GraphSAGE 代码解析(三) - aggregators.py

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GraphSAGE 代码解析(一) - unsupervised_train.py

GraphSAGE 代码解析(二) - layers.py

GraphSAGE 代码解析(四) - models.py

1. class MeanAggregator(Layer):

该类主要用于实现

1. __init__() 

__init_() 用于获取并初始化成员变量 dropout, bias(False), act(ReLu), concat(False), input_dim, output_dim, name(Variable scopr)

用glorot()方法初始化节点v的权值矩阵 vars['self_weights'] 和邻居节点均值u的权值矩阵 vars['neigh_weights']

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

若logging为True,则调用 layers.py 中 class Layer()的成员函数_log_vars(), 生成vars中各个变量的直方图。

glorot()

其中，glorot() 在inits.py中定义，用于权值初始化。(from .inits import glorot)

均匀分布初始化方法，又称Xavier均匀初始化，参数从 [-limit, limit] 的均匀分布产生，其中limit为 sqrt(6 / (fan_in + fan_out))。fan_in为权值张量的输入单元数，fan_out是权重张量的输出单元数。该函数返回 [fan_in, fan_out]大小的Variable。

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

2. _call(inputs)

class MeanAggregator(Layer) 中的 _call(inputs) 函数是对父类class Layer(object)方法_call(inputs)的重写。

用于实现最上方的迭代更新式子。

在layer.py 中定义的 class Layer(object)中，执行特殊函数def __call__(inputs) 时有： outputs = self._call(inputs)调用_call(inputs) 方法，也即在这里调用子类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：输出的非0元素是原来的 “1/keep_prob” 倍，以保证总和不变。

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)

这里注意在concat后其维数变为之前的2倍。

3. class MeanAggregator(Layer) 代码

class MeanAggregator(Layer):
    """
    Aggregates via mean followed by matmul and non-linearity.
    """

    def __init__(self, input_dim, output_dim, neigh_input_dim=None,
            dropout=0., bias=False, act=tf.nn.relu, 
            name=None, concat=False, **kwargs):
        super(MeanAggregator, self).__init__(**kwargs)

        self.dropout = dropout
        self.bias = bias
        self.act = act
        self.concat = concat

        if neigh_input_dim is None:
            neigh_input_dim = input_dim

        if name is not None:
            name = '/' + name
        else:
            name = ''

        with tf.variable_scope(self.name + name + '_vars'):
            self.vars['neigh_weights'] = glorot([neigh_input_dim, output_dim],
                                                        name='neigh_weights')
            self.vars['self_weights'] = glorot([input_dim, output_dim],
                                                        name='self_weights')
            if self.bias:
                self.vars['bias'] = zeros([self.output_dim], name='bias')

        if self.logging:
            self._log_vars()

        self.input_dim = input_dim
        self.output_dim = output_dim

    def _call(self, inputs):
        self_vecs, neigh_vecs = inputs

        neigh_vecs = tf.nn.dropout(neigh_vecs, 1-self.dropout)
        self_vecs = tf.nn.dropout(self_vecs, 1-self.dropout)
        neigh_means = tf.reduce_mean(neigh_vecs, axis=1)
       
        # [nodes] x [out_dim]
        from_neighs = tf.matmul(neigh_means, self.vars['neigh_weights'])

        from_self = tf.matmul(self_vecs, self.vars["self_weights"])
         
        if not self.concat:
            output = tf.add_n([from_self, from_neighs])
        else:
            output = tf.concat([from_self, from_neighs], axis=1)

        # bias
        if self.bias:
            output += self.vars['bias']
       
        return self.act(output)

2. class GCNAggregator(Layer)

这里__init__()与MeanAggregator基本相同，在_call()的实现中略有不同。

def _call(self, inputs):
    self_vecs, neigh_vecs = inputs

    neigh_vecs = tf.nn.dropout(neigh_vecs, 1-self.dropout)
    self_vecs = tf.nn.dropout(self_vecs, 1-self.dropout)
    means = tf.reduce_mean(tf.concat([neigh_vecs, 
        tf.expand_dims(self_vecs, axis=1)], axis=1), axis=1)
   
    # [nodes] x [out_dim]
    output = tf.matmul(means, self.vars['weights'])

    # bias
    if self.bias:
        output += self.vars['bias']
   
    return self.act(output)

其中对means求解时，

1. 先将self_vecs行列转换(tf.expand_dims(self_vecs, axis=1)),

2. 之后self_vecs的行数与neigh_vecs行数相同时，将二者concat, 即相当于在原先的neigh_vecs矩阵后面新增一列self_vecs的转置

3. 最后将得到的矩阵每行求均值，即得means.

之后means与权值矩阵vars['weights']求内积，并加上vars['bias'], 最终将该值带入激活函数(ReLu)。

下面举个例子简单说明(例子中省略了点乘W的操作)：

import tensorflow as tf

neigh_vecs = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
self_vecs = [2, 3, 4]

means = tf.reduce_mean(tf.concat([neigh_vecs,
                                  tf.expand_dims(self_vecs, axis=1)], axis=1), axis=1)

print(tf.shape(self_vecs))

print(tf.expand_dims(self_vecs, axis=0))
# Tensor("ExpandDims_1:0", shape=(1, 3), dtype=int32)

print(tf.expand_dims(self_vecs, axis=1))
# Tensor("ExpandDims_2:0", shape=(3, 1), dtype=int32)

sess = tf.Session()
print(sess.run(tf.expand_dims(self_vecs, axis=1)))
# [[2]
#  [3]
#  [4]]

print(sess.run(tf.concat([neigh_vecs,
                          tf.expand_dims(self_vecs, axis=1)], axis=1)))
# [[1 2 3 2]
#  [4 5 6 3]
#  [7 8 9 4]]

print(means)
# Tensor("Mean:0", shape=(3,), dtype=int32)

print(sess.run(tf.reduce_mean(tf.concat([neigh_vecs,
                                         tf.expand_dims(self_vecs, axis=1)], axis=1), axis=1)))
# [2 4 7]

# [[1 2 3 2]   = 8 // 4  = 2
#  [4 5 6 3]   = 18 // 4 = 4
#  [7 8 9 4]]  = 28 // 4 = 7

bias = [1]
output = means + bias
print(sess.run(output))
# [3 5 8]
# [2 + 1, 4 + 1, 7 + 1] = [3, 5, 8]