A Sigmoid transformation provides rescaling of continuous numeric data in a more sophisticated way than the Rescaling transformation function. In a Sigmoid transformation, a numeric column is transformed using a type of sigmoid or s-shaped function. One of these, called a logit function, produces a continuously increasing value between 0 and 1. Another called the modified logit function, is twice the logit minus 1 and produces a value between -1 and 1. A third, called the hyperbolic tangent function, also produces a value between -1 and 1.
Note that the logit function is the same as the function previously called the sigmoid function, and the hyperbolic tangent function is the same as the math function of the same name. These non-linear transformations are generally more useful in data mining than a linear Rescaling transformation.
The logit value is calculated as:
The modified logit value is calculated as:
which is equivalent to:
The hyperbolic tangent value is calculated as: