# Exercise 16.1 - Solution¶

## Zachary’s karate club - semi-supervised node classification¶

In this exercise, we investigate semi-supervised node classification using Graph Convolutional Networks on Zachary’s Karate Club dataset introduced in Example 10.2. Sometime ago there was a dispute between the manager and the coach of the karate club which led to a split of the club into four groups.

Can we use Graph Convolutional Networks to predict the affiliation of each member given the social network of the community and the memberships of only four people?

The exercise uses spektral and networkx. If you don't have yet installed both packages, do so by executing:

In [ ]:
import sys
!{sys.executable} -m pip install spektral
!{sys.executable} -m pip install networkx

In [18]:
from tensorflow import keras
import matplotlib.pyplot as plt
import networkx as nx
import numpy as np
import spektral

print("spektral", spektral.__version__)
print("keras", keras.__version__)

spektral 1.0.6
keras 2.4.0


You can find the original data set here.

In [3]:
import gdown
import os

output = 'karate_club.npz'

if os.path.exists(output) == False:


In [4]:
print("adjacency matrix\n", adj)

adjacency matrix
[[0. 1. 1. ... 1. 0. 0.]
[1. 0. 1. ... 0. 0. 0.]
[1. 1. 0. ... 0. 1. 0.]
...
[1. 0. 0. ... 0. 1. 1.]
[0. 0. 1. ... 1. 0. 1.]
[0. 0. 0. ... 1. 1. 0.]]

In [5]:
print("features\n", features)

features
[[1. 0. 0. ... 0. 0. 0.]
[0. 1. 0. ... 0. 0. 0.]
[0. 0. 1. ... 0. 0. 0.]
...
[0. 0. 0. ... 1. 0. 0.]
[0. 0. 0. ... 0. 1. 0.]
[0. 0. 0. ... 0. 0. 1.]]

In [6]:
labels_one_hot = f["labels_one_hot"]

def one_hot_to_labels(labels_one_hot):
return np.sum([(labels_one_hot[:, i] == 1) * (i + 1) for i in range(4)], axis=0)

labels = one_hot_to_labels(labels_one_hot)

print("labels:", labels)

labels: [2 2 3 2 1 1 1 2 4 3 1 2 2 2 4 4 1 2 4 2 4 2 4 4 3 3 4 3 3 4 4 3 4 4]


### Plot data¶

In [7]:
g = nx.from_numpy_matrix(adj)  # define nx graph

fig, _ = plt.subplots(1)
nx.draw(g, pos=nx.random_layout(g), cmap=plt.get_cmap('jet'), node_color=np.log(one_hot_to_labels(labels_one_hot)),
node_size=np.sum(200 * labels_one_hot, axis=-1) + 150)
plt.tight_layout()


Each node symbolizes one member of the Karate Club, and the edges indicate a close social relationship. The colors indicate the group affiliation of each member.

We can further make a more sophisticated visualization of the data, by plotting the graph using the spring_layout

In [8]:
np.random.seed(2)
fig, _ = plt.subplots(1)
nx.draw(g, pos=nx.spring_layout(g), cmap=plt.get_cmap('jet'), node_color=np.log(one_hot_to_labels(labels_one_hot)),
node_size= np.sum(200 * labels_one_hot, axis=-1) + 150)
plt.tight_layout()


### Preparation of data¶

In the following, we prepare our data. Let us assume that after the splitting of the karate club, we only have information from 4 members. In this case, each member is part of another group.

This will give us a nice example for a weakly supervised learning task.

In [9]:
np.random.seed(2)

# Pick randomly one karate fighter from each class
labels_to_keep = np.array([np.random.choice(np.nonzero(labels_one_hot[:, c])[0]) for c in range(4)])

In [10]:
np.random.seed(2)
fig, axes = plt.subplots(1)
nx.draw(g, cmap=plt.get_cmap('jet'), node_color="grey",
node_size=150)

np.seterr(divide = 'ignore')
np.random.seed(2)
node_size=450, ax=axes)
np.seterr(divide = 'warn')
plt.tight_layout()


These data we will now use for performing semi-supervised node classification using graph convolutional networks.

### Model definition¶

In the following we preprocess the data and create a Graph Convolutional Network to classify the nodes of the graph (determine the membership of each karate fighter). For more details see Sec.10.4.1 of the book.

