# Zero-Mean Scaling¶

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

References

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