s Curves ErDqrersivesuasesU “Ss- shape" curve A wide variety of sigmoid functions have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions(which go from 0 to 1), such as the Virtuous cycle what you kno integrals of the logistic field of the job, how distribution. the norma things can be growth distribution and student's t Vicious cycle distribution probability density functions o2012 Juan C, Mendez and whitney Johnson, all rights reserved
“S-shape”curve A wide variety of sigmoid functions have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic distribution, the normal distribution, and Student's tdistribution probability density functions
“Ss- shape" curve Logistic function Error function 1 f(a) f(r)=erf(a)=2 1+e-x / hyperbolic tangent Generalised logistic function f(a)=tanh a f(x)=(1+e2)a,a>0 Smoothstep function arctangent function -1 c≤1 f(a)=arctan a (1-2)dn) ∫(1-u2) N≥ sgn(a) c≥1 Gudermannian function Specific algebraic functions f(a)=gd(e) =/ cosh t f(x)= Error function f(a)=erf(c 2 /
“S-shape”curve
S-shape"curve Often sigmoid function refers to the special case of the logistic function shown in the first figure and √1+x defined by the formula tanh(r) arctan(2) S(a) 1+e-x 一gd(票x) 0.5 1+|x Other examples of similar shapes include the gompertz curve (used in modeling systems that 0.5 saturate at large values of x) and 0.5 the ogee curve(used in the of some dams). Sigmoid functions have have domain of all real numbers. with return value monotonically increasing most often from o to 1 or alternative 1 to 1
“ S -shape ”curve Often, sigmoid function refers to the special case of the logistic function shown in the first figure and defined by the formula Other examples of similar shapes include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have have domain of all real numbers, with return value monotonically increasing most often from 0 to 1 or alternatively from −1 to 1
“Ss- shape" curve a logistic function or logistic curve is a common"S" shape(sigmoid curve), with equation L where 1+e-k(x-20) 0.5 e=the natural logarithm base(also known as Euler's number) x0= the x-value of the sigmoid's midpoint, L= the curve's maximum value. and k= the steepness of the curve The logistic function finds applications in a range of fields, including artificial neural networks, biology (especially ecology ), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, and statistics
A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: where e = the natural logarithm base (also known as Euler's number), x0 = the x-value of the sigmoid's midpoint, L = the curve's maximum value, and k = the steepness of the curve. The logistic function finds applications in a range of fields, including artificial neural networks, biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, and statistics. “S-shape”curve