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

*Equal-frequency Interval Binning* algorithm partitions the data values into disjoint subsets, which have the same number of data samples. The original data are then summarized in each pre-defined subset.

.. rubric:: Input Parameters

+--------------------+--------------------------------------------+----------------------------------------+------------------------------------------------+---------+
| Parameter          | Type                                       | Constraint                             | Description                                    | Remarks |
+====================+============================================+========================================+================================================+=========+
| :math:`Y`          | :math:`Y \in \mathbb R^N`                  | :math:`N \in \mathbb{N}`               | Input data vector of length :math:`N`          |         |
+--------------------+--------------------------------------------+----------------------------------------+------------------------------------------------+---------+
| :math:`n`          | :math:`n \in \mathbb N`                    |                                        |                                                |         |
+--------------------+--------------------------------------------+----------------------------------------+------------------------------------------------+---------+

.. rubric:: Output Parameters

+----------------------------+----------------------------------------------------+------------------------------------------------------------+-------------------------------------------------+---------+
| Parameter                  | Type                                               | Constraint                                                 | Description                                     | Remarks |
+============================+====================================================+============================================================+=================================================+=========+
| :math:`\hat{Y}`            | :math:`\hat{Y} \in \mathbb R^M`                    | :math:`M \in \mathbb{N}, \quad M \lt N`                    | Output data vector of length :math:`M`          |         |
+----------------------------+----------------------------------------------------+------------------------------------------------------------+-------------------------------------------------+---------+

.. rubric:: Single Steps using the Algorithm

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

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

.. rubric:: References

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