1_first.py

"""
.. currentmodule:: dgl

DGL at a Glance
=========================

**Author**: `Minjie Wang <https://jermainewang.github.io/>`_, Quan Gan, `Jake
Zhao <https://cs.nyu.edu/~jakezhao/>`_, Zheng Zhang

DGL is a Python package dedicated to deep learning on graphs, built atop
existing tensor DL frameworks (e.g. Pytorch, MXNet) and simplifying the
implementation of graph-based neural networks.

The goal of this tutorial:

- Understand how DGL enables computation on graph from a high level.
- Train a simple graph neural network in DGL to classify nodes in a graph.

At the end of this tutorial, we hope you get a brief feeling of how DGL works.

*This tutorial assumes basic familiarity with pytorch.*
"""

###############################################################################
# Tutorial problem description
# ----------------------------
#
# The tutorial is based on the "Zachary's karate club" problem. The karate club
# is a social network that includes 34 members and documents pairwise links
# between members who interact outside the club.  The club later divides into
# two communities led by the instructor (node 0) and the club president (node
# 33). The network is visualized as follows with the color indicating the
# community:
#
# .. image:: https://data.dgl.ai/tutorial/img/karate-club.png
#    :align: center
#
# The task is to predict which side (0 or 33) each member tends to join given
# the social network itself.


###############################################################################
# Step 1: Creating a graph in DGL
# -------------------------------
# Create the graph for Zachary's karate club as follows:

import dgl
import numpy as np

def build_karate_club_graph():
    # All 78 edges are stored in two numpy arrays. One for source endpoints
    # while the other for destination endpoints.
    src = np.array([1, 2, 2, 3, 3, 3, 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10, 10,
        10, 11, 12, 12, 13, 13, 13, 13, 16, 16, 17, 17, 19, 19, 21, 21,
        25, 25, 27, 27, 27, 28, 29, 29, 30, 30, 31, 31, 31, 31, 32, 32,
        32, 32, 32, 32, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 33, 33,
        33, 33, 33, 33, 33, 33, 33, 33, 33, 33])
    dst = np.array([0, 0, 1, 0, 1, 2, 0, 0, 0, 4, 5, 0, 1, 2, 3, 0, 2, 2, 0, 4,
        5, 0, 0, 3, 0, 1, 2, 3, 5, 6, 0, 1, 0, 1, 0, 1, 23, 24, 2, 23,
        24, 2, 23, 26, 1, 8, 0, 24, 25, 28, 2, 8, 14, 15, 18, 20, 22, 23,
        29, 30, 31, 8, 9, 13, 14, 15, 18, 19, 20, 22, 23, 26, 27, 28, 29, 30,
        31, 32])
    # Edges are directional in DGL; Make them bi-directional.
    u = np.concatenate([src, dst])
    v = np.concatenate([dst, src])
    # Construct a DGLGraph
    return dgl.DGLGraph((u, v))

###############################################################################
# Print out the number of nodes and edges in our newly constructed graph:

G = build_karate_club_graph()
print('We have %d nodes.' % G.number_of_nodes())
print('We have %d edges.' % G.number_of_edges())

###############################################################################
# Visualize the graph by converting it to a `networkx
# <https://networkx.github.io/documentation/stable/>`_ graph:

import networkx as nx
# Since the actual graph is undirected, we convert it for visualization
# purpose.
nx_G = G.to_networkx().to_undirected()
# Kamada-Kawaii layout usually looks pretty for arbitrary graphs
pos = nx.kamada_kawai_layout(nx_G)
nx.draw(nx_G, pos, with_labels=True, node_color=[[.7, .7, .7]])

###############################################################################
# Step 2: Assign features to nodes or edges
# --------------------------------------------
# Graph neural networks associate features with nodes and edges for training.
# For our classification example, since there is no input feature, we assign each node
# with a learnable embedding vector.

# In DGL, you can add features for all nodes at once, using a feature tensor that
# batches node features along the first dimension. The code below adds the learnable
# embeddings for all nodes:

import torch
import torch.nn as nn
import torch.nn.functional as F

embed = nn.Embedding(34, 5)  # 34 nodes with embedding dim equal to 5
G.ndata['feat'] = embed.weight

###############################################################################
# Print out the node features to verify:

# print out node 2's input feature
print(G.ndata['feat'][2])

# print out node 10 and 11's input features
print(G.ndata['feat'][[10, 11]])

###############################################################################
# Step 3: Define a Graph Convolutional Network (GCN)
# --------------------------------------------------
# To perform node classification, use the Graph Convolutional Network
# (GCN) developed by `Kipf and Welling <https://arxiv.org/abs/1609.02907>`_. Here
# is the simplest definition of a GCN framework. We recommend that you 
# read the original paper for more details.
#
# - At layer :math:`l`, each node :math:`v_i^l` carries a feature vector :math:`h_i^l`.
# - Each layer of the GCN tries to aggregate the features from :math:`u_i^{l}` where
#   :math:`u_i`'s are neighborhood nodes to :math:`v` into the next layer representation at
#   :math:`v_i^{l+1}`. This is followed by an affine transformation with some
#   non-linearity.
#
# The above definition of GCN fits into a **message-passing** paradigm: Each
# node will update its own feature with information sent from neighboring
# nodes. A graphical demonstration is displayed below.
#
# .. image:: https://data.dgl.ai/tutorial/1_first/mailbox.png
#    :alt: mailbox
#    :align: center
#
# In DGL, we provide implementations of popular Graph Neural Network layers under
# the `dgl.<backend>.nn` subpackage. The :class:`~dgl.nn.pytorch.GraphConv` module
# implements one Graph Convolutional layer.

from dgl.nn.pytorch import GraphConv

###############################################################################
# Define a deeper GCN model that contains two GCN layers:

class GCN(nn.Module):
    def __init__(self, in_feats, hidden_size, num_classes):
        super(GCN, self).__init__()
        self.conv1 = GraphConv(in_feats, hidden_size)
        self.conv2 = GraphConv(hidden_size, num_classes)

    def forward(self, g, inputs):
        h = self.conv1(g, inputs)
        h = torch.relu(h)
        h = self.conv2(g, h)
        return h

# The first layer transforms input features of size of 5 to a hidden size of 5.
# The second layer transforms the hidden layer and produces output features of
# size 2, corresponding to the two groups of the karate club.
net = GCN(5, 5, 2)

###############################################################################
# Step 4: Data preparation and initialization
# -------------------------------------------
#
# We use learnable embeddings to initialize the node features. Since this is a
# semi-supervised setting, only the instructor (node 0) and the club president
# (node 33) are assigned labels. The implementation is available as follow.

inputs = embed.weight
labeled_nodes = torch.tensor([0, 33])  # only the instructor and the president nodes are labeled
labels = torch.tensor([0, 1])  # their labels are different

###############################################################################
# Step 5: Train then visualize
# ----------------------------
# The training loop is exactly the same as other PyTorch models.
# We (1) create an optimizer, (2) feed the inputs to the model,
# (3) calculate the loss and (4) use autograd to optimize the model.
import itertools

optimizer = torch.optim.Adam(itertools.chain(net.parameters(), embed.parameters()), lr=0.01)
all_logits = []
for epoch in range(50):
    logits = net(G, inputs)
    # we save the logits for visualization later
    all_logits.append(logits.detach())
    logp = F.log_softmax(logits, 1)
    # we only compute loss for labeled nodes
    loss = F.nll_loss(logp[labeled_nodes], labels)

    optimizer.zero_grad()
    loss.backward()
    optimizer.step()

    print('Epoch %d | Loss: %.4f' % (epoch, loss.item()))

###############################################################################
# This is a rather toy example, so it does not even have a validation or test
# set. Instead, Since the model produces an output feature of size 2 for each node, we can
# visualize by plotting the output feature in a 2D space.
# The following code animates the training process from initial guess
# (where the nodes are not classified correctly at all) to the end
# (where the nodes are linearly separable).

import matplotlib.animation as animation
import matplotlib.pyplot as plt

def draw(i):
    cls1color = '#00FFFF'
    cls2color = '#FF00FF'
    pos = {}
    colors = []
    for v in range(34):
        pos[v] = all_logits[i][v].numpy()
        cls = pos[v].argmax()
        colors.append(cls1color if cls else cls2color)
    ax.cla()
    ax.axis('off')
    ax.set_title('Epoch: %d' % i)
    nx.draw_networkx(nx_G.to_undirected(), pos, node_color=colors,
            with_labels=True, node_size=300, ax=ax)

fig = plt.figure(dpi=150)
fig.clf()
ax = fig.subplots()
draw(0)  # draw the prediction of the first epoch
plt.close()

###############################################################################
# .. image:: https://data.dgl.ai/tutorial/1_first/karate0.png
#    :height: 300px
#    :width: 400px
#    :align: center

###############################################################################
# The following animation shows how the model correctly predicts the community
# after a series of training epochs.

ani = animation.FuncAnimation(fig, draw, frames=len(all_logits), interval=200)

###############################################################################
# .. image:: https://data.dgl.ai/tutorial/1_first/karate.gif
#    :height: 300px
#    :width: 400px
#    :align: center

###############################################################################
# Next steps
# ----------
# 
# In the :doc:`next tutorial <2_basics>`, we will go through some more basics
# of DGL, such as reading and writing node/edge features.