04_22_GraphML_Lecture04.ipynb

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        "<a href=\"https://colab.research.google.com/github/ua-datalab/GraphML/blob/main/04_22_GraphML_Lecture04.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "markdown",
      "source": [
        "# **Introduction to Graph Convolutional Networks (GCNs)**"
      ],
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      "cell_type": "markdown",
      "source": [
        "### **Before we start, change the Runtime to T4**"
      ],
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        "\n",
        "### In this tutorial, we will explore Graph Convolutional Networks (GCNs), a powerful tool for dealing with data structured as graphs. We'll start with an understanding of convolution in traditional settings, explain how GCNs adapt this to graph data, and discuss the advantages of GCNs over simpler models. Lastly, we'll touch on some applications of GCNs across various fields."
      ],
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        "## **What is a Convolution?**\n",
        "\n",
        "### In traditional signal processing, convolution is a mathematical operation on two functions that produces a third function expressing how the shape of one is modified by the other. In the context of deep learning, especially in convolutional neural networks (CNNs) used for image processing, convolution operates by sliding a filter (kernel) across the image and computing the dot product of the filter with the image regions it covers."
      ],
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      "cell_type": "markdown",
      "source": [
        "### Mathematical Representation"
      ],
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      "cell_type": "markdown",
      "source": [
        "### For a discrete function \\( f \\) (e.g., an image) and a filter \\( g \\), convolution is defined as:\n",
        "\n",
        "$$\n",
        "(f * g)[t] = \\sum_{\\tau=-\\infty}^{\\infty} f[\\tau] \\cdot g[t - \\tau]\n",
        "$$\n",
        "\n",
        "\n",
        "### In CNNs, this operation helps in detecting features such as edges and textures by applying various filters to the input image.\n"
      ],
      "metadata": {
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      "cell_type": "markdown",
      "source": [
        "## **What is a Graph Convolutional Network (GCN)?**\n",
        "\n",
        "### Graphs, consisting of nodes (vertices) and edges (connections), pose a unique challenge for the convolution operation due to their irregular structure. GCNs address this by redefining convolution for graph data."
      ],
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        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "$$\n",
        "H^{(l+1)} = \\sigma \\left( \\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} H^{(l)} W^{(l)} \\right)\n",
        "$$\n",
        "\n",
        "where:\n",
        "- $ \\tilde{A} = A + I $ — the adjacency matrix $ A $ with added self-connections $ I $ (identity matrix).\n",
        "- $ \\tilde{D} $ is the degree matrix of $ \\tilde{A} $, with $ \\tilde{D}_{ii} = \\sum_j \\tilde{A}_{ij} $.\n",
        "- $ H^{(l)} $ represents the node features at layer $ l $.\n",
        "- $ W^{(l)} $ is the weight matrix for layer \\( l \\).\n",
        "- $ \\sigma $ is a non-linear activation function, such as ReLU.\n"
      ],
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      "source": [
        "#### Step-by-Step Breakdown:\n",
        "\n",
        "1. **Adjacency Matrix with Self-Connections:**\n",
        "   - $  \\tilde{A} = A + I  $\n",
        "   - Here, $A $ is the original adjacency matrix of the graph, and $ I $ is the identity matrix. Adding $ I $ incorporates self-loops, allowing each node to consider its own features along with its neighbors' features.\n",
        "\n",
        "2. **Degree Matrix of $ \\tilde{A} $:**\n",
        "   - $ \\tilde{D} $ is calculated as the degree matrix of $ \\tilde{A} $.\n",
        "   - $ \\tilde{D}_{ii} = \\sum_j \\tilde{A}_{ij} $\n",
        "   - This matrix is diagonal, where each entry $ \\tilde{D}_{ii} $ is the sum of the weights of all edges connected to node $ i $, including the self-loop.\n",
        "\n",
        "3. **Normalized Adjacency Matrix:**\n",
        "   - The term $ \\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} $ represents the normalization of $ \\tilde{A} $ by $ \\tilde{D} $.\n",
        "   - This normalization balances the influence of high-degree and low-degree nodes, making the model less sensitive to variations in node degree.\n",
        "\n",
        "4. **Feature Matrix at Layer $ l $:**\n",
        "   - $ H^{(l)} $\n",
        "   - Represents the matrix of node features at the $ l $-th layer. Each row corresponds to a node's features.\n",
        "\n",
        "5. **Weight Matrix for Layer $ l $:**\n",
        "   - $ W^{(l)} $\n",
        "   - This is a learnable parameter matrix that transforms node features from one layer to the next.\n",
        "\n",
        "6. **Activation Function:**\n",
        "   - $ \\sigma $\n",
        "   - A non-linear activation function like ReLU (Rectified Linear Unit). This function is applied element-wise to the result of the matrix multiplication, introducing non-linearity into the model, which helps the network learn complex patterns.\n",
        "\n"
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      "source": [
        "### **How It All Comes Together:**\n",
        "\n",
        "- The normalized adjacency matrix $ \\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} $ multiplies the feature matrix $ H^{(l)} $, effectively aggregating and normalizing the features from each node’s neighbors.\n",
        "- The result is then multiplied by the weight matrix $ W^{(l)} $, which transforms the features into a new feature space.\n",
        "- Finally, the activation function $ \\sigma $ is applied to introduce non-linearity and to generate the output $ H^{(l+1)} $, which serves as the input for the next layer or as the final output of the network if it is the last layer.\n"
      ],
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      "source": [
        "### **GCN vs. Vanilla Graph Neural Networks ( as given in Tutorial 3)**\n",
        "---\n",
        "\n",
        "\n",
        "Recollect that for **Vanilla Graph Networks** we have,\n",
        "\n",
        "Given a graph with adjacency matrix $ \\tilde{A} $, feature matrix $ X $, and weight matrix $ W $, the updated feature matrix $ H $ can be calculated using the formula:\n",
        "\n",
        "$$\n",
        "H = \\sigma \\left( \\tilde{A}^{\\top} X W^{\\top} \\right)\n",
        "$$\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "### Now for GCNs,we have\n",
        "\n",
        "$$\n",
        "H = \\sigma \\left( \\tilde{D}^{-1} \\tilde{A} X W^{\\top} \\right)\n",
        "$$\n",
        "\n",
        "This formula implies that each node's feature vector is first spread across its neighbors according to $A$, then scaled down by the inverse of its degree, effectively normalizing the contribution of each node by its degree.\n",
        "\n",
        "### This prevents nodes with high degrees from dominating the feature aggregation process."
      ],
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      "cell_type": "markdown",
      "source": [
        "### **Normalized Form Using $ \\tilde{D}^{-\\frac{1}{2}}$**\n",
        "\n"
      ],
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      "cell_type": "markdown",
      "source": [
        "### The normalization approach introduced by [Kipf and Welling](https://arxiv.org/abs/1609.02907) enhances the above formulation by applying a symmetric normalization using the square roots of $\\tilde{D}$.\n",
        "\n",
        "#### This method helps in maintaining a balanced scale of feature propagation. Hence the feature transformation matrix becomes\n",
        "\n",
        "$$\n",
        "\\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} X W^{\\top}\n",
        "$$\n"
      ],
      "metadata": {
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    },
    {
      "cell_type": "markdown",
      "source": [
        "#### The product $\\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}}$ results in a symmetrically normalized adjacency matrix that ensures the magnitude of feature vectors remains consistent across the graph, thus avoiding numerical instabilities and improving the learning dynamics."
