",
      "Requirement already satisfied: setuptools in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from protobuf>=3.11.0->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (41.4.0)\n",
      "Requirement already satisfied: toml in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pre-commit->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (0.10.0)\n",
      "Requirement already satisfied: virtualenv>=15.2 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pre-commit->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (16.7.9)\n",
      "Requirement already satisfied: pyyaml in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pre-commit->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (5.1.2)\n",
      "Requirement already satisfied: nodeenv>=0.11.1 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pre-commit->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.3.4)\n",
      "Requirement already satisfied: aspy.yaml in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pre-commit->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.3.0)\n",
      "Requirement already satisfied: identify>=1.0.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pre-commit->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.4.10)\n",
      "Requirement already satisfied: cfgv>=2.0.0 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from pre-commit->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (2.0.1)\n",
      "Requirement already satisfied: MarkupSafe>=0.23 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from Jinja2>=2.5->Flask-Babel>=1.0.0->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (1.1.1)\n",
      "Requirement already satisfied: zipp>=0.5 in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from importlib-metadata; python_version < \"3.8\"->flake8>=3.7.9->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (0.6.0)\n",
      "Requirement already satisfied: more-itertools in /opt/conda/envs/python35-paddle120-env/lib/python3.7/site-packages (from zipp>=0.5->importlib-metadata; python_version < \"3.8\"->flake8>=3.7.9->visualdl>=2.0.0b; python_version >= \"3\"->pgl) (7.2.0)\n"
     ]
    }
   ],
   "source": [
    "# 安装依赖\n",
    "!pip install pgl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx # networkx是一个常用的绘制复杂图形的Python包。\n",
    "\n",
    "import pgl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 构建graph\n",
    "\n",
    "在进行deepwalk游走之前，我们需要构建一个图网络。\n",
    "\n",
    "图网络的构建需要用到Graph类，Graph类的具体实现可以参考 `PGL/pgl/graph.py`\n",
    "\n",
    "下面我们简单展示一下如果构建一个图网络："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_graph():\n",
    "    # 定义节点的个数；每个节点用一个数字表示，即从0~9\n",
    "    num_node = 10\n",
    "    # 添加节点之间的边，每条边用一个tuple表示为: (src, dst)\n",
    "    edge_list = [(2, 0), (2, 1), (3, 1),(4, 0), (0, 5), \n",
    "             (6, 0), (6, 4), (5, 6), (7, 0), (1, 7),\n",
    "             (2, 7), (7, 3), (8, 0), (9, 7)]\n",
    "\n",
    "    g = pgl.graph.Graph(num_nodes = num_node, edges = edge_list)\n",
    "\n",
    "    return g\n",
    "\n",
    "# 创建一个图对象，用于保存图网络的各种数据。\n",
    "g = build_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def display_graph(g):\n",
    "    nx_G = nx.Graph()\n",
    "    nx_G.add_nodes_from(range(g.num_nodes))\n",
    "    nx_G.add_edges_from(g.edges)\n",
    "    \n",
    "    pos = nx.spring_layout(nx_G, iterations=50)\n",
    "    \n",
    "    nx.draw(nx_G, \n",
    "            pos,\n",
    "            with_labels=True,\n",
    "            node_color=['y','g','g','g','y','y','y','g','y','g'], \n",
    "            node_size=1000)\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "display_graph(g)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Deepwalk 采样\n",
    "\n",
    "对于给定的节点，DeepWalk会等概率的选取下一个相邻节点加入路径，直至达到最大路径长度，或者没有下一个节点可选。\n",
    "\n",
    "<img src=\"https://ai-studio-static-online.cdn.bcebos.com/159e470f09bb4e12bae080a4733d46d0861a08e812e643d5b8b7f080b16f2e38\" width=\"85%\" height=\"85%\" />\n",
    "\n",
    "因此, 假如我们想要得到一条walk, 我们需要输入一个graph, 起始节点ID, 游走的深度walk_len。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def deepwalk(graph, start_node, walk_len):\n",
    "    walk = [start_node] # 初始化游走序列\n",
    "\n",
    "    for d in range(walk_len): # 最大长度范围内进行采样\n",
    "        current_node = walk[-1] \n",
    "        successors = graph.successor(np.array([current_node])) # graph.successor: 获取当前节点的后继邻居\n",
    "        print(\"当前节点: %d\" % current_node)\n",
    "        print(\"后继邻居\", successors[0])\n",
    "        succ = successors[0]\n",
    "        if len(succ) == 0:\n",
    "            break\n",
    "        next_node = np.random.choice(succ, 1)\n",
    "        walk.extend(next_node)\n",
    "        \n",
    "    return walk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "当前节点: 2\n",
      "后继邻居 [0 1 7]\n",
      "当前节点: 0\n",
      "后继邻居 [5]\n",
      "当前节点: 5\n",
      "后继邻居 [6]\n",
      "当前节点: 6\n",
      "后继邻居 [0 4]\n",
      "[2, 0, 5, 6, 4]\n"
     ]
    }
   ],
   "source": [
    "walk = deepwalk(g, 2, 4)\n",
    "print(walk)"
   ]
  }
 ],
 "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": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}