Zero-Mean Scaling

Global Algorithm - Multi-Dimensional algorithm

Zero-Mean Scaling algorithm is a algorithm of normalization which uses the mean and standard deviation of the data set to normalize each data point. The basic formulas are stated as follows:

$$\hat{Y}_i = \frac{(Y_i - \mu)}{\sigma}$$

for a one-dimensional data vector,

$$\hat{Y}_{i,j} = \frac{(Y_{i,j} - \mu)}{\sigma}$$

for a two-dimensional data matrix,

$$\hat{Y}_{i,j,k} = \frac{(Y_{i,j,k} - \mu)}{\sigma}$$

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. $\mu$ is the mean, and $\sigma$ is the standard deviation of the input data.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
$Y$	$Y \in \mathbb R^{N_1}, \mathbb R^{N_1 \times N_2}, \text{ or } \mathbb R^{N_1 \times N_2 \times N_3}, \ldots$	$N_1, N_2, N_3 \in \mathbb{N}$
$\mu$	$\mu \in \mathbb{R}$		Mean value of $Y$
$\sigma$	$\sigma \in \mathbb{R}$		Standard deviation of $Y$

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 Zero-Mean Scaling

References

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