      ],
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      "cell_type": "markdown",
      "source": [
        "So, generalized expression of a GCN layer becomes,\n",
        "\n",
        "\n",
        "$$\n",
        "H^{(l+1)} = \\sigma \\left( \\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} H^{(l)} W^{(l)} \\right)\n",
        "$$"
      ],
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      "cell_type": "markdown",
      "source": [
        "## GCNs improve upon vanilla graph neural networks in several ways:\n",
        "\n",
        "- **Normalization**: GCNs use the symmetric normalization $ \\tilde{D}^{-\\frac{1}{2}} \\tilde{A} \\tilde{D}^{-\\frac{1}{2}} $ which scales the feature aggregation by the degrees of the nodes, preventing high-degree nodes from dominating due to their larger number of connections.\n",
        "- **Self-connections**: The addition of the identity matrix $ I $ to $ A $ allows each node to consider its own features alongside its neighbors', helping preserve each node's original features through layers.\n",
        "- **Trainable Transformations**: The weight matrix $ W^{(l)} $ in GCNs is trainable, allowing the network to learn optimal feature transformations through backpropagation.\n",
        "\n",
        "## Applications of Graph Convolutional Networks\n",
        "\n",
        "GCNs find applications in various domains, such as:\n",
        "\n",
        "- **Social Network Analysis**: Detecting communities, predicting interactions, and understanding network dynamics.\n",
        "- **Recommendation Systems**: Enhancing recommendations by learning complex user-item relationships embedded in the network.\n",
        "- **Molecular Chemistry**: Predicting molecular properties by modeling molecular structures as graphs.\n",
        "- **Computer Vision**: Managing tasks involving non-grid data like point clouds or mesh structures."
      ],
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      "cell_type": "markdown",
      "source": [
        "### Even though the mechanism of standard convolution operation differs, the fundamental principles of convolution hold -\n",
        "\n",
        "*   Local Information Processing,\n",
        "*   Feature extraction\n",
        "*   Use of shared learnable filters\n",
        "\n",
        "### Therefore, the term \"convolution\" is used metaphorically to describe these operations in GCNs.\n",
        "\n",
        "### It highlights the network's ability to perform similar tasks as CNNs but adapted for data that inherently lacks a Euclidean structure, instead possessing complex relational and topological structures."
      ],
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    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Let's understand by examples**"
      ],
      "metadata": {
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      }
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np"
      ],
      "metadata": {
        "id": "MCAIzk0_BoOX"
      },
      "execution_count": 1,
      "outputs": []
    },
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      "cell_type": "markdown",
      "source": [
        "## Example\n",
        "\n",
        "### Considering the following adjacency matrix $ A $"
      ],
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      "cell_type": "code",
      "source": [
        "A = np.array([\n",
        "    [0, 1, 1, 1],\n",
        "    [1, 0, 0, 0],\n",
        "    [1, 0, 0, 1],\n",
        "    [1, 0, 1, 0]])"
      ],
      "metadata": {
        "id": "_vBtLjBIDuYX"
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      "execution_count": 2,
      "outputs": []
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      "cell_type": "code",
      "source": [
        "# Create a graph from the adjacency matrix\n",
        "G = nx.from_numpy_array(A)\n",
        "mapping = {i: i + 1 for i in range(len(G.nodes))}\n",
        "G = nx.relabel_nodes(G, mapping)\n",
        "\n",
        "# Draw the graph with labels starting from 1\n",
        "plt.figure(figsize=(4, 4))\n",
        "nx.draw(G, with_labels=True, font_color='#ffffff', node_size=1000, node_color=\"#00b4d9\", font_size=15, font_weight='bold', edge_color='gray')\n",
        "plt.title(\"Graph Representation of the Adjacency Matrix A\")\n",
        "plt.show()"
      ],
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      "execution_count": 3,
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              "<Figure size 400x400 with 1 Axes>"
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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Degree matrix** $ D $\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "5n8gHMIZE4Yu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "D = np.diag(np.sum(A, axis=1))\n",
        "D"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ep1ithxuE2-d",
        "outputId": "dc811904-7b66-4c97-d108-5cf5c0325e1b"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3, 0, 0, 0],\n",
              "       [0, 1, 0, 0],\n",
              "       [0, 0, 2, 0],\n",
              "       [0, 0, 0, 2]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Inverse of D:**\n",
        " $ {D}^{-1} $"
      ],
      "metadata": {
        "id": "iUQiXL3MHvyY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "invD = np.linalg.inv(D)\n",
        "invD"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "e338y2jGDudP",
        "outputId": "64e840e3-200e-486d-e7df-363b8c240f37"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.33333333, 0.        , 0.        , 0.        ],\n",
              "       [0.        , 1.        , 0.        , 0.        ],\n",
              "       [0.        , 0.        , 0.5       , 0.        ],\n",
              "       [0.        , 0.        , 0.        , 0.5       ]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **adding self loops to adjacency matrix**:  $ \\tilde{A}  = A + I$"
      ],
      "metadata": {
        "id": "0H32It3AJJY-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Adash = A + np.identity(4)"
      ],
      "metadata": {
        "id": "faw4MKz3JH6H"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "Adash"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vjimE8X4JTe3",
        "outputId": "d74df179-3ea7-4353-e8cc-8684af0f23b1"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 1., 1., 1.],\n",
              "       [1., 1., 0., 0.],\n",
              "       [1., 0., 1., 1.],\n",
              "       [1., 0., 1., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **New Degree Matrix - considering self loops:** $ \\tilde{D} $\n"
      ],
      "metadata": {
        "id": "HSSjlA8fJYWP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Ddash = np.diag(np.sum(Adash, axis=1))"
      ],
      "metadata": {
        "id": "RQXkqo0jJX-_"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "Ddash"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RR25DwhGJhGp",
        "outputId": "f51805ef-4c66-4b11-96ed-ee469a922f29"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[4., 0., 0., 0.],\n",
              "       [0., 2., 0., 0.],\n",
              "       [0., 0., 3., 0.],\n",
              "       [0., 0., 0., 3.]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Inverse of the new D matrix:   $ \\tilde{D}^{-1} $"
      ],
      "metadata": {
        "id": "tHzB6psoJm2p"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "invDdash = np.linalg.inv(Ddash)"
      ],
      "metadata": {
        "id": "9KvUclnWJm_5"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "invDdash"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D_woq_z1JnFJ",
        "outputId": "74a3c72c-91c4-4a3d-855b-b9c629252b58"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.25      , 0.        , 0.        , 0.        ],\n",
              "       [0.        , 0.5       , 0.        , 0.        ],\n",
              "       [0.        , 0.        , 0.33333333, 0.        ],\n",
              "       [0.        , 0.        , 0.        , 0.33333333]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **$\\tilde{D}^{-1} \\tilde{A}$**"
      ],
      "metadata": {
        "id": "Ci3ASco9W20K"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dinv_x_A = np.multiply(invDdash, Adash)\n",
        "dinv_x_A"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "s9WWWq3YDuke",
