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Unverified Commit 0bdc437b authored by Minjie Wang's avatar Minjie Wang Committed by GitHub
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[Doc] Update colab tutorials with spmatrix (#5220) 

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* Created using Colaboratory

* Created using Colaboratory

* Created using Colaboratory

* Created using Colaboratory

* Created using Colaboratory
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notebooks/sparse/gcn.ipynb
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...@@ -54,7 +54,7 @@ ...@@ -54,7 +54,7 @@
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"execution_count": 2, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -71,7 +71,9 @@ ...@@ -71,7 +71,9 @@
"## Graph Convolutional Layer\n", "## Graph Convolutional Layer\n",
"\n", "\n",
"Mathematically, the graph convolutional layer is defined as:\n", "Mathematically, the graph convolutional layer is defined as:\n",
"$$f(X^{(l)}, A) = \\sigma(\\hat{D}^{-\\frac{1}{2}}\\hat{A}\\hat{D}^{-\\frac{1}{2}}X^{(l)}W^{(l)})$$", "\n",
"$$f(X^{(l)}, A) = \\sigma(\\hat{D}^{-\\frac{1}{2}}\\hat{A}\\hat{D}^{-\\frac{1}{2}}X^{(l)}W^{(l)})$$\n",
"\n",
"with $\\hat{A} = A + I$, where $A$ denotes the adjacency matrix and $I$ denotes the identity matrix, $\\hat{D}$ refers to the diagonal node degree matrix of $\\hat{A}$ and $W^{(l)}$ denotes a trainable weight matrix. $\\sigma$ refers to a non-linear activation (e.g. relu).\n", "with $\\hat{A} = A + I$, where $A$ denotes the adjacency matrix and $I$ denotes the identity matrix, $\\hat{D}$ refers to the diagonal node degree matrix of $\\hat{A}$ and $W^{(l)}$ denotes a trainable weight matrix. $\\sigma$ refers to a non-linear activation (e.g. relu).\n",
"\n", "\n",
"The code below shows how to implement it using the `dgl.sparse` package. The core operations are:\n", "The code below shows how to implement it using the `dgl.sparse` package. The core operations are:\n",
...@@ -114,7 +116,7 @@ ...@@ -114,7 +116,7 @@
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"id": "Y4I4EhHQ_kKb" "id": "Y4I4EhHQ_kKb"
}, },
"execution_count": 3, "execution_count": null,
"outputs": [] "outputs": []
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{ {
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"id": "BHX3vRjDWJTO" "id": "BHX3vRjDWJTO"
}, },
"execution_count": 4, "execution_count": null,
"outputs": [] "outputs": []
}, },
{ {
...@@ -179,9 +181,9 @@ ...@@ -179,9 +181,9 @@
" loss_fcn = nn.CrossEntropyLoss()\n", " loss_fcn = nn.CrossEntropyLoss()\n",
"\n", "\n",
" # Preprocess to get the adjacency matrix of the graph.\n", " # Preprocess to get the adjacency matrix of the graph.\n",
" src, dst = g.edges()\n", " indices = torch.stack(g.edges())\n",
" N = g.num_nodes()\n", " N = g.num_nodes()\n",
" A = dglsp.from_coo(dst, src, shape=(N, N))\n", " A = dglsp.spmatrix(indices, shape=(N, N))\n",
"\n", "\n",
" for epoch in range(100):\n", " for epoch in range(100):\n",
" model.train()\n", " model.train()\n",
...@@ -229,7 +231,7 @@ ...@@ -229,7 +231,7 @@
}, },
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"execution_count": 5, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -280,4 +282,4 @@ ...@@ -280,4 +282,4 @@
} }
} }
] ]
} }
\ No newline at end of file
notebooks/sparse/graph_diffusion.ipynb
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...@@ -31,7 +31,7 @@ ...@@ -31,7 +31,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": null,
"metadata": { "metadata": {
"id": "F6eQWmWn7lqh", "id": "F6eQWmWn7lqh",
"colab": { "colab": {
...@@ -101,9 +101,9 @@ ...@@ -101,9 +101,9 @@
"dgl_g = dataset[0]\n", "dgl_g = dataset[0]\n",
"\n", "\n",
"# Get its adjacency matrix.\n", "# Get its adjacency matrix.\n",
"src, dst = dgl_g.edges()\n", "indices = torch.stack(dgl_g.edges())\n",
"N = dgl_g.num_nodes()\n", "N = dgl_g.num_nodes()\n",
"A = dglsp.from_coo(dst, src, shape=(N, N))\n", "A = dglsp.spmatrix(indices, shape=(N, N))\n",
