I'm trying to use support vector machine (on Matlab) for a data driven blackbox-system identification. The problem is the format of the data. Then, for every sample of the data, the input is a vector (time Serie) and the Output as well. Both have the same length.
I'm not trying to predict any value in the future (so plz dont mix it up with one-step ahead prediction etc ...). Let's say that I have 10 samples that I created from the 10 expremients I've done. Every experiment (sample) is characterized through a different Input/Output Vectors (Values) :
Experiment 1 : Input1 = [0 3 15 25 40 100 ... 0] and Output1 = [0 24.2 33 44 ... 0]. of length L = n
Experiment 2 : Input2 = [0 4 16 45 60 110 ... 0] and Output1 = [0 13.2 14 47 ... 0]. of length L = n (same length = const)
until Experiment 10 : Input10 = [0 2 11 24 55 101 ... 0] and Output10 = [0 12.2 31 47 ... 0]. of length L = n.
Now that I've done this 10 times (so I have 10 samples for the same system ) I would like to know how can I use my data for training a SVM (Regression). Since for every Sample my output is not only a value but a Vector. I cannot append the time sequences together, since that would cause a discontinuity in the sequence.
I'm using Matlab so I downloaded both toolboxes : LibSVM and also LS-SVM. ! I uploaded a picture here that describes the process I'm trying to explain ! Thank you :)
If it is mandatory to use SVM, you can try using multiple SVM models (n number of models) to generate the each an every element in the output vector. For an example, use the following setup.
SVM Model 1:
Input 1 = [0 3 15 25 40 100 ... 0]
output 1: 0
input 2: [0 4 16 45 60 110 ... 0]
output 2: 0
and so on..
SVM Model 2:
Input1 = [0 3 15 25 40 100 ... 0]
output 1: 24.2
Input 2 = [0 4 16 45 60 110 ... 0]
output 2: 13.2
and so on...
.......
.......
up to SVM Model n
Input n = [0 2 11 24 55 101 ... 0]
output n = 0
That means you have to train n SVMs to learn the influence from each element in the input time series to each element in the output sequence.
A better idea is that you can try using an autoencoder to learn the relationship between the input and output sequence.
Dear Chaaleb Mohamed Amine,
I would probably use windowing or multiple SVRs as Ravimal Bandara suggested but I guess you are asking for a method that will give all outputs at once. You may check the following paper and the MATLAB toolbox they provide.
Article Multi-output least-squares support vector regression machines
https://github.com/pzczxs/MLSSVR
Thank you for all your suggestions about methodology of SVM as a soultion to Black box machine's issue. I will try to use all purposed methods and for your kind contributions ,i am really greatful.
Best regards
Chaaleb
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