        "outputId": "433bad4e-059d-4c2d-cbe2-683a8ac7a7c2"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.25      , 0.        , 0.        , 0.        ],\n",
              "       [0.        , 0.5       , 0.        , 0.        ],\n",
              "       [0.        , 0.        , 0.33333333, 0.        ],\n",
              "       [0.        , 0.        , 0.        , 0.33333333]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Working out examples from previous Tutorials**"
      ],
      "metadata": {
        "id": "Eqa2HJjnY2-S"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install -q torch_geometric"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0HIdtEBib2QY",
        "outputId": "fee7ac8c-bd00-4150-8442-ad516537fda2"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[?25l     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/1.1 MB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/1.1 MB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[91m━\u001b[0m\u001b[90m╺\u001b[0m\u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/1.1 MB\u001b[0m \u001b[31m485.3 kB/s\u001b[0m eta \u001b[36m0:00:03\u001b[0m\r\u001b[2K     \u001b[91m━━━━\u001b[0m\u001b[90m╺\u001b[0m\u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.1/1.1 MB\u001b[0m \u001b[31m1.0 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[91m━━━━━━━━━\u001b[0m\u001b[90m╺\u001b[0m\u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.3/1.1 MB\u001b[0m \u001b[31m1.8 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[91m━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[90m╺\u001b[0m\u001b[90m━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.5/1.1 MB\u001b[0m \u001b[31m3.0 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[91m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m\u001b[90m╺\u001b[0m \u001b[32m1.1/1.1 MB\u001b[0m \u001b[31m5.0 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.1/1.1 MB\u001b[0m \u001b[31m4.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25h"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from torch_geometric.datasets import Planetoid,FacebookPagePage\n",
        "from torch_geometric.utils import degree\n",
        "from collections import Counter\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "lx-l7kIrb2TU"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **The Cora Dataset**"
      ],
      "metadata": {
        "id": "3AaxYzn9dNPP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Import dataset from PyTorch Geometric\n",
        "dataset = Planetoid(root=\".\", name=\"Cora\")\n",
        "data = dataset[0]\n",
        "degrees = degree(data.edge_index[0]).numpy()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a6IidYsEb2Vp",
        "outputId": "10523e80-a097-4b47-fa19-9212acfb4e8a"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.x\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.tx\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.allx\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.y\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.ty\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.ally\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.graph\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.cora.test.index\n",
            "Processing...\n",
            "Done!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# degrees\n",
        "numbers = Counter(degrees)"
      ],
      "metadata": {
        "id": "Qh4KVTb6b2YG"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.set_xlabel('Node Degree')\n",
        "ax.set_ylabel('Number of Nodes')\n",
        "ax.set_title('Distribution of Node Degrees in the Cora Graph')  # Adding a title\n",
        "\n",
        "# Creating the bar plot\n",
        "bars = ax.bar(numbers.keys(), numbers.values(), color='skyblue')  # Color the bars\n",
        "\n",
        "# Adding grid for better readability\n",
        "ax.set_axisbelow(True)\n",
        "ax.yaxis.grid(True, color='#EEEEEE')\n",
        "ax.xaxis.grid(False)\n",
        "\n",
        "# Optionally, add a gentle x-axis limit extension\n",
        "ax.set_xlim(min(numbers.keys()) - 0.5, max(numbers.keys()) + 0.5)\n",
        "\n",
        "# Optionally, add labels on top of each bar\n",
        "for bar in bars:\n",
        "    yval = bar.get_height()\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "78WfPqq_b2aw",
        "outputId": "6bb69c1b-03ee-4c4f-f10b-c67bb588ef01"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "### This distribution appears to be exponential with a heavy tail: it spans from 1 neighbor (485 nodes) to 168 neighbors (just 1 node)! Such a dataset is a prime example for a degree normalization process to address this imbalance."
      ],
      "metadata": {
        "id": "7TCOC5gldBJ-"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "---"
      ],
      "metadata": {
        "id": "Ixmw6ww6fav5"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Pytorch Geometric Graph Convolutional Network: on the Cora dataset"
      ],
      "metadata": {
        "id": "MFWFG87tfczS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "import torch.nn.functional as F\n",
        "\n",
        "from torch_geometric.nn import GCNConv"
      ],
      "metadata": {
        "id": "A3Oe0BmJb2nx"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def accuracy(pred_y, y):\n",
        "    return ((pred_y == y).sum() / len(y)).item()"
      ],
      "metadata": {
        "id": "jMMRJkmab2qP"
      },
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class GCN(torch.nn.Module):\n",
        "    \"\"\"GCN\"\"\"\n",
        "    def __init__(self, dim_in, dim_h, dim_out):\n",
        "        super().__init__()\n",
        "        self.gcn1 = GCNConv(dim_in, dim_h)\n",
        "        self.gcn2 = GCNConv(dim_h, dim_out)\n",
        "\n",
        "    def forward(self, x, edge_index):\n",
        "        h = self.gcn1(x,edge_index)\n",
        "        h = torch.relu(h)\n",
        "        h = self.gcn2(h, edge_index)\n",
        "\n",
        "        return F.log_softmax(h, dim=1)\n",
        "\n",
        "    def fit(self, data, epochs):\n",
        "        criterion = torch.nn.CrossEntropyLoss()\n",
        "        optimizer = torch.optim.Adam(self.parameters(),\n",
        "                                      lr=0.01,\n",
        "                                      weight_decay=5e-4)\n",
        "\n",
        "        self.train()\n",
        "        for epoch in range(epochs+1):\n",
        "            optimizer.zero_grad()\n",
        "            out = self(data.x, data.edge_index)\n",
        "            loss = criterion(out[data.train_mask], data.y[data.train_mask])\n",
        "            acc = accuracy(out[data.train_mask].argmax(dim=1),data.y[data.train_mask])\n",
        "            loss.backward()\n",
        "            optimizer.step()\n",
        "\n",
        "            if(epoch % 20 == 0):\n",
        "                val_loss = criterion(out[data.val_mask], data.y[data.val_mask])\n",
        "                val_acc = accuracy(out[data.val_mask].argmax(dim=1),\n",
        "                                  data.y[data.val_mask])\n",
        "                print(f'Epoch {epoch:>3} | Train Loss: {loss:.3f} | Train Acc:'f' {acc*100:>5.2f}% | Val Loss: {val_loss:.2f} | 'f'Val Acc: {val_acc*100:.2f}%')\n",
        "\n",
        "    @torch.no_grad()\n",
        "    def test(self, data):\n",
        "        self.eval()\n",
        "        out = self(data.x, data.edge_index)\n",
        "        acc = accuracy(out.argmax(dim=1)[data.test_mask], data.y[data.test_mask])\n",
        "        return acc"
      ],
      "metadata": {
        "id": "9EzbzEpWb2so"
      },
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Create the Vanilla GNN model on Cora\n",
        "gcn = GCN(dataset.num_features, 16, dataset.num_classes)\n",
        "print(gcn)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yo80olsOgeeW",
        "outputId": "aa4d5155-9f62-4fa3-b77a-3d85de502c2d"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GCN(\n",
            "  (gcn1): GCNConv(1433, 16)\n",
            "  (gcn2): GCNConv(16, 7)\n",
            ")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Train\n",
        "gcn.fit(data, epochs=100)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8wGnI_ZHgejS",
