Recommender System - User embeddings in Softmax based Deep Neural Network Model

Question

Google's Recommendation System course include a section on Retrieval , where it is mentioned that recommendations can be made by checking similarity between user embedding Ψ(X) and movie embedding Vj.

How to get particular user embedding through Ψ(X)? Going through below code (which can be found here ), output in create_network() should be Ψ(X), so how would we extract embedding of particular user to create user recommendations?

def build_softmax_model(rated_movies, embedding_cols, hidden_dims):
  """Builds a Softmax model for MovieLens.
  Args:
    rated_movies: DataFrame of traing examples.
    embedding_cols: A dictionary mapping feature names (string) to embedding
      column objects. This will be used in tf.feature_column.input_layer() to
      create the input layer.
    hidden_dims: int list of the dimensions of the hidden layers.
  Returns:
    A CFModel object.
  """
  def create_network(features):
    """Maps input features dictionary to user embeddings.
    Args:
      features: A dictionary of input string tensors.
    Returns:
      outputs: A tensor of shape [batch_size, embedding_dim].
    """
    # Create a bag-of-words embedding for each sparse feature.
    inputs = tf.feature_column.input_layer(features, embedding_cols)
    # Hidden layers.
    input_dim = inputs.shape[1].value
    for i, output_dim in enumerate(hidden_dims):
      w = tf.get_variable(
          "hidden%d_w_" % i, shape=[input_dim, output_dim],
          initializer=tf.truncated_normal_initializer(
              stddev=1./np.sqrt(output_dim))) / 10.
      outputs = tf.matmul(inputs, w)
      input_dim = output_dim
      inputs = outputs
    return outputs

  train_rated_movies, test_rated_movies = split_dataframe(rated_movies)
  train_batch = make_batch(train_rated_movies, 200)
  test_batch = make_batch(test_rated_movies, 100)

  with tf.variable_scope("model", reuse=False):
    # Train
    train_user_embeddings = create_network(train_batch)
    train_labels = select_random(train_batch["label"])
  with tf.variable_scope("model", reuse=True):
    # Test
    test_user_embeddings = create_network(test_batch)
    test_labels = select_random(test_batch["label"])
    movie_embeddings = tf.get_variable(
        "input_layer/movie_id_embedding/embedding_weights")

  test_loss = softmax_loss(
      test_user_embeddings, movie_embeddings, test_labels)
  train_loss = softmax_loss(
      train_user_embeddings, movie_embeddings, train_labels)
  _, test_precision_at_10 = tf.metrics.precision_at_k(
      labels=test_labels,
      predictions=tf.matmul(test_user_embeddings, movie_embeddings, transpose_b=True),
      k=10)

  metrics = (
      {"train_loss": train_loss, "test_loss": test_loss},
      {"test_precision_at_10": test_precision_at_10}
  )
  embeddings = {"movie_id": movie_embeddings}
  return CFModel(embeddings, train_loss, metrics)

CFModel is a helper class to train model using SGD.

Answer 1

如果将单个用户的特征向量传递给嵌入模型，则其输出 Ψ(X) 将是该用户的查询向量，形状为 [1, embedding_dim]。