Imagine a car is driving on a long street (= x-axis). The car can go in both directions and it will arbitrarily change its direction. I'm trying to formulate an Inputvector to tell a neural Network which area of the street was driven on and how often that area was driven on. What is known are the exact coordinates (x - coordinates) of the car with corresponding time stamps. The neural network needs to be updated every minute, so I have to come up with an intelligent way how to "summarize" one minute of movement of the car.
My ideas: I could calculate the following from the available position data with timestamps:
- weighted mean of the coordinates of the car
- the range (i.e. xmax - xmin)
- the travelled distance within one minute
these three inputs already give the neural network a good idea on how the street was being used. However, what if the car drives two times like depicted in this picture:
Both cases would result in the same mean position
0.5, the same range
1 and the same travelled distance
left: 5*1 = 5, right: 6*0.33 + 1 + 6*0.33 = 5 However, the middle part of the street was driven on less on the right than on the left. How can I differentiate between these two cases?
A different approach to this problem as a whole would be to instead of using mean + range + travelled distance, I just divide the street into 10 parts and tell the neural network which part was being used how intensely. E.G. for the case of the picture on the right where mostly the first and the last third of the axis was being used the input would be something like:
[0.15, 0.15, 0.15, 0.1, 0, 0, 0.1, 0.15, 0.15, 0.15]
However, what I don't like about this approach is that first of all it's not very precise cause I'm classifying the street into 10 parts, I would prefer to have a continuous solution. Also, It will generate too many inputs (I have to do it for 3 axes x,y,z) so I will have 30 inputs and the problem is that I will also need some other inputs for different reasons so the directional inputs will be too "heavy" altogether.
Maybe someone of you knows a different approach how to deal with that kind of problem. Or maybe I have to use some special kind of neural network architecture (something like a time delayed neural network with 60 time delayed one-second inputs instead of a single one-minute input) Help would be greatly appreciated.