# Min-Max Scaling¶

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
$$Y$$ $$Y \in \mathbb R^{N_1}, \mathbb R^{N_1 \times N_2}, \text{ or } \mathbb R^{N_1 \times N_2 \times N_3}, \ldots$$ $$N_1, N_2, N_3 \in \mathbb{N}$$ None None
$$\text{min}^{\text{new}}$$ $$\text{min}^{\text{new}} \in \mathbb R$$ $$\text{min}^{\text{new}} \leq \text{max}^{\text{new}}$$ None None
$$\text{max}^{\text{new}}$$ $$\text{max}^{\text{new}} \in \mathbb R$$ $$\text{min}^{\text{new}} \leq \text{max}^{\text{new}}$$ None None

Output Parameters

Parameter Type Constraint Description Remarks
$$\hat{Y}$$ $$\hat{Y} \in (\text{min}^{\text{new}}, \text{max}^{\text{new}})^{N_1}, (\text{min}^{\text{new}}, \text{max}^{\text{new}})^{N_1 \times N_2}, \text{ or } (\text{min}^{\text{new}}, \text{max}^{\text{new}})^{N_1 \times N_2 \times N_3}, \ldots$$ $$N_1, N_2, N_3 \in \mathbb{N}$$ None None

Single Steps using the Algorithm

References

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