如何合并数值模型和嵌入序列模型来处理 RNN 中的类别

我想为我的分类特征构建一个带有嵌入的单层 LSTM 模型。我目前有数字特征和一些分类特征，例如位置，它不能进行单热编码，例如使用pd.get_dummies()由于计算复杂性，这正是我最初打算做的。

让我们想象一个例子：

样本数据

data = {
    'user_id': [1,1,1,1,2,2,3],
    'time_on_page': [10,20,30,20,15,10,40],
    'location': ['London','New York', 'London', 'New York', 'Hong Kong', 'Tokyo', 'Madrid'],
    'page_id': [5,4,2,1,6,8,2]
}
d = pd.DataFrame(data=data)
print(d)
   user_id  time_on_page   location  page_id
0        1            10     London        5
1        1            20   New York        4
2        1            30     London        2
3        1            20   New York        1
4        2            15  Hong Kong        6
5        2            10      Tokyo        8
6        3            40     Madrid        2

让我们看看访问网站的人。我正在跟踪数字数据，例如页面停留时间等。分类数据包括：位置（超过 1000 个唯一值）、Page_id（> 1000 个唯一值）、Author_id（超过 100 个唯一值）。最简单的解决方案是对所有内容进行 one-hot 编码，并将其放入具有可变序列长度的 LSTM 中，每个时间步对应于不同的页面视图。

上面的DataFrame将生成7个训练样本，序列长度可变。例如，对于user_id=2我将有 2 个训练样本：

[ ROW_INDEX_4 ] and [ ROW_INDEX_4, ROW_INDEX_5 ]

Let X是训练数据，我们看第一个训练样本X[0].

从上图中，我的分类特征是X[0][:, n:].

在创建序列之前，我将分类变量分解为[0,1... number_of_cats-1], using pd.factorize()所以数据在X[0][:, n:]是与其索引对应的数字。

我需要创建一个Embedding分别针对每个类别特征？例如。每个的嵌入x_*n, x_*n+1, ..., x_*m?

如果是这样，我如何将其放入 Keras 代码中？

model = Sequential()

model.add(Embedding(?, ?, input_length=variable)) # How do I feed the data into this embedding? Only the categorical inputs.

model.add(LSTM())
model.add(Dense())
model.add.Activation('sigmoid')
model.compile()

model.fit_generator() # fits the `X[i]` one by one of variable length sequences.

我的解决思路：

看起来像这样的东西：

我可以在每个分类特征 (m-n) 上训练 Word2Vec 模型，以对任何给定值进行矢量化。例如。伦敦将在 3 个维度上进行矢量化。假设我使用 3 维嵌入。然后我将所有内容放回到 X 矩阵中，该矩阵现在将有 n + 3(n-m)，并使用 LSTM 模型来训练它？

我只是认为应该有一种更简单/更聪明的方法。

正如您提到的，一种解决方案是对分类数据进行 one-hot 编码（或者甚至以基于索引的格式按原样使用它们），并将它们与数值数据一起馈送到 LSTM 层。当然，这里也可以有两个 LSTM 层，一个用于处理数值数据，另一个用于处理分类数据（采用单热编码格式或基于索引的格式），然后合并它们的输出。

另一种解决方案是为每个分类数据设置一个单独的嵌入层。每个嵌入层可能有自己的嵌入维度（正如上面所建议的，您可能有多个 LSTM 层来分别处理数值和分类特征）：

num_cats = 3 # number of categorical features
n_steps = 100 # number of timesteps in each sample
n_numerical_feats = 10 # number of numerical features in each sample
cat_size = [1000, 500, 100] # number of categories in each categorical feature
cat_embd_dim = [50, 10, 100] # embedding dimension for each categorical feature

numerical_input = Input(shape=(n_steps, n_numerical_feats), name='numeric_input')
cat_inputs = []
for i in range(num_cats):
    cat_inputs.append(Input(shape=(n_steps,1), name='cat' + str(i+1) + '_input'))

cat_embedded = []
for i in range(num_cats):
    embed = TimeDistributed(Embedding(cat_size[i], cat_embd_dim[i]))(cat_inputs[i])
    cat_embedded.append(embed)

cat_merged = concatenate(cat_embedded)
cat_merged = Reshape((n_steps, -1))(cat_merged)
merged = concatenate([numerical_input, cat_merged])
lstm_out = LSTM(64)(merged)

model = Model([numerical_input] + cat_inputs, lstm_out)
model.summary()

