Unitnorm Scaling

Global Algorithm - Multi-Dimensional algorithm

Unitnorm Scaling algorithm uses the following formula to normalize data:

$$\hat{Y}_i = \frac{Y_i}{\|Y\|_2}$$

for a one-dimensional data vector,

$$\hat{Y}_{i,j} = \frac{Y_{i,j}}{\|Y\|_2}$$

for a two-dimensional data matrix,

$$\hat{Y}_{i,j,k} = \frac{Y_{i,j,k}}{\|Y\|_2}$$

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. $||\cdot||_2$ represents the Euclidean norm.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
$Y$	$Y \in \mathbb R^{N_1}, \mathbb R^{N_1 \times N_2}, \text{ or } \mathbb R^{N_1 \times N_2 \times N_3}, \ldots$	$N_1, N_2, N_3 \in \mathbb{N}$

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 Unitnorm Scaling