FM对于特征的组合仅限于二阶，缺少对特征之间深层次关系的抽取。因此，NFM提出来就是在FM的基础上引入神经网络，实现对特征的深层次抽取。NFM的模型结构图如下所示： 模型的结构如上图所示，首先输入就是离散化的特征，然后再进行embedding操作，获得每一个特征的向量表示。接着就到了Bi-interaction Pooling层，这里其实就是FM部分。FM的公式如下图所示： 去掉最外层的累加号，我们得到的是一个长度为K的向量，也就是embedding部分的长度。然后再对这个向量送入几层全连接层即可，最后输出ctr预估值。这就是NFM的整体思路。
权重构建，就是初始化一下embedding部分的数据，以及全连接部分的权重。然后就可以实现计算图了。 权重部分如下：
def _initWeights(self): weights = dict() # embedding weights['feature_embedding'] = tf.Variable(tf.random_normal(shape=[self.featureSize, self.embeddingSize], mean=0.0, stddev=0.001), name='feature_embedding') weights['feature_bias'] = tf.Variable(tf.random_normal(shape=[self.featureSize, 1], mean=0.0, stddev=0.001), name='feature_embedding') weights['bias'] = tf.Variable(tf.random_normal(shape=[1]), name='bias') # deep weights['layers_{}'.format(0)] = tf.Variable(tf.random_normal(shape=[self.embeddingSize, self.deepLayers[0]], mean=0, stddev=0.001), name='layers_{}'.format(0)) weights['bias_{}'.format(0)] = tf.Variable(tf.random_normal(shape=[1, self.deepLayers[0]]), name='bias_{}'.format(0)) for i in range(1, len(self.deepLayers)): weights['layers_{}'.format(i)] = tf.Variable(tf.random_normal(shape=[self.deepLayers[i-1], self.deepLayers[i]], mean=0.0, stddev=0.001), name='bias_{}'.format(i)) weights['bias_{}'.format(i)] = tf.Variable(tf.random_normal(shape=[1, self.deepLayers[i]]), name='bias_{}'.format(i)) weights['layers_output'] = tf.Variable(tf.random_normal(shape=[self.deepLayers[-1], 1], mean=0.0, stddev=0.001), name='layers_output') weights['bias_output'] = tf.Variable(tf.random_normal(shape=[1]), name='bias_output') return weights计算图部分：
def _initGraph(self): self.weights = self._initWeights() self.featureIndex = tf.placeholder(shape=[None, None], dtype=tf.int32) self.featureValue = tf.placeholder(shape=[None, None], dtype=tf.float32) self.label = tf.placeholder(shape=[None, 1], dtype=tf.float32) self.dropoutKeepDeep = tf.placeholder(tf.float32, shape=[None], name='dropout_deep_deep') self.trainPhase = tf.placeholder(tf.bool, name='train_phase') # embedding self.embedding = tf.nn.embedding_lookup(self.weights['feature_embedding'], self.featureIndex) featureValue = tf.reshape(self.featureValue, shape=[-1, self.fieldSize, 1]) self.embedding = tf.multiply(self.embedding, featureValue) # none fieldSize embeddingSize # 一次项 self.yFirstOrder = tf.nn.embedding_lookup(self.weights['feature_bias'], self.featureIndex) self.yFirstOrder = tf.reduce_sum(tf.multiply(self.yFirstOrder, featureValue), 2) # square->sum self.squaredSum = tf.reduce_sum(tf.square(self.embedding), 1) # sum->square self.sumedSquare = tf.square(tf.reduce_sum(self.embedding, 1)) self.ySecondOrder = 0.5 * tf.subtract(self.sumedSquare, self.squaredSum) # deep self.yDeep = self.ySecondOrder for i in range(0, len(self.deepLayers)): self.yDeep = tf.matmul(self.yDeep, self.weights['layers_{}'.format(i)]) + self.weights['bias_{}'.format(i)] self.yDeep = self.deepLayerActivation(self.yDeep) self.yDeep = tf.nn.dropout(self.yDeep, self.dropoutDeep[i + 1]) # bias # self.y_bias = self.weights['bias'] * tf.ones_like(self.label) # out self.out = tf.add_n([tf.reduce_sum(self.yFirstOrder, axis=1, keep_dims=True), tf.reduce_sum(self.yDeep, axis=1, keep_dims=True)])OK，NFM就简单介绍这些。思路相比与前面几篇比较简单，实现相对容易一些。
https://www.comp.nus.edu.sg/~xiangnan/papers/sigir17-nfm.pdf https://www.jianshu.com/p/4e65723ee632
