# Unitnorm Scaling¶

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