Table 1 Mathematical formulation of four common sigmoid transfer functions
Function | Transfer function | Transfer function in EMA |
|---|---|---|
S1 | \(T\left(x\right)=\frac{1}{1+{\mathrm{e}}^{-2x}}\) | \(T\left({BEMA}_{i}^{d}(t)\right)=\frac{1}{1+{\mathrm{e}}^{-2{BEMA}_{i}^{d}(t)}}\) |
S2 | \(T\left(x\right)=\frac{1}{1+{\mathrm{e}}^{-x}}\) | \(T\left({BEMA}_{i}^{d}(t)\right)=\frac{1}{1+{\mathrm{e}}^{-{BEMA}_{i}^{d}(t)}}\) |
S3 | \(T\left(x\right)=\frac{1}{1+{\mathrm{e}}^{(-\frac{x}{2})}}\) | \(T\left({BEMA}_{i}^{d}(t)\right)=\frac{1}{1+{\mathrm{e}}^{(-\frac{{BEMA}_{i}^{d}(t)}{2})}}\) |
S4 | \(T\left(x\right)=\frac{1}{1+{\mathrm{e}}^{(-\frac{x}{3})}}\) | \(T\left({BEMA}_{i}^{d}(t)\right)=\frac{1}{1+{\mathrm{e}}^{(-\frac{{BEMA}_{i}^{d}(t)}{3})}}\) |