Additionally, we create a mask for masking the memberships of all karate fighter except the four members (labels_to_keep) when training the GCN.

In [11]:
train_mask = np.zeros(shape=labels_one_hot.shape[0], dtype=np.bool)


val_mask:
[ True  True  True  True False  True  True  True  True  True  True  True
True  True  True  True  True  True  True False  True  True  True  True
True  True  True  True  True  True  True False  True False]

[False False False False  True False False False False False False False
False False False False False False False  True False False False False
False False False False False False False  True False  True]

In [12]:
# Preprocessing and preparing of data
y_train = labels_one_hot * train_mask[..., np.newaxis]
y_val = labels_one_hot * val_mask[..., np.newaxis]

X = np.identity(34)  # create input for the DNN (the existence of each person (one-hot encoded))


To add a GCN layer to the model use spektral.layers.GCNConv()[feature_input, adjacency], where feature_input denotes the input features and adjacency the normalized (pre-processed) adjacency matrix ($\hat{A}$).
Note that the adjacency matrix has to be passed to each GCN layer.

In [13]:
F = 4  # number of features
N = adj.shape[0]  # number of nodes

X_in = keras.layers.Input(shape=(N,))
fltr_in = keras.layers.Input(shape=(N,))
x = spektral.layers.GCNConv(F, activation='tanh', use_bias=False)([X_in, fltr_in])
x = keras.layers.Dropout(0.4)(x)
x = spektral.layers.GCNConv(F, activation='tanh', use_bias=False)([x, fltr_in])
x = keras.layers.Dropout(0.4)(x)
x = spektral.layers.GCNConv(2, activation='tanh', use_bias=False, name="embedding")([x, fltr_in])
x = keras.layers.Dropout(0.4)(x)
output = spektral.layers.GCNConv(4, activation='softmax', use_bias=False)([x, fltr_in])

model = keras.models.Model(inputs=[X_in, fltr_in], outputs=output)

print(model.summary())

Model: "model"
__________________________________________________________________________________________________
Layer (type)                    Output Shape         Param #     Connected to
==================================================================================================
input_1 (InputLayer)            [(None, 34)]         0
__________________________________________________________________________________________________
input_2 (InputLayer)            [(None, 34)]         0
__________________________________________________________________________________________________
gcn_conv (GCNConv)              (None, 4)            136         input_1[0][0]
input_2[0][0]
__________________________________________________________________________________________________
dropout (Dropout)               (None, 4)            0           gcn_conv[0][0]
__________________________________________________________________________________________________
gcn_conv_1 (GCNConv)            (None, 4)            16          dropout[0][0]
input_2[0][0]
__________________________________________________________________________________________________
dropout_1 (Dropout)             (None, 4)            0           gcn_conv_1[0][0]
__________________________________________________________________________________________________
embedding (GCNConv)             (None, 2)            8           dropout_1[0][0]
input_2[0][0]
__________________________________________________________________________________________________
dropout_2 (Dropout)             (None, 2)            0           embedding[0][0]
__________________________________________________________________________________________________
gcn_conv_2 (GCNConv)            (None, 4)            8           dropout_2[0][0]
input_2[0][0]
==================================================================================================
Total params: 168
Trainable params: 168
Non-trainable params: 0
__________________________________________________________________________________________________
None


### Semi-supervised training of the GCN¶

For training the model, you can make use of the code skeletons below. To mask during training the DNN predictions for nodes for which labels are not known masking must be applied. This will guarantee that only the predictions made for the four nodes contribute to the objective.

For implementing this condition to perform semi-supervised node classification, you can make use of the sample_weight argument of model.train_on_batch().

Note that in this exercise, in contrast to most other exercises, we have to train the network on a single data structure (an undirected graph). Thus, the input data are always [X, fltr], and the targets are labels_one_hot.