"print(A.to_dense())" "print(A.to_dense())"
], ],
"metadata": { "metadata": {
...@@ -113,7 +113,7 @@ ...@@ -113,7 +113,7 @@
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}, },
"execution_count": 2, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -134,7 +134,9 @@ ...@@ -134,7 +134,9 @@
"cell_type": "markdown", "cell_type": "markdown",
"source": [ "source": [
"We use the graph convolution matrix from Graph Convolution Networks as the diffusion matrix in this example. The graph convolution matrix is defined as:\n", "We use the graph convolution matrix from Graph Convolution Networks as the diffusion matrix in this example. The graph convolution matrix is defined as:\n",
"$$\\tilde{A} = \\hat{D}^{-\\frac{1}{2}}\\hat{A}\\hat{D}^{-\\frac{1}{2}}$$", "\n",
"$$\\tilde{A} = \\hat{D}^{-\\frac{1}{2}}\\hat{A}\\hat{D}^{-\\frac{1}{2}}$$\n",
"\n",
"with $\\hat{A} = A + I$, where $A$ denotes the adjacency matrix and $I$ denotes the identity matrix, $\\hat{D}$ refers to the diagonal node degree matrix of $\\hat{A}$." "with $\\hat{A} = A + I$, where $A$ denotes the adjacency matrix and $I$ denotes the identity matrix, $\\hat{D}$ refers to the diagonal node degree matrix of $\\hat{A}$."
], ],
"metadata": { "metadata": {
...@@ -159,7 +161,7 @@ ...@@ -159,7 +161,7 @@
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"outputId": "b03ef3dc-dcf5-494e-9191-30591d09f138" "outputId": "b03ef3dc-dcf5-494e-9191-30591d09f138"
}, },
"execution_count": 3, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -204,7 +206,7 @@ ...@@ -204,7 +206,7 @@
"metadata": { "metadata": {
"id": "DXb0uKqXDZKb" "id": "DXb0uKqXDZKb"
}, },
"execution_count": 4, "execution_count": null,
"outputs": [] "outputs": []
}, },
{ {
...@@ -249,7 +251,7 @@ ...@@ -249,7 +251,7 @@
}, },
"outputId": "be93263e-2283-4db7-caff-2e15e75ceb02" "outputId": "be93263e-2283-4db7-caff-2e15e75ceb02"
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"execution_count": 5, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "execute_result", "output_type": "execute_result",
...@@ -5601,7 +5603,7 @@ ...@@ -5601,7 +5603,7 @@
"metadata": { "metadata": {
"id": "__U3Hsp_S0SR" "id": "__U3Hsp_S0SR"
}, },
"execution_count": 6, "execution_count": null,
"outputs": [] "outputs": []
}, },
{ {
...@@ -5678,9 +5680,9 @@ ...@@ -5678,9 +5680,9 @@
"\n", "\n",
"# Create the sparse adjacency matrix A (note that W was used as the notation\n", "# Create the sparse adjacency matrix A (note that W was used as the notation\n",
"# for adjacency matrix in the original paper).\n", "# for adjacency matrix in the original paper).\n",
"src, dst = g.edges()\n", "indices = torch.stack(g.edges())\n",
"N = g.num_nodes()\n", "N = g.num_nodes()\n",
"A = dglsp.from_coo(dst, src, shape=(N, N))\n", "A = dglsp.spmatrix(indices, shape=(N, N))\n",
"\n", "\n",
"# Calculate the graph convolution matrix.\n", "# Calculate the graph convolution matrix.\n",
"I = dglsp.identity(A.shape, device=dev)\n", "I = dglsp.identity(A.shape, device=dev)\n",
...@@ -5708,7 +5710,7 @@ ...@@ -5708,7 +5710,7 @@
}, },
"outputId": "19e86f6a-c7f1-4b40-8cfc-58a181fc30d7" "outputId": "19e86f6a-c7f1-4b40-8cfc-58a181fc30d7"
}, },
"execution_count": 7, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -5754,4 +5756,4 @@ ...@@ -5754,4 +5756,4 @@
} }
} }
] ]
} }
\ No newline at end of file
notebooks/sparse/graph_transformer.ipynb
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...@@ -227,9 +227,9 @@ ...@@ -227,9 +227,9 @@
" )\n", " )\n",
"\n", "\n",
" def forward(self, g, X, pos_enc):\n", " def forward(self, g, X, pos_enc):\n",
" src, dst = g.edges()\n", " indices = torch.stack(g.edges())\n",
" N = g.num_nodes()\n", " N = g.num_nodes()\n",
" A = dglsp.from_coo(dst, src, shape=(N, N))\n", " A = dglsp.spmatrix(indices, shape=(N, N))\n",
" h = self.atom_encoder(X) + self.pos_linear(pos_enc)\n", " h = self.atom_encoder(X) + self.pos_linear(pos_enc)\n",
" for layer in self.layers:\n", " for layer in self.layers:\n",
" h = layer(A, h)\n", " h = layer(A, h)\n",
