Min-Max ScalingΒΆ

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.