In [14]:
learning_rate = 0.01
epochs = 2000

loss='categorical_crossentropy',
weighted_metrics=['acc'])

In [15]:
history = []

for i in range(epochs):
loss, acc = model.train_on_batch([X, fltr], labels_one_hot,

val_loss, val_acc = model.test_on_batch([X, fltr], labels_one_hot, sample_weight=val_mask)
history.append([val_loss, val_acc])

if i % 100 == 0:
print("iteration:", i, "val_loss:", val_loss, "val_accuracy:", val_acc)
print("iteration:", i, "loss:", loss, "accuracy:", acc)

iteration: 0 val_loss: 1.220716118812561 val_accuracy: 0.20000000298023224
iteration: 0 loss: 0.16210822761058807 accuracy: 0.25
iteration: 100 val_loss: 0.8142460584640503 val_accuracy: 0.5666666626930237
iteration: 100 loss: 0.07607047259807587 accuracy: 0.5
iteration: 200 val_loss: 0.7158778309822083 val_accuracy: 0.6000000238418579
iteration: 200 loss: 0.05839081481099129 accuracy: 0.75
iteration: 300 val_loss: 0.66419917345047 val_accuracy: 0.6000000238418579
iteration: 300 loss: 0.0749407410621643 accuracy: 0.75
iteration: 400 val_loss: 0.6143096685409546 val_accuracy: 0.6333333253860474
iteration: 400 loss: 0.03915657475590706 accuracy: 1.0
iteration: 500 val_loss: 0.5422644019126892 val_accuracy: 0.800000011920929
iteration: 500 loss: 0.038086000829935074 accuracy: 0.75
iteration: 600 val_loss: 0.5167407989501953 val_accuracy: 0.8666666746139526
iteration: 600 loss: 0.09346935898065567 accuracy: 0.75
iteration: 700 val_loss: 0.47521546483039856 val_accuracy: 0.8666666746139526
iteration: 700 loss: 0.019280560314655304 accuracy: 1.0
iteration: 800 val_loss: 0.47116196155548096 val_accuracy: 0.8666666746139526
iteration: 800 loss: 0.022175412625074387 accuracy: 1.0
iteration: 900 val_loss: 0.4794115126132965 val_accuracy: 0.8666666746139526
iteration: 900 loss: 0.023522397503256798 accuracy: 1.0
iteration: 1000 val_loss: 0.44566527009010315 val_accuracy: 0.8666666746139526
iteration: 1000 loss: 0.019912123680114746 accuracy: 1.0
iteration: 1100 val_loss: 0.47822806239128113 val_accuracy: 0.8666666746139526
iteration: 1100 loss: 0.0250545684248209 accuracy: 1.0
iteration: 1200 val_loss: 0.44681262969970703 val_accuracy: 0.8666666746139526
iteration: 1200 loss: 0.013429190963506699 accuracy: 1.0
iteration: 1300 val_loss: 0.43512454628944397 val_accuracy: 0.8666666746139526
iteration: 1300 loss: 0.020627062767744064 accuracy: 1.0
iteration: 1400 val_loss: 0.4363212287425995 val_accuracy: 0.8666666746139526
iteration: 1400 loss: 0.021992037072777748 accuracy: 1.0
iteration: 1500 val_loss: 0.41837286949157715 val_accuracy: 0.8666666746139526
iteration: 1500 loss: 0.013688452541828156 accuracy: 1.0
iteration: 1600 val_loss: 0.4596754014492035 val_accuracy: 0.8666666746139526
iteration: 1600 loss: 0.014334342442452908 accuracy: 1.0
iteration: 1700 val_loss: 0.45348453521728516 val_accuracy: 0.8666666746139526
iteration: 1700 loss: 0.009742897003889084 accuracy: 1.0
iteration: 1800 val_loss: 0.43000349402427673 val_accuracy: 0.8666666746139526
iteration: 1800 loss: 0.05205704644322395 accuracy: 0.75
iteration: 1900 val_loss: 0.4394140839576721 val_accuracy: 0.8666666746139526
iteration: 1900 loss: 0.01599077135324478 accuracy: 1.0


### Plot training history¶

In [16]:
fig, axes = plt.subplots(2, figsize=(12,8))
if type(history) == dict:
loss = history["val_loss"]
acc = history["val_acc"]
else:
loss, acc = np.split(np.array(history), 2, axis=-1)
x = np.arange(len(loss))
axes[0].plot(x, loss, c="navy")
axes[0].set_yscale("log")
axes[0].set_ylabel("Validation loss")
axes[1].plot(x, acc, c="firebrick")
axes[1].set_ylabel("Validation accuracy")
axes[1].set_ylim(0, 1)
axes[0].set_xlabel("Iterations")
axes[1].set_xlabel("Iterations")
plt.tight_layout()