How can I reconstruct a phase space of a time series and computer the FRP using FCM iterations>

Question

I have a given time series X-transposed = (8.41, 9.09, 1.41, -7.57, -9.59, -2.79, 6.57, 9.89, 4.12, -5.44) and dimension (d) of 2, time delay(τ) of 2, 2 clusters (c), and a fuzzy exponent of 3.

I want to, first, manually reconstruct the phase space of X that would result in Y = (y1, y2, . . . , yM), where M = N − (d − 1)τ is given as yi = (ti, ti+τ, ..., ti+(d−1)τ), i = 1,..., N − (d − 1)τ.

Secondly, I need to compute the recurrence plot of the reconstructed phase space using just 3 Fuzzy C-mean iterations. Baring in mind that I need to initialize the fuzzy membership matrix by assigning the equal possibility of all elements belonging to each cluster (make sure the sum of all membership grades = 1).

Lastly, I want to show the values of all elements of the computed FRP.

Any help would be really appreciated. I am completely at a loss here and I am at a complete standstill. For reference, this is what i have managed to do so far, but I am sure it is wrong! 1 2

PS: Please see image for FCM algorithm3