Min-Max Scaling

Global Algorithm - Multi-Dimensional algorithm

The basic formula of Min-Max Scaling algorithm is stated as follows:

$$\hat{Y}_i = \frac{Y_i - min(Y)}{max(Y)-min(Y)} \cdot (\text{max}^{\text{new}} - \text{min}^{\text{new}}) + \text{min}^{\text{new}}$$

for a one-dimensional data vector,

$$\hat{Y}_{i,j} = \frac{Y_{i,j} - min(Y)}{max(Y)-min(Y)} \cdot (\text{max}^{\text{new}} - \text{min}^{\text{new}}) + \text{min}^{\text{new}}$$

for a two-dimensional data matrix, and

$$\hat{Y}_{i,j,k} = \frac{Y_{i,j,k} - min(Y)}{max(Y)-min(Y)} \cdot (\text{max}^{\text{new}} - \text{min}^{\text{new}}) + \text{min}^{\text{new}}$$

for a three-dimensional data matrix, where $Y$ represents the input data and $i, j, k$ represent the corresponding indices for the data entry considered.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
$Y$	$Y \in \mathbb R^{N_1}, \mathbb R^{N_1 \times N_2}, \text{ or } \mathbb R^{N_1 \times N_2 \times N_3}, \ldots$	$N_1, N_2, N_3 \in \mathbb{N}$
$\text{min}^{\text{new}}$	$\text{min}^{\text{new}} \in \mathbb R$	$\text{min}^{\text{new}} \leq \text{max}^{\text{new}}$
$\text{max}^{\text{new}}$	$\text{max}^{\text{new}} \in \mathbb R$	$\text{min}^{\text{new}} \leq \text{max}^{\text{new}}$

Output Parameters

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

Single Steps using the Algorithm

• Data Scaling with Min-Max Scaling

References

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