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

*Decimal Scaling* algorithm takes each value and divides it by ten to an exponent, :math:`c`\ , which moves the decimal point so that all values fall into the interval :math:`(-1, 1)`\ . The basic formula is as follows:

.. math::

    \hat{Y} = \frac{Y}{10^c} \, \text{,}

where :math:`Y` can be a vector or a multi-dimensional matrix. :math:`c` is the smallest integer such that the maximum value of :math:`\hat{Y}` is smaller than :math:`1`\ .

.. 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}`                   |             |         |
+--------------------+--------------------------------------------------------------------------------------------------------------------------------------------------------------------+--------------------------------------------------------+-------------+---------+
| :math:`c`          | :math:`c \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/DataScalingWithDecimalScaling/index`

.. rubric:: References

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