============================
Equal-width Interval Binning
============================
:doc:`/WorkProcessClassifiers/GlobalAlgorithm/index` - :doc:`/WorkProcessClassifiers/OneDimensionalAlgorithm/index`

*Equal-width Interval Binning* algorithm divides the range of values into :math:`k` subintervals of equal width that is determined by

.. math::

   h = \frac{max(Y)-min(Y)}{k}.



.. rubric:: Input Parameters

+--------------------+-------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+-------------+---------+
| Parameter          | Type                                                                                | Constraint                                                                                                                        | Description | Remarks |
+====================+=====================================================================================+===================================================================================================================================+=============+=========+
| :math:`Y`          | :math:`Y \in \mathbb R^N`                  or :math:`Y`          is continuous data | For discrete data, :math:`N \in \mathbb{N}`              \         ; for continuous data, input data bounded from below and above |             |         |
+--------------------+-------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+-------------+---------+
| :math:`k`          | :math:`k \in \mathbb N`                                                             |                                                                                                                                   |             |         |
+--------------------+-------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------+-------------+---------+

.. rubric:: Output Parameters

+----------------------------+--------------------------------------------------------+------------+----------------------------------------------------+---------+
| Parameter                  | Type                                                   | Constraint | Description                                        | Remarks |
+============================+========================================================+============+====================================================+=========+
| :math:`\hat{Y}`            | :math:`\hat{Y} \in \mathbb R^{k+1}`                    |            | Discrete data set of length :math:`k+1`            |         |
+----------------------------+--------------------------------------------------------+------------+----------------------------------------------------+---------+

.. rubric:: Single Steps using the Algorithm

* :doc:`/DataPreprocessing/DataDiscretization/DataDiscretizationWithEqualWidthIntervalBinning/index`

* :doc:`/DataPreprocessing/DataReduction/NumerosityReduction/DataReductionWithEqualWidthIntervalBinning/index`

.. rubric:: References

- J.\  Dougherty, R. Kohavi, M. Sahami, Supervised and Unsupervised Discrimination of Continuous Features, Proceedings of the 12th International Conference, Morgan Kaufman, pp. 194-202, 1995.

  `http://robotics.stanford.edu/users/sahami/papers-dir/disc.pdf <http://robotics.stanford.edu/users/sahami/papers-dir/disc.pdf>`__