Decimal Scaling

Global Algorithm - Multi-Dimensional algorithm

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
$Y$	$Y \in \mathbb R^{N_1}, \mathbb R^{N_1 \times N_2}, \text{ or } \mathbb R^{N_1 \times N_2 \times N_3}, \ldots$	$N_1, N_2, N_3 \in \mathbb{N}$
$c$	$c \in \mathbb{N}$

Output Parameters

Parameter	Type	Constraint	Description	Remarks
$\hat{Y}$	$\hat{Y} \in (-1,1)^{N_1}, (-1,1)^{N_1 \times N_2}, \text{ or } (-1,1)^{N_1 \times N_2 \times N_3}, \ldots$	$N_1, N_2, N_3 \in \mathbb{N}$

Single Steps using the Algorithm

• Data Scaling with Decimal Scaling

References

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