1. class MeanAggregator(Layer):

該類主要用於實現

1. __init__() 

__init_() 用於獲取並初始化成員變數 dropout, bias(False), act(ReLu), concat(False), input_dim, output_dim, name(Variable scopr)

用glorot()方法初始化節點v的權值矩陣 vars['self_weights'] 和鄰居節點均值u的權值矩陣 vars['neigh_weights']

用零向量初始化vars['bias']。(見inits.py: zeros(shape))

若logging為True,則呼叫 layers.py 中 class Layer()的成員函式_log_vars(), 生成vars中各個變數的直方圖。

glorot()

其中，glorot() 在inits.py中定義，用於權值初始化。(from .inits import glorot)

均勻分佈初始化方法，又稱Xavier均勻初始化，引數從 [-limit, limit] 的均勻分佈產生，其中limit為 sqrt(6 / (fan_in + fan_out))。fan_in為權值張量的輸入單元數，fan_out是權重張量的輸出單元數。該函式返回 [fan_in, fan_out]大小的Variable。

1 def glorot(shape, name=None):
2     """Glorot & Bengio (AISTATS 2010) init."""
3     init_range = np.sqrt(6.0/(shape[0]+shape[1]))
4     initial = tf.random_uniform(shape, minval=-init_range, maxval=init_range, dtype=tf.float32)
5     return tf.Variable(initial, name=name)

2. _call(inputs)

class MeanAggregator(Layer) 中的 _call(inputs) 函式是對父類class Layer(object)方法_call(inputs)的重寫。

用於實現最上方的迭代更新式子。

在layer.py 中定義的 class Layer(object)中，執行特殊函式def __call__(inputs) 時有： outputs = self._call(inputs)呼叫_call(inputs) 方法，也即在這裡呼叫子類MeanAggregator(Layer)中的_call(inputs)方法。

tf.nn.dropout(x, keep_prob, noise_shape=None, seed=None, name=None)

With probability keep_prob, outputs the input element scaled up by 1 / keep_prob, otherwise outputs 0. The scaling is so that the expected sum is unchanged.

注意：輸出的非0元素是原來的 “1/keep_prob” 倍，以保證總和不變。

tf.add_n(inputs, name=None)

Adds all input tensors element-wise.

Args:
inputs: A list of Tensor or IndexedSlices objects, each with same shape and type.
name: A name for the operation (optional).
Returns:
A Tensor of same shape and type as the elements of inputs.

Raises:
ValueError: If inputs don't all have same shape and dtype or the shape cannot be inferred.

output = tf.concat([from_self, from_neighs], axis=1)

這裡注意在concat後其維數變為之前的2倍。

3. class MeanAggregator(Layer) 程式碼

 1 class MeanAggregator(Layer):
 2     """
 3     Aggregates via mean followed by matmul and non-linearity.
 4     """
 5 
 6     def __init__(self, input_dim, output_dim, neigh_input_dim=None,
 7             dropout=0., bias=False, act=tf.nn.relu, 
 8             name=None, concat=False, **kwargs):
 9         super(MeanAggregator, self).__init__(**kwargs)
10 
11         self.dropout = dropout
12         self.bias = bias
13         self.act = act
14         self.concat = concat
15 
16         if neigh_input_dim is None:
17             neigh_input_dim = input_dim
18 
19         if name is not None:
20             name = '/' + name
21         else:
22             name = ''
23 
24         with tf.variable_scope(self.name + name + '_vars'):
25             self.vars['neigh_weights'] = glorot([neigh_input_dim, output_dim],
26                                                         name='neigh_weights')
27             self.vars['self_weights'] = glorot([input_dim, output_dim],
28                                                         name='self_weights')
29             if self.bias:
30                 self.vars['bias'] = zeros([self.output_dim], name='bias')
31 
32         if self.logging:
33             self._log_vars()
34 
35         self.input_dim = input_dim
36         self.output_dim = output_dim
37 
38     def _call(self, inputs):
39         self_vecs, neigh_vecs = inputs
40 
41         neigh_vecs = tf.nn.dropout(neigh_vecs, 1-self.dropout)
42         self_vecs = tf.nn.dropout(self_vecs, 1-self.dropout)
43         neigh_means = tf.reduce_mean(neigh_vecs, axis=1)
44        
45         # [nodes] x [out_dim]
46         from_neighs = tf.matmul(neigh_means, self.vars['neigh_weights'])
47 
48         from_self = tf.matmul(self_vecs, self.vars["self_weights"])
49          
50         if not self.concat:
51             output = tf.add_n([from_self, from_neighs])
52         else:
53             output = tf.concat([from_self, from_neighs], axis=1)
54 
55         # bias
56         if self.bias:
57             output += self.vars['bias']
58        
59         return self.act(output)