...@@ -418,4 +418,4 @@ ...@@ -418,4 +418,4 @@
}, },
"nbformat": 4, "nbformat": 4,
"nbformat_minor": 0 "nbformat_minor": 0
} }
\ No newline at end of file
notebooks/sparse/hgnn.ipynb
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...@@ -57,7 +57,7 @@ ...@@ -57,7 +57,7 @@
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"outputId": "5b5106f6-074b-42a5-fc4c-4936efd2cef8" "outputId": "5b5106f6-074b-42a5-fc4c-4936efd2cef8"
}, },
"execution_count": 1, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -108,9 +108,9 @@ ...@@ -108,9 +108,9 @@
"import dgl.sparse as dglsp\n", "import dgl.sparse as dglsp\n",
"import torch\n", "import torch\n",
"\n", "\n",
"H = dglsp.from_coo(\n", "H = dglsp.spmatrix(\n",
" torch.LongTensor([0, 1, 2, 2, 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 9, 9, 10]),\n", " torch.LongTensor([[0, 1, 2, 2, 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 9, 9, 10],\n",
" torch.LongTensor([0, 0, 0, 1, 3, 4, 2, 1, 0, 2, 3, 4, 2, 1, 3, 1, 3, 2, 4, 4])\n", " [0, 0, 0, 1, 3, 4, 2, 1, 0, 2, 3, 4, 2, 1, 3, 1, 3, 2, 4, 4]])\n",
")\n", ")\n",
"\n", "\n",
"print(H.to_dense())" "print(H.to_dense())"
...@@ -122,7 +122,7 @@ ...@@ -122,7 +122,7 @@
}, },
"outputId": "a1a576f6-1559-479c-9f3e-93e41a56833d" "outputId": "a1a576f6-1559-479c-9f3e-93e41a56833d"
}, },
"execution_count": 2, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -168,7 +168,7 @@ ...@@ -168,7 +168,7 @@
}, },
"outputId": "ffe2c441-8c2c-48a7-cef2-4ef6e96548ec" "outputId": "ffe2c441-8c2c-48a7-cef2-4ef6e96548ec"
}, },
"execution_count": 3, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -187,8 +187,9 @@ ...@@ -187,8 +187,9 @@
"## Hypergraph Neural Network (HGNN) Layer\n", "## Hypergraph Neural Network (HGNN) Layer\n",
"\n", "\n",
"The [HGNN layer](https://arxiv.org/pdf/1809.09401.pdf) is defined as:\n", "The [HGNN layer](https://arxiv.org/pdf/1809.09401.pdf) is defined as:\n",
"$$f(X^{(l)}, H; W^{(l)}) = \\sigma(L X^{(l)} W^{(l)})$$", "\n",
"$$L = D_v^{-1/2} H B D_e^{-1} H^\\top D_v^{-1/2}$$", "$$f(X^{(l)}, H; W^{(l)}) = \\sigma(L X^{(l)} W^{(l)})$$$$L = D_v^{-1/2} H B D_e^{-1} H^\\top D_v^{-1/2}$$\n",
"\n",
"where\n", "where\n",
"* $H \\in \\mathbb{R}^{N \\times M}$ is the incidence matrix of hypergraph with $N$ nodes and $M$ hyperedges.\n", "* $H \\in \\mathbb{R}^{N \\times M}$ is the incidence matrix of hypergraph with $N$ nodes and $M$ hyperedges.\n",
"* $D_v \\in \\mathbb{R}^{N \\times N}$ is a diagonal matrix representing node degrees, whose $i$-th diagonal element is $\\sum_{j=1}^M H_{ij}$.\n", "* $D_v \\in \\mathbb{R}^{N \\times N}$ is a diagonal matrix representing node degrees, whose $i$-th diagonal element is $\\sum_{j=1}^M H_{ij}$.\n",
...@@ -247,7 +248,7 @@ ...@@ -247,7 +248,7 @@
"metadata": { "metadata": {
"id": "58WnPtPvT2mx" "id": "58WnPtPvT2mx"
}, },
"execution_count": 4, "execution_count": null,
"outputs": [] "outputs": []
}, },
{ {
...@@ -272,8 +273,8 @@ ...@@ -272,8 +273,8 @@
" dataset = CoraGraphDataset()\n", " dataset = CoraGraphDataset()\n",
"\n", "\n",
" graph = dataset[0]\n", " graph = dataset[0]\n",
" src, dst = graph.edges()\n", " indices = torch.stack(graph.edges())\n",
" H = dglsp.from_coo(dst, src)\n", " H = dglsp.spmatrix(indices)\n",
" H = H + dglsp.identity(H.shape)\n", " H = H + dglsp.identity(H.shape)\n",
"\n", "\n",
" X = graph.ndata[\"feat\"]\n", " X = graph.ndata[\"feat\"]\n",
...@@ -286,7 +287,7 @@ ...@@ -286,7 +287,7 @@
"metadata": { "metadata": {
"id": "qI0j1J9pwTFg" "id": "qI0j1J9pwTFg"
}, },
"execution_count": 5, "execution_count": null,
"outputs": [] "outputs": []
}, },
{ {
...@@ -354,7 +355,7 @@ ...@@ -354,7 +355,7 @@
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}, },
"execution_count": 6, "execution_count": null,
"outputs": [ "outputs": [
{ {
"output_type": "stream", "output_type": "stream",
...@@ -406,4 +407,4 @@ ...@@ -406,4 +407,4 @@
} }
} }
] ]
} }
\ No newline at end of file
notebooks/sparse/quickstart.ipynb
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