# Decimal Scaling¶

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

References

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