How to make series circle shift invariant
A possible way to approach the problem would be to extract the maximum values of the discrete circular convolution of each pre-normalized sequence with an NXN matrix formed by the elements of an orthonormal base of the Nx1 sequence space.

The output of this step would be a Nx1 vector that would contain a measure of the similitude of each sequence with the each base sequence. If base sequences are adequately chosen, similar sequences should have similar output vectors, and an operator like mean square difference between outputs should tell how similar are two input sequences.