Htydjtk

I have a time-series dataframe like this

         feat1  feat2  target

date id                      

0    1      12     16     192

     2      15      6      90

     3       2      9      18

1    1       0      3       0

     2       0      9       0

     3      56      9     504

2    1       5      9      45

     2       6      9      54

     3       5      8      40

and my problem is for regression.

What I know about the LSTM sequences, is that normally, the row_id is the date, so you build sequences of n rows.

In my data, as you can see, it's different. In each row that refers to the date, I have 3 more rows representing a product.

What I have thinked for make the sequence to my problem, my sequence will be of 2 days:

sequence = [day0,day1],[day1,day2]

For every date, I have

date0 = [id1,id2,id3].

For every id, I have:

id = [feat1,feat2].

the sequence[0], and it would be something like

[

    [

        [12,16],

        [15,6],

        [2,9]

    ],[

        [0,3],

        [0.9],

        [56,9]

    ]

]

Is this valid?

Will the LSTM layer understand this? Or do I have to do some kind of extra transformation?

Your data format is

                         feature1   feature2   target

             product1    1          12         2

 timestamp   product2    2          6          3

             product3    4          3          4

There are two designs for two assumptions:

1. Products are not related to each other. Therefore, each product could be modeled separately. That is, each timestamp is X(t) = [feature1, feature2] or, including the target, X(t)|y(t) = [feature1, feature2, target]. And we build a model for each product separately. In summary, LSTM receives two 1 x 3 sequences for t-1 and t, and outputs a 1 x 1 target for t + 1. In notation:
   $$(overbrace{X_{t-1}|y_{t-1}}^{1 times 3}, overbrace{X_{t}|y_{t}}^{1 times 3}) rightarrow overbrace{y_{t+1}}^{1 times 1}$$



2. 
   

   Products are related to each other, meaning product1 can help product2 to predict its target. For this, we just need to flatten the 3 x 2 matrix to a 1 x 6 vector, where the order of values does not matter. That is,

   
   
   

   X(t) = [product1_feature1, product1_feature2, ..., product3_feature2]
   
   

   
   
   

   or

   
   
   

   X(t) = [product1_feature1, product2_feature1, ..., product3_feature2]
   
   

   
   
   

   We can also add the targets, for example

   
   
   

   X(t)|y(t) = [product1_feature1, product2_feature1, ..., product3_feature2, target1, ..., target3]
   
   

   
   
   

   This way, dimension of each timestamp would be 9 (6 + 3), and a sequence of two timestamps would be

   
   
   

   [
   
     [product1_feature1, product2_feature1, ..., product3_feature2, target1, ..., target3], # t-1
   
     [product1_feature1, product2_feature1, ..., product3_feature2, target1, ..., target3]  # t
   
   ]
   
   

   
   
   

   corresponding to a three dimensional target [target1, ..., target3] at t + 1.

   
   
   

   In summary, LSTM receives two 1 x 9 sequences for t-1 and t, and outputs a 1 x 3 target for t + 1. In notation:
   $$(overbrace{X_{t-1}|y_{t-1}}^{1 times 9}, overbrace{X_{t}|y_{t}}^{1 times 9}) rightarrow overbrace{y_{t+1}}^{1 times 3}$$