Decimal ScalingΒΆ

Decimal Scaling algorithm takes each value and divides it by ten to an exponent, \(c\), which moves the decimal point so that all values fall into the interval \((-1, 1)\). The basic formula is as follows:

\[\hat{Y} = \frac{Y}{10^c} \, \text{,}\]

where \(Y\) can be a vector or a multi-dimensional matrix. \(c\) is the smallest integer such that the maximum value of \(\hat{Y}\) is smaller than \(1\).

Input Parameters

Parameter Type Constraint Description Remarks
\(Y\) \(Y \in \mathbb R^{N_1}, \mathbb R^{N_1 \times N_2}, \text{ or } \mathbb R^{N_1 \times N_2 \times N_3}, \ldots\) \(N_1, N_2, N_3 \in \mathbb{N}\) None None
\(c\) \(c \in \mathbb{N}\) None None None

Output Parameters

Parameter Type Constraint Description Remarks
\(\hat{Y}\) \(\hat{Y} \in (-1,1)^{N_1}, (-1,1)^{N_1 \times N_2}, \text{ or } (-1,1)^{N_1 \times N_2 \times N_3}, \ldots\) \(N_1, N_2, N_3 \in \mathbb{N}\) None None

Single Steps using the Algorithm

References

    1. Han, M. Kamber and J. Pei, Data Mining - Concepts and Techniques, 3rd ed., Amsterdam: Morgan Kaufmann Publishers, 2012.