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