        "outputId": "fa59399d-64a0-4ea0-cb75-6d603750caaf"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch   0 | Train Loss: 1.948 | Train Acc: 15.00% | Val Loss: 1.95 | Val Acc: 15.60%\n",
            "Epoch  20 | Train Loss: 0.108 | Train Acc: 100.00% | Val Loss: 0.78 | Val Acc: 77.40%\n",
            "Epoch  40 | Train Loss: 0.016 | Train Acc: 100.00% | Val Loss: 0.77 | Val Acc: 77.80%\n",
            "Epoch  60 | Train Loss: 0.016 | Train Acc: 100.00% | Val Loss: 0.76 | Val Acc: 77.60%\n",
            "Epoch  80 | Train Loss: 0.018 | Train Acc: 100.00% | Val Loss: 0.75 | Val Acc: 78.00%\n",
            "Epoch 100 | Train Loss: 0.016 | Train Acc: 100.00% | Val Loss: 0.75 | Val Acc: 77.80%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test\n",
        "acc = gcn.test(data)\n",
        "print(f'\\nGCN test accuracy on Cora Dataset: {acc*100:.2f}%\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "okoVghJygemG",
        "outputId": "9ad1ade3-0b59-4bb9-f852-85ff75d9954c"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "GCN test accuracy on Cora Dataset: 80.40%\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **The FB Page-Page dataset**"
      ],
      "metadata": {
        "id": "2BwyCL1FhJqh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Import dataset from PyTorch Geometric\n",
        "dataset = FacebookPagePage(root=\".\")\n",
        "data = dataset[0]\n",
        "\n",
        "# Create masks\n",
        "data.train_mask = range(18000)\n",
        "data.val_mask = range(18001, 20000)\n",
        "data.test_mask = range(20001, 22470)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QpdV9CmUgeog",
        "outputId": "26aece61-0d5b-47bf-e64e-20a8ec755573"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Downloading https://graphmining.ai/datasets/ptg/facebook.npz\n",
            "Processing...\n",
            "Done!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Get list of degrees for each node\n",
        "degrees = degree(data.edge_index[0]).numpy()\n",
        "\n",
        "# Count the number of nodes for each degree\n",
        "numbers = Counter(degrees)"
      ],
      "metadata": {
        "id": "NeptG_pEgerW"
      },
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.set_xlabel('Node Degree')\n",
        "ax.set_ylabel('Number of Nodes')\n",
        "ax.set_title('Distribution of Node Degrees in the Facebook Page-Page Graph')  # Adding a title\n",
        "\n",
        "# Creating the bar plot\n",
        "bars = ax.bar(numbers.keys(), numbers.values(), color='skyblue')  # Color the bars\n",
        "\n",
        "# Adding grid for better readability\n",
        "ax.set_axisbelow(True)\n",
        "ax.yaxis.grid(True, color='#EEEEEE')\n",
        "ax.xaxis.grid(False)\n",
        "\n",
        "# Optionally, add a gentle x-axis limit extension\n",
        "ax.set_xlim(min(numbers.keys()) - 0.5, max(numbers.keys()) + 0.5)\n",
        "\n",
        "# Optionally, add labels on top of each bar\n",
        "for bar in bars:\n",
        "    yval = bar.get_height()\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "Y-421Q4ggetu",
        "outputId": "8dd52e70-e253-4be3-f5d8-65c5a5424665"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "### The distribution of node degrees is notably skewed, ranging from 1 to 709 neighbors. For this reason, the Facebook Page-Page dataset presents an exciting case to apply a Graph Convolutional Network (GCN)."
      ],
      "metadata": {
        "id": "NK1vwuQ8h6cm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "gcn = GCN(dataset.num_features, 16, dataset.num_classes)\n",
        "print(gcn)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "olkKDLFegewe",
        "outputId": "a9e5f7df-6e01-4e83-d8f0-314a246dc460"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GCN(\n",
            "  (gcn1): GCNConv(128, 16)\n",
            "  (gcn2): GCNConv(16, 4)\n",
            ")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Train\n",
        "gcn.fit(data, epochs=100)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sJQw_IgygezX",
        "outputId": "4b8c3b4c-e5bd-4511-c430-f5b61f2b081a"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch   0 | Train Loss: 1.504 | Train Acc: 21.83% | Val Loss: 1.50 | Val Acc: 21.31%\n",
            "Epoch  20 | Train Loss: 0.447 | Train Acc: 84.36% | Val Loss: 0.45 | Val Acc: 85.04%\n",
            "Epoch  40 | Train Loss: 0.319 | Train Acc: 89.50% | Val Loss: 0.32 | Val Acc: 89.39%\n",
            "Epoch  60 | Train Loss: 0.279 | Train Acc: 91.13% | Val Loss: 0.28 | Val Acc: 91.35%\n",
            "Epoch  80 | Train Loss: 0.258 | Train Acc: 92.08% | Val Loss: 0.26 | Val Acc: 92.00%\n",
            "Epoch 100 | Train Loss: 0.243 | Train Acc: 92.68% | Val Loss: 0.25 | Val Acc: 92.45%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test\n",
        "acc = gcn.test(data)\n",
        "print(f'\\nGCN test accuracy on Facebook Page-Page Dataset: {acc*100:.2f}%\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lN7Ehj32ge1v",
        "outputId": "8df117d6-08ac-4771-903d-9e10cb147e9c"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "GCN test accuracy on Facebook Page-Page Dataset: 91.54%\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Comparing MLP, Vanilla GNN and GCN"
      ],
      "metadata": {
        "id": "WB39UEqXjj3_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "| Dataset  | MLP             | Vanilla GNN              | GCN |\n",
        "|:----------:|:-----------------:|:------------------:| :-------------: |\n",
        "| Cora     | 53.40% | 75.00%  |80.60 % |\n",
        "| Facebook Page-Page | 75.13% | 82.67%  | 91.21%|"
      ],
      "metadata": {
        "id": "FFApQVCbkjuu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "kugNzSTak-bh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# GCN on the CiteSeer and Pubmed dataset from Tutorial 3"
      ],
      "metadata": {
        "id": "lq3g-1YIkqnv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dataset_CSeer = Planetoid(root=\".\", name=\"CiteSeer\")\n",
        "data_graph_CSeer = dataset_CSeer[0] # get the citeseer graph\n",
        "\n",
        "dataset_PM = Planetoid(root=\".\", name=\"PubMed\")\n",
        "data_graph_PM = dataset_PM[0] # the Pubmed graph"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RwY2TAn5ge4W",
        "outputId": "a4409800-4029-49b0-81c9-40a8c0e99c91"
      },
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.citeseer.x\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.citeseer.tx\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.citeseer.allx\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.citeseer.y\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.citeseer.ty\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.citeseer.ally\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.citeseer.graph\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.citeseer.test.index\n",
            "Processing...\n",
            "Done!\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.pubmed.x\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.pubmed.tx\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.pubmed.allx\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.pubmed.y\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.pubmed.ty\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.pubmed.ally\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.pubmed.graph\n",
            "Downloading https://github.com/kimiyoung/planetoid/raw/master/data/ind.pubmed.test.index\n",
            "Processing...\n",
            "Done!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **GCN on Citeseer**"
      ],
      "metadata": {
        "id": "Tl-4E2PnlSFO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "gcn = GCN(dataset_CSeer.num_features, 16, dataset_CSeer.num_classes)\n",
        "print(gcn)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wPzG-WvBlQ1O",
        "outputId": "e31b3328-429c-49bf-e56b-549ee6f71a01"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GCN(\n",
            "  (gcn1): GCNConv(3703, 16)\n",
            "  (gcn2): GCNConv(16, 6)\n",
            ")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Train\n",
        "gcn.fit(data_graph_CSeer, epochs=100)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c1emgm7llQ3e",
        "outputId": "041776fd-3916-4670-e19d-e3b07346c062"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch   0 | Train Loss: 1.795 | Train Acc: 18.33% | Val Loss: 1.80 | Val Acc: 16.60%\n",
            "Epoch  20 | Train Loss: 0.026 | Train Acc: 100.00% | Val Loss: 1.13 | Val Acc: 63.60%\n",
            "Epoch  40 | Train Loss: 0.009 | Train Acc: 100.00% | Val Loss: 1.10 | Val Acc: 66.20%\n",
            "Epoch  60 | Train Loss: 0.013 | Train Acc: 100.00% | Val Loss: 1.05 | Val Acc: 67.60%\n",
            "Epoch  80 | Train Loss: 0.013 | Train Acc: 100.00% | Val Loss: 1.04 | Val Acc: 66.60%\n",
            "Epoch 100 | Train Loss: 0.012 | Train Acc: 100.00% | Val Loss: 1.03 | Val Acc: 68.20%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test\n",
        "acc = gcn.test(data_graph_CSeer)\n",
        "print(f'\\nGCN test accuracy on CiteSeer Dataset: {acc*100:.2f}%\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HmzhAwFLlQ6I",
        "outputId": "75d74638-ce39-4bb4-8265-8ed5eb1eb934"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "GCN test accuracy on CiteSeer Dataset: 67.90%\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **GCN on Pubmed**"
      ],
      "metadata": {
        "id": "n2KmzLHdls3K"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "gcn = GCN(dataset_PM.num_features, 16, dataset_PM.num_classes)\n",
        "print(gcn)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "q36MZcTIlQ8u",
        "outputId": "13c4ce40-b6ab-4df6-9f58-3f45c3aad10f"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GCN(\n",
            "  (gcn1): GCNConv(500, 16)\n",
            "  (gcn2): GCNConv(16, 3)\n",
            ")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Train\n",
        "gcn.fit(data_graph_PM, epochs=100)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "u_KhC2qWlQ_P",
        "outputId": "4aae914f-ecf9-404d-c3a7-b0e4606e0f02"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch   0 | Train Loss: 1.098 | Train Acc: 40.00% | Val Loss: 1.10 | Val Acc: 38.60%\n",
            "Epoch  20 | Train Loss: 0.631 | Train Acc: 95.00% | Val Loss: 0.83 | Val Acc: 75.60%\n",
            "Epoch  40 | Train Loss: 0.249 | Train Acc: 98.33% | Val Loss: 0.62 | Val Acc: 76.80%\n",
            "Epoch  60 | Train Loss: 0.131 | Train Acc: 100.00% | Val Loss: 0.58 | Val Acc: 77.40%\n",
            "Epoch  80 | Train Loss: 0.099 | Train Acc: 100.00% | Val Loss: 0.57 | Val Acc: 78.20%\n",
            "Epoch 100 | Train Loss: 0.082 | Train Acc: 100.00% | Val Loss: 0.56 | Val Acc: 78.40%\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test\n",
        "acc = gcn.test(data_graph_PM)\n",
        "print(f'\\nGCN test accuracy on PubMed Dataset: {acc*100:.2f}%\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8kMJF93qlRB-",
        "outputId": "145d55d6-1d3a-4329-e1d0-4d61ba8ac017"
      },
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "GCN test accuracy on PubMed Dataset: 78.90%\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# @title Model Comparison\n",
        "%%html\n",
        "<table style=\"width:70%; margin-left:auto; margin-right:auto;\" border=\"1\">\n",
        "  <tr style=\"background-color: #f2f2f2;\">\n",
        "    <th style=\"padding: 10px; text-align:center;\">Dataset</th>\n",
        "    <th style=\"padding: 10px; text-align:center;\">MLP (Tutorial 3)</th>\n",
        "    <th style=\"padding: 10px; text-align:center;\">Vanilla GNN (Tutorial 3)</th>\n",
        "    <th style=\"padding: 10px; text-align:center;\">GCN </th>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td style=\"padding: 10px; text-align:center;\">Cora</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">53.40%</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">75.00%</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">80.60%</td>\n",
        "  </tr>\n",
        "  <tr style=\"background-color: #f9f9f9;\">\n",
        "    <td style=\"padding: 10px; text-align:center;\">Facebook Page-Page</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">75.13%</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">82.67%</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">91.21%</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td style=\"padding: 10px; text-align:center;\">CiteSeer</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">52.70%</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">65.50%</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">68.10%</td>\n",
        "  </tr>\n",
        "  <tr style=\"background-color: #f9f9f9;\">\n",
        "    <td style=\"padding: 10px; text-align:center;\">PubMed</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">71.90%</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">76.50%</td>\n",
        "    <td style=\"padding: 10px; text-align:center;\">79.10%</td>\n",
        "  </tr>\n",
        "</table>\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 228
        },
        "cellView": "form",
        "id": "wHH5YGMMlREg",
        "outputId": "db28fb81-f414-4e01-854d-c28fe8799090"
      },
      "execution_count": 190,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<table style=\"width:70%; margin-left:auto; margin-right:auto;\" border=\"1\">\n",
              "  <tr style=\"background-color: #f2f2f2;\">\n",
              "    <th style=\"padding: 10px; text-align:center;\">Dataset</th>\n",
              "    <th style=\"padding: 10px; text-align:center;\">MLP (Tutorial 3)</th>\n",
              "    <th style=\"padding: 10px; text-align:center;\">Vanilla GNN (Tutorial 3)</th>\n",
              "    <th style=\"padding: 10px; text-align:center;\">GCN </th>\n",
              "  </tr>\n",
              "  <tr>\n",
              "    <td style=\"padding: 10px; text-align:center;\">Cora</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">53.40%</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">75.00%</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">80.60%</td>\n",
              "  </tr>\n",
              "  <tr style=\"background-color: #f9f9f9;\">\n",
              "    <td style=\"padding: 10px; text-align:center;\">Facebook Page-Page</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">75.13%</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">82.67%</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">91.21%</td>\n",
              "  </tr>\n",
              "  <tr>\n",
              "    <td style=\"padding: 10px; text-align:center;\">CiteSeer</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">52.70%</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">65.50%</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">68.10%</td>\n",
              "  </tr>\n",
              "  <tr style=\"background-color: #f9f9f9;\">\n",
              "    <td style=\"padding: 10px; text-align:center;\">PubMed</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">71.90%</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">76.50%</td>\n",
              "    <td style=\"padding: 10px; text-align:center;\">79.10%</td>\n",
              "  </tr>\n",
              "</table>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "---\n",
        "---\n"
      ],
      "metadata": {
        "id": "qMSXiRutocxv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Node Regression**"
      ],
      "metadata": {
        "id": "f-Fl3mz3ofjW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from torch_geometric.datasets import WikipediaNetwork\n",
        "import torch_geometric.transforms as T"
      ],
      "metadata": {
        "id": "aKYKdhlrlRHX"
      },
      "execution_count": 38,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Wikipedia Chameleon Dataset** - **Predicting web traffic with node regression**"
      ],
      "metadata": {
        "id": "P3ESs7r3ox5f"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### We will be utilizing the [Wikipedia Network dataset](https://arxiv.org/abs/1909.13021) which comprises three page-page networks: Chameleons, Crocodiles, and Squirrels. Specifically, the Chameleons network has 2,277 nodes and 31,421 edges, the Crocodiles network contains 11,631 nodes and 170,918 edges, and the Squirrels network includes 5,201 nodes and 198,493 edges.\n",
        "\n",
        "### In these networks, each node represents an article and the edges denote mutual links between these articles. The features of each node indicate the presence of specific words within the articles. The primary objective of using this dataset is to predict the logarithmic average of the monthly traffic for December 2018."