以下是模型摘要：

Layer (type)                    Output Shape         Param #     Connected to                     
==================================================================================================
cat1_input (InputLayer)         (None, 100, 1)       0                                            
__________________________________________________________________________________________________
cat2_input (InputLayer)         (None, 100, 1)       0                                            
__________________________________________________________________________________________________
cat3_input (InputLayer)         (None, 100, 1)       0                                            
__________________________________________________________________________________________________
time_distributed_1 (TimeDistrib (None, 100, 1, 50)   50000       cat1_input[0][0]                 
__________________________________________________________________________________________________
time_distributed_2 (TimeDistrib (None, 100, 1, 10)   5000        cat2_input[0][0]                 
__________________________________________________________________________________________________
time_distributed_3 (TimeDistrib (None, 100, 1, 100)  10000       cat3_input[0][0]                 
__________________________________________________________________________________________________
concatenate_1 (Concatenate)     (None, 100, 1, 160)  0           time_distributed_1[0][0]         
                                                                 time_distributed_2[0][0]         
                                                                 time_distributed_3[0][0]         
__________________________________________________________________________________________________
numeric_input (InputLayer)      (None, 100, 10)      0                                            
__________________________________________________________________________________________________
reshape_1 (Reshape)             (None, 100, 160)     0           concatenate_1[0][0]              
__________________________________________________________________________________________________
concatenate_2 (Concatenate)     (None, 100, 170)     0           numeric_input[0][0]              
                                                                 reshape_1[0][0]                  
__________________________________________________________________________________________________
lstm_1 (LSTM)                   (None, 64)           60160       concatenate_2[0][0]              
==================================================================================================
Total params: 125,160
Trainable params: 125,160
Non-trainable params: 0
__________________________________________________________________________________________________

然而，您可以尝试另一种解决方案：只为所有分类特征使用一个嵌入层。不过，它涉及一些预处理：您需要重新索引所有类别以使它们彼此不同。例如，第一个分类特征中的类别将从 1 到size_first_cat然后第二个分类特征中的类别将从size_first_cat + 1 to size_first_cat + size_second_cat等等。然而，在此解决方案中，所有分类特征都将具有相同的嵌入维度，因为我们仅使用一个嵌入层。

Update:现在我想了想，你还可以在数据预处理阶段甚至模型中重塑分类特征来摆脱TimeDistributed层和Reshape层（这也可能会提高训练速度）：

numerical_input = Input(shape=(n_steps, n_numerical_feats), name='numeric_input')
cat_inputs = []
for i in range(num_cats):
    cat_inputs.append(Input(shape=(n_steps,), name='cat' + str(i+1) + '_input'))

cat_embedded = []
for i in range(num_cats):
    embed = Embedding(cat_size[i], cat_embd_dim[i])(cat_inputs[i])
    cat_embedded.append(embed)

cat_merged = concatenate(cat_embedded)
merged = concatenate([numerical_input, cat_merged])
lstm_out = LSTM(64)(merged)

model = Model([numerical_input] + cat_inputs, lstm_out)

至于拟合模型，您需要分别为每个输入层提供其对应的 numpy 数组，例如：

X_tr_numerical = X_train[:,:,:n_numerical_feats]

# extract categorical features: you can use a for loop to this as well.
# note that we reshape categorical features to make them consistent with the updated solution
X_tr_cat1 = X_train[:,:,cat1_idx].reshape(-1, n_steps) 
X_tr_cat2 = X_train[:,:,cat2_idx].reshape(-1, n_steps)
X_tr_cat3 = X_train[:,:,cat3_idx].reshape(-1, n_steps)

# don't forget to compile the model ...

# fit the model
model.fit([X_tr_numerical, X_tr_cat1, X_tr_cat2, X_tr_cat3], y_train, ...)

# or you can use input layer names instead
model.fit({'numeric_input': X_tr_numerical,
           'cat1_input': X_tr_cat1,
           'cat2_input': X_tr_cat2,
           'cat3_input': X_tr_cat3}, y_train, ...)

如果您想使用fit_generator()没有区别：

# if you are using a generator
def my_generator(...):

    # prep the data ...

    yield [batch_tr_numerical, batch_tr_cat1, batch_tr_cat2, batch_tr_cat3], batch_tr_y

    # or use the names
    yield {'numeric_input': batch_tr_numerical,
           'cat1_input': batch_tr_cat1,
           'cat2_input': batch_tr_cat2,
           'cat3_input': batch_tr_cat3}, batch_tr_y

model.fit_generator(my_generator(...), ...)

# or if you are subclassing Sequence class
class MySequnece(Sequence):
    def __init__(self, x_set, y_set, batch_size):
        # initialize the data

    def __getitem__(self, idx):
        # fetch data for the given batch index (i.e. idx)

        # same as the generator above but use `return` instead of `yield`

model.fit_generator(MySequence(...), ...)