Characterizing Network Anomaly Traffic with Euclidean Distance-Based Multiscale Fuzzy Entropy
Algorithm 1
EDM-fuzzy algorithm.
Inputs:
Time series: .
Time scale: .
Vector dimension: .
Tolerance coefficient: .
Standard deviation of time series X : SD.
Output:
EDM-Fuzzy entropy value of time series X at time scale τ.
(1)
for to
(2)
;
(3)
for to
(4)
Coarse-graining the time series ;
(5)
end for
(6)
end for
(7)
for to
(8)
for to
(9)
Calculate the mean of each vector
;
(10)
Move the vectors
;
(11)
end for
(12)
for to
(13)
for to
(14)
Calculate the Euclidean distance of the two
vectors and :
;
(15)
Calculate the similarity between and vectors
;
(16)
end for
(17)
Calculate the average similarity between vector
and the other vectors
;
(18)
end for
(19)
Compute the average of , that is,
;
(20)
Set dimensional length of vectors to and repeat step 8∼19 to calculate average similarity between each pair of points vectors in coarse-grained time series; you can get and
(21)
;
(22)
;
(23)
Compute the Euclidean distance based on fuzzy
sample entropy value for every ,
;
(24)
end for
(25)
Compute the fuzzy sample entropy value for the original time series at time scale