      ],
      "metadata": {
        "id": "MjBXA9z4quc-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dataset = WikipediaNetwork(root=\".\", name=\"chameleon\", transform = T.RandomNodeSplit(num_val=200, num_test=500))"
      ],
      "metadata": {
        "id": "jbG0Q46Jo7ca"
      },
      "execution_count": 157,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data = dataset[0]"
      ],
      "metadata": {
        "id": "tTntNAhksaTh"
      },
      "execution_count": 158,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Print information about the dataset\n",
        "print(f'Dataset: {dataset}')\n",
        "print('-------------------')\n",
        "print(f'Number of graphs: {len(dataset)}')\n",
        "print(f'Number of nodes: {data.x.shape[0]}')\n",
        "print(f'Number of unique features: {dataset.num_features}')\n",
        "print(f'Number of classes: {dataset.num_classes}')\n",
        "\n",
        "# Print information about the graph\n",
        "print(f'\\nGraph:')\n",
        "print('------')\n",
        "print(f'Edges are directed: {data.is_directed()}')\n",
        "print(f'Graph has isolated nodes: {data.has_isolated_nodes()}')\n",
        "print(f'Graph has loops: {data.has_self_loops()}')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Lna8-oato7fc",
        "outputId": "6baef06b-380e-4778-ab9d-b464687dcc11"
      },
      "execution_count": 159,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Dataset: WikipediaNetwork()\n",
            "-------------------\n",
            "Number of graphs: 1\n",
            "Number of nodes: 2277\n",
            "Number of unique features: 2325\n",
            "Number of classes: 5\n",
            "\n",
            "Graph:\n",
            "------\n",
            "Edges are directed: True\n",
            "Graph has isolated nodes: False\n",
            "Graph has loops: True\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### We have encountered an issue with our dataset: it indicates that there are five classes, but our objective is to perform node regression, not classification. Upon closer examination, it turns out that these \"classes\" actually represent bins into which continuous values, that we aim to predict, have been grouped."
      ],
      "metadata": {
        "id": "ZTBS9XqutO21"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Get regression values"
      ],
      "metadata": {
        "id": "n90P6oBTrakz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from io import BytesIO\n",
        "from urllib.request import urlopen\n",
        "from zipfile import ZipFile\n",
        "\n",
        "url = 'https://snap.stanford.edu/data/wikipedia.zip'\n",
        "with urlopen(url) as zurl:\n",
        "    with ZipFile(BytesIO(zurl.read())) as zfile:\n",
        "        zfile.extractall('.')"
      ],
      "metadata": {
        "id": "mrT9E6I0o7kr"
      },
      "execution_count": 160,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import torch\n",
        "df = pd.read_csv('/content/wikipedia/chameleon/musae_chameleon_target.csv')\n",
        "values = np.log10(df['target'])\n",
        "data.y = torch.tensor(values)\n",
        "data.y"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "EfKggfv8o7n0",
        "outputId": "cf1a7730-c61f-4b2e-cc72-62e2e26b3f6b"
      },
      "execution_count": 161,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([2.2330, 3.9079, 3.9329,  ..., 1.9956, 4.3598, 2.4409],\n",
              "       dtype=torch.float64)"
            ]
          },
          "metadata": {},
          "execution_count": 161
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Get list of degrees for each node\n",
        "degrees = degree(data.edge_index[0]).numpy()\n",
        "\n",
        "# Count the number of nodes for each degree\n",
        "numbers = Counter(degrees)"
      ],
      "metadata": {
        "id": "ABMYo5Iio7qj"
      },
      "execution_count": 162,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, ax = plt.subplots()\n",
        "ax.set_xlabel('Node Degree')\n",
        "ax.set_ylabel('Number of Nodes')\n",
        "ax.set_title('Distribution of Node Degrees in the Wikipedia Chameleon Graph')  # Adding a title\n",
        "\n",
        "# Creating the bar plot\n",
        "bars = ax.bar(numbers.keys(), numbers.values(), color='skyblue')  # Color the bars\n",
        "\n",
        "# Adding grid for better readability\n",
        "ax.set_axisbelow(True)\n",
        "ax.yaxis.grid(True, color='#EEEEEE')\n",
        "ax.xaxis.grid(False)\n",
        "\n",
        "# Optionally, add a gentle x-axis limit extension\n",
        "ax.set_xlim(min(numbers.keys()) - 0.5, max(numbers.keys()) + 0.5)\n",
        "\n",
        "# Optionally, add labels on top of each bar\n",
        "for bar in bars:\n",
        "    yval = bar.get_height()\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "_SGKznkio7wC",
        "outputId": "52491f6d-9721-486c-be71-56e14fe788ec"
      },
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Distribution of our Regression Variable**\n"
      ],
      "metadata": {
        "id": "iTDdvNWNsp2y"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import seaborn as sns\n",
        "from scipy.stats import norm\n",
        "df['target'] = values\n",
        "sns.displot(df['target'], bins=20, kde=True,stat=\"probability\",)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 506
        },
        "id": "4OEOm_JEsmVK",
        "outputId": "fd559684-3689-4c5a-a3f9-5e96c765fc82"
      },
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 500x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **MLP for node regression**"
      ],
      "metadata": {
        "id": "gEqWcN1qtcrg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "from torch.nn import Linear, Module\n",
        "import torch.nn.functional as F\n",
        "\n",
        "class MLP(Module):\n",
        "\n",
        "    def __init__(self, dim_in, dim_h, dim_out):\n",
        "        super().__init__()\n",
        "        self.linear1 = Linear(dim_in, dim_h)\n",
        "        self.linear2 = Linear(dim_h, dim_out)\n",
        "\n",
        "    def forward(self, x):\n",
        "        x = self.linear1(x)\n",
        "        x = torch.relu(x)\n",
        "        x = self.linear2(x)\n",
        "        return x  # No activation function for regression\n",
        "\n",
        "    def fit(self, data, epochs):\n",
        "        criterion = torch.nn.MSELoss()  # Change loss function to MSE\n",
        "        optimizer = torch.optim.Adam(self.parameters(), lr=0.01, weight_decay=5e-4)\n",
        "        self.train()\n",
        "\n",
        "        for epoch in range(epochs + 1):\n",
        "            optimizer.zero_grad()\n",
        "            out = self(data.x)\n",
