Consider x1 = (8.41, 9.09, 1.41, -7.57, -9.59, -2.79, 6.57, 9.89, 4.12, -5.44), embedding dimension d = 2, time delay =

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Consider X1 8 41 9 09 1 41 7 57 9 59 2 79 6 57 9 89 4 12 5 44 Embedding Dimension D 2 Time Delay 1 (77.2 KiB) Viewed 53 times

Consider x1 = (8.41, 9.09, 1.41, -7.57, -9.59, -2.79, 6.57, 9.89, 4.12, -5.44), embedding dimension d = 2, time delay = =2, number of clusters c = 2, fuzzy exponent = 3, you need to manually perform the following tasks. 1. Reconstruct the phase space of x. The formula for the phase-space reconstruction of the original time series (tı, t2, ..., tx) that results in Y = (y1, y2, ..., ym), where M= N - (d - 1)T is given as Yi = (ti, titty..., ti+(d=1)), i = 1,...,N - (d - 1)T. (1) 2. Compute the fuzzy recurrence plot (FRP) of the reconstructed phase space using only 3 iterations of the fuzzy c-means (FCM) algorithm. You 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), based on which you compute the fuzzy partition. Show the values of all elements of the computed FRP.