(5) The improved Logistic map.
Subsequently, Chinese scholars Wang and Hu put forward to a special Logistic map designated as the improved Logistic map [19] in order to distinguish from the traditional Logistic map.
From the above Eq. (7), we can notice that the proposed chaotic sequence based on weighted processing is a special case of the improved Logistic map chaotic sequences.
By Setting x n = z n +1)/2 and c=4, Eq. (4) is changed to the improved Logistic map within symmetrical region as below.
Furthermore, a chaotic sequence using the improved Logistic map without any processing has the worst performance in balance because its balance coefficient is always more than 0.06 at various code length.
Generally, the one-dimensional discrete chaotic maps can be applied to generate pseudo-random sequences, that is to say a qualified initial value is selected firstly and then a decimal chaotic sequence of length N is formed after N iterations according to chaotic map, for instance, the Chebyshev map, Tent map, Bernoulli map, Logistic map, and improved Logistic map.
when z n ∈(−1,1), the generated sequence is in the state of chaos, and the binary quantization threshold is 0. In addition, they derived the mathematical expression of statistical properties of chaotic sequences generated by the improved Logistic map and found that their statistical properties are identical with those of white noise.
Even when the distributions of weights estimated by random forests and logistic regression in our simulations were comparable (both with a number of large weights), trimming substantially improved logistic regression but not random forests (which performed well without trimming).
The improved logistic regression based algorithms F2 and F3 also runs very fast.