        "            loss = criterion(out[data.train_mask], data.y[data.train_mask])\n",
        "\n",
        "            loss.backward()\n",
        "            optimizer.step()\n",
        "\n",
        "            if epoch % 20 == 0:\n",
        "                val_loss = criterion(out[data.val_mask], data.y[data.val_mask])\n",
        "                print(f'Epoch {epoch:>3} | Train Loss: {loss:.3f} | Val Loss: {val_loss:.2f}')\n",
        "\n",
        "    @torch.no_grad()\n",
        "    def test(self, data):\n",
        "        self.eval()\n",
        "        out = self(data.x)\n",
        "        test_loss = torch.nn.functional.mse_loss(out[data.test_mask], data.y[data.test_mask])\n",
        "        return test_loss\n"
      ],
      "metadata": {
        "id": "_igPwcEto7yr"
      },
      "execution_count": 163,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import torch\n",
        "\n",
        "if torch.cuda.is_available():\n",
        "    device = torch.device(\"cuda\")\n",
        "    print(\"CUDA is available. Using GPU.\")\n",
        "else:\n",
        "    device = torch.device(\"cpu\")\n",
        "    print(\"CUDA not available. Using CPU.\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M05XYJyxAJHE",
        "outputId": "09a1f5b0-f075-4ea9-86a9-5eec081e9543"
      },
      "execution_count": 164,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "CUDA is available. Using GPU.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Assuming 'data' is an object or dictionary containing 'x', 'y', and masks\n",
        "data.x = data.x.to(device)\n",
        "data.y = data.y.to(device)\n",
        "data.train_mask = data.train_mask.to(device)\n",
        "data.val_mask = data.val_mask.to(device)"
      ],
      "metadata": {
        "id": "Gifk0TuqAUjM"
      },
      "execution_count": 165,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data.y = data.y.to(torch.float32).flatten().unsqueeze(1)"
      ],
      "metadata": {
        "id": "tO9_hGR6vPiD"
      },
      "execution_count": 167,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data.y.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fdu5SoxoDurG",
        "outputId": "7d65bb96-387e-4351-b514-d5ad22276a17"
      },
      "execution_count": 168,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([2277, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 168
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Create the Vanilla MLP regression model**"
      ],
      "metadata": {
        "id": "36iJKGj2uz-Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mlp = MLP(dataset.num_features, 128, 1).to(device)\n",
        "print(mlp)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b-ByjADBo71g",
        "outputId": "65200ca0-fa99-4d68-9156-a5376c8dcfe3"
      },
      "execution_count": 169,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "MLP(\n",
            "  (linear1): Linear(in_features=2325, out_features=128, bias=True)\n",
            "  (linear2): Linear(in_features=128, out_features=1, bias=True)\n",
            ")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Train\n",
        "mlp.fit(data, epochs=200)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cpYKmrJ0o74X",
        "outputId": "171db4ee-4310-4967-9f55-ff7065c81267"
      },
      "execution_count": 170,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch   0 | Train Loss: 11.471 | Val Loss: 11.13\n",
            "Epoch  20 | Train Loss: 1.037 | Val Loss: 1.55\n",
            "Epoch  40 | Train Loss: 0.259 | Val Loss: 1.03\n",
            "Epoch  60 | Train Loss: 0.115 | Val Loss: 0.83\n",
            "Epoch  80 | Train Loss: 0.088 | Val Loss: 0.75\n",
            "Epoch 100 | Train Loss: 0.077 | Val Loss: 0.76\n",
            "Epoch 120 | Train Loss: 0.069 | Val Loss: 0.79\n",
            "Epoch 140 | Train Loss: 0.063 | Val Loss: 0.80\n",
            "Epoch 160 | Train Loss: 0.059 | Val Loss: 0.81\n",
            "Epoch 180 | Train Loss: 0.057 | Val Loss: 0.83\n",
            "Epoch 200 | Train Loss: 0.055 | Val Loss: 0.81\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test\n",
        "loss = mlp.test(data)\n",
        "print(f'\\nMLP test loss on Wikipedia Chameleon dataset: {loss:.5f}\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YKIrydMQo781",
        "outputId": "11660e21-6488-402b-8f16-d7c9b5b69440"
      },
      "execution_count": 171,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "MLP test loss on Wikipedia Chameleon dataset: 1.02798\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Sklearn metrics**"
      ],
      "metadata": {
        "id": "yvZynEh3yP3a"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.metrics import mean_squared_error, mean_absolute_error"
      ],
      "metadata": {
        "id": "8wQX1JXyo7_V"
      },
      "execution_count": 172,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "out = mlp(data.x)"
      ],
      "metadata": {
        "id": "zEZwZ1EUyfA8"
      },
      "execution_count": 173,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = out.cpu().squeeze()[data.test_mask.cpu()].detach().numpy()\n"
      ],
      "metadata": {
        "id": "RtbILs_Hy1qn"
      },
      "execution_count": 174,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "mse = mean_squared_error(data.y[data.test_mask].squeeze().cpu(), y_pred)\n",
        "mae = mean_absolute_error(data.y[data.test_mask].squeeze().cpu(), y_pred)\n"
      ],
      "metadata": {
        "id": "m0BqlvNJA2rA"
      },
      "execution_count": 175,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "print('=' * 13 + '  MLP on Wikipedia Chameleon Dataset ' + '=' * 13)\n",
        "print(f'MSE = {mse:.4f} | RMSE = {np.sqrt(mse):.4f} | MAE = {mae:.4f}')\n",
        "print('=' * 57)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vXJe-GKn09d8",
        "outputId": "0feb5b0f-35e4-4833-d79d-ec6c22138c5a"
      },
      "execution_count": 176,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "=============  MLP on Wikipedia Chameleon Dataset =============\n",
            "MSE = 1.0280 | RMSE = 1.0139 | MAE = 0.7373\n",
            "=========================================================\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **GCN on Wikipedia Chamelon Dataset**"
      ],
      "metadata": {
        "id": "uLX0lkLN5TpG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from torch_geometric.nn import GCNConv"
      ],
      "metadata": {
        "id": "ogibY-GI7-zg"
      },
      "execution_count": 177,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "class GCN(torch.nn.Module):\n",
        "    def __init__(self, dim_in, dim_h, dim_out):\n",
        "        super().__init__()\n",
        "        self.gcn1 = GCNConv(dim_in, dim_h*4)\n",
        "        self.gcn2 = GCNConv(dim_h*4, dim_h*2)\n",
