### Matrix Factorization ###
# Input variables
user_input = Input(shape=(1,), dtype='int32', name = 'user_input')
item_input = Input(shape=(1,), dtype='int32', name = 'item_input')

User_Embedding = Embedding(input_dim = n_users, output_dim = latent_dim, name = 'user_embedding', input_length=1,embeddings_regularizer = regularizers.l2(1e-5))
Item_Embedding = Embedding(input_dim = n_prods, output_dim = latent_dim, name = 'item_embedding', input_length=1,embeddings_regularizer = regularizers.l2(1e-5))

# Crucial to flatten an embedding vector!
user_latent = Flatten()(User_Embedding(user_input))
item_latent = Flatten()(Item_Embedding(item_input))

# Element-wise product of user and item embeddings
predict_vector = merge([user_latent, item_latent], mode = 'mul')

# Final prediction layer
prediction = Dense(1, activation='sigmoid', init='lecun_uniform', name = 'prediction')(predict_vector)

MF_model = Model(input=[user_input, item_input],output=prediction)