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.