        "        self.gcn3 = GCNConv(dim_h*2, dim_h)\n",
        "        self.linear = torch.nn.Linear(dim_h, dim_out)\n",
        "\n",
        "    def forward(self, x, edge_index):\n",
        "        h = self.gcn1(x, edge_index)\n",
        "        h = torch.relu(h)\n",
        "        h = F.dropout(h, p=0.5, training=self.training)\n",
        "        h = self.gcn2(h, edge_index)\n",
        "        h = torch.relu(h)\n",
        "        h = F.dropout(h, p=0.5, training=self.training)\n",
        "        h = self.gcn3(h, edge_index)\n",
        "        h = torch.relu(h)\n",
        "        h = self.linear(h)\n",
        "        return h\n",
        "\n",
        "    def fit(self, data, epochs):\n",
        "        optimizer = torch.optim.Adam(self.parameters(),lr=0.02,weight_decay=5e-4)\n",
        "\n",
        "        self.train()\n",
        "        for epoch in range(epochs+1):\n",
        "            optimizer.zero_grad()\n",
        "            out = self(data.x, data.edge_index)\n",
        "            loss = F.mse_loss(out.squeeze()[data.train_mask], data.y[data.train_mask].float())\n",
        "            loss.backward()\n",
        "            optimizer.step()\n",
        "            if epoch % 20 == 0:\n",
        "                val_loss = F.mse_loss(out.squeeze()[data.val_mask], data.y[data.val_mask])\n",
        "                print(f\"Epoch {epoch:>3} | Train Loss: {loss:.5f} | Val Loss: {val_loss:.5f}\")\n",
        "\n",
        "    def test(self, data):\n",
        "        self.eval()\n",
        "        out = self(data.x, data.edge_index)\n",
        "        return F.mse_loss(out.squeeze()[data.test_mask], data.y[data.test_mask].float())"
      ],
      "metadata": {
        "id": "1J12ndZ721x-"
      },
      "execution_count": 178,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "data.y.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bhLiTQIyDGgZ",
        "outputId": "618b9369-583e-43c4-b873-cf475431f18c"
      },
      "execution_count": 179,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([2277, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 179
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data.y = data.y.to(torch.float32).flatten()"
      ],
      "metadata": {
        "id": "whOeLD128HUw"
      },
      "execution_count": 180,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Create the Vanilla GNN model\n",
        "gcn = GCN(dataset.num_features, 1024, 1).to(device)\n",
        "print(gcn)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IKXmWbhF210g",
        "outputId": "c6518fcd-09bf-4d8c-cfad-bc47dc7db647"
      },
      "execution_count": 181,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GCN(\n",
            "  (gcn1): GCNConv(2325, 4096)\n",
            "  (gcn2): GCNConv(4096, 2048)\n",
            "  (gcn3): GCNConv(2048, 1024)\n",
            "  (linear): Linear(in_features=1024, out_features=1, bias=True)\n",
            ")\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = data.to(device)"
      ],
      "metadata": {
        "id": "2vj-tNgfBfZa"
      },
      "execution_count": 182,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Train\n",
        "gcn.fit(data, epochs=200)\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "auDII55s54jJ",
        "outputId": "8a4b48ff-ad40-4079-9f3b-5a4ea67cc008"
      },
      "execution_count": 183,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Epoch   0 | Train Loss: 11.62447 | Val Loss: 11.29704\n",
            "Epoch  20 | Train Loss: 12.44890 | Val Loss: 12.10543\n",
            "Epoch  40 | Train Loss: 12.53433 | Val Loss: 12.18985\n",
            "Epoch  60 | Train Loss: 5.70775 | Val Loss: 5.63519\n",
            "Epoch  80 | Train Loss: 0.76001 | Val Loss: 0.77969\n",
            "Epoch 100 | Train Loss: 0.44456 | Val Loss: 0.61861\n",
            "Epoch 120 | Train Loss: 0.39790 | Val Loss: 0.65277\n",
            "Epoch 140 | Train Loss: 0.30105 | Val Loss: 0.69059\n",
            "Epoch 160 | Train Loss: 0.30744 | Val Loss: 0.60631\n",
            "Epoch 180 | Train Loss: 0.31705 | Val Loss: 0.57054\n",
            "Epoch 200 | Train Loss: 0.27112 | Val Loss: 0.55806\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Test\n",
        "loss = gcn.test(data)\n",
        "print(f'\\nGCN test loss: {loss:.5f}\\n')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MWkrzV6t55_h",
        "outputId": "dd8e18d3-2b25-40e3-f3c2-e41fd9270c92"
      },
      "execution_count": 184,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "GCN test loss: 0.59467\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "out = gcn(data.x, data.edge_index)"
      ],
      "metadata": {
        "id": "rn5-CmxC212x"
      },
      "execution_count": 185,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "out = out.cpu()"
      ],
      "metadata": {
        "id": "V-TwjM0cCFwj"
      },
      "execution_count": 186,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred = out.squeeze()[data.test_mask.cpu()].detach().numpy()\n"
      ],
      "metadata": {
        "id": "wa7fVOdjCHkj"
      },
      "execution_count": 187,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "mse = mean_squared_error(data.y[data.test_mask].squeeze().cpu(), y_pred)\n",
        "mae = mean_absolute_error(data.y[data.test_mask].squeeze().cpu(), y_pred)"
      ],
      "metadata": {
        "id": "0XXj3Gt2CY8-"
      },
      "execution_count": 188,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "print('=' * 13 + '  GCN Wikipedia Chameleon Dataset  ' + '=' * 13)\n",
        "print(f'MSE = {mse:.4f} | RMSE = {np.sqrt(mse):.4f} | MAE = {mae:.4f}')\n",
        "print('=' * 57)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "N2KBebYy6wf_",
        "outputId": "f798fab6-e127-47a9-bbc3-9384932dd49e"
      },
      "execution_count": 189,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "=============  GCN Squirrel Chameleon Dataset  =============\n",
            "MSE = 0.5947 | RMSE = 0.7711 | MAE = 0.6059\n",
            "=========================================================\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Comparison**\n"
      ],
      "metadata": {
        "id": "5FYUSk4aD_xF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "| Model & Dataset                          | MSE  ⬇  | RMSE  ⬇ | MAE  ⬇  |\n",
        "|------------------------------------------|--------|--------|--------|\n",
        "| **MLP** on Wikipedia Chameleon Dataset       | 1.0280 | 1.0139 | 0.7373 |\n",
        "| **GCN** on Wikipedia Chameleon Dataset        | 0.5947 | 0.7711 | 0.6059 |"
      ],
      "metadata": {
        "id": "1JkyKi1zEeQi"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Thank you!"
      ],
      "metadata": {
        "id": "eHJwqDfSE755"
      }
    }
  ]
}