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.