2. class GCNAggregator(Layer)

這裡__init__()與MeanAggregator基本相同，在_call()的實現中略有不同。

 1 def _call(self, inputs):
 2     self_vecs, neigh_vecs = inputs
 3 
 4     neigh_vecs = tf.nn.dropout(neigh_vecs, 1-self.dropout)
 5     self_vecs = tf.nn.dropout(self_vecs, 1-self.dropout)
 6     means = tf.reduce_mean(tf.concat([neigh_vecs, 
 7         tf.expand_dims(self_vecs, axis=1)], axis=1), axis=1)
 8    
 9     # [nodes] x [out_dim]
10     output = tf.matmul(means, self.vars['weights'])
11 
12     # bias
13     if self.bias:
14         output += self.vars['bias']
15    
16     return self.act(output)

其中對means求解時，

1. 先將self_vecs行列轉換(tf.expand_dims(self_vecs, axis=1)),

2. 之後self_vecs的行數與neigh_vecs行數相同時，將二者concat, 即相當於在原先的neigh_vecs矩陣後面新增一列self_vecs的轉置

3. 最後將得到的矩陣每行求均值，即得means.

之後means與權值矩陣vars['weights']求內積，並加上vars['bias'], 最終將該值帶入啟用函式(ReLu)。

下面舉個例子簡單說明(例子中省略了點乘W的操作)：

 1 import tensorflow as tf
 2 
 3 neigh_vecs = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
 4 self_vecs = [2, 3, 4]
 5 
 6 means = tf.reduce_mean(tf.concat([neigh_vecs,
 7                                   tf.expand_dims(self_vecs, axis=1)], axis=1), axis=1)
 8 
 9 print(tf.shape(self_vecs))
10 
11 print(tf.expand_dims(self_vecs, axis=0))
12 # Tensor("ExpandDims_1:0", shape=(1, 3), dtype=int32)
13 
14 print(tf.expand_dims(self_vecs, axis=1))
15 # Tensor("ExpandDims_2:0", shape=(3, 1), dtype=int32)
16 
17 sess = tf.Session()
18 print(sess.run(tf.expand_dims(self_vecs, axis=1)))
19 # [[2]
20 #  [3]
21 #  [4]]
22 
23 print(sess.run(tf.concat([neigh_vecs,
24                           tf.expand_dims(self_vecs, axis=1)], axis=1)))
25 # [[1 2 3 2]
26 #  [4 5 6 3]
27 #  [7 8 9 4]]
28 
29 print(means)
30 # Tensor("Mean:0", shape=(3,), dtype=int32)
31 
32 print(sess.run(tf.reduce_mean(tf.concat([neigh_vecs,
33                                          tf.expand_dims(self_vecs, axis=1)], axis=1), axis=1)))
34 # [2 4 7]
35 
36 # [[1 2 3 2]   = 8 // 4  = 2
37 #  [4 5 6 3]   = 18 // 4 = 4
38 #  [7 8 9 4]]  = 28 // 4 = 7
39 
40 bias = [1]
41 output = means + bias
42 print(sess.run(output))
43 # [3 5 8]
44 # [2 + 1, 4 + 1, 7 + 1] = [3, 5, 8]