================
Unitnorm Scaling
================
:doc:`/WorkProcessClassifiers/GlobalAlgorithm/index` - :doc:`/WorkProcessClassifiers/MultiDimensionalAlgorithm/index`

*Unitnorm Scaling* algorithm uses the following formula to normalize data:

.. math::

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

for a one-dimensional data vector,

.. math::

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

for a two-dimensional data matrix,

.. math::

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

for a three-dimensional data matrix, where :math:`Y` represents the input data and :math:`i, j, k` represent the corresponding indices for the data entry considered. :math:`||\cdot||_2` represents the Euclidean norm.

.. rubric:: Input Parameters

+--------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------+-------------+---------+
| Parameter          | Type                                                                                                                                                               | Constraint                                             | Description | Remarks |
+====================+====================================================================================================================================================================+========================================================+=============+=========+
| :math:`Y`          | :math:`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`                                               | :math:`N_1, N_2, N_3 \in \mathbb{N}`                   |             |         |
+--------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------+-------------+---------+

.. rubric:: Output Parameters

+----------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------+-------------+---------+
| Parameter                  | Type                                                                                                                                                           | Constraint                                             | Description | Remarks |
+============================+================================================================================================================================================================+========================================================+=============+=========+
| :math:`\hat{Y}`            | :math:`\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`                                              | :math:`N_1, N_2, N_3 \in \mathbb{N}`                   |             |         |
+----------------------------+----------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------+-------------+---------+

.. rubric:: Single Steps using the Algorithm

* :doc:`/DataPreprocessing/DataTransformation/DataScaling/DataScalingWithUnitnormScaling/index`