================== Maximum Likelihood ================== :doc:`/WorkProcessClassifiers/GlobalAlgorithm/index` - :doc:`/WorkProcessClassifiers/OneDimensionalAlgorithm/index` *Maximum Likelihood* algorithm decides whether a value is a value outside the region of interest based on that value's distance from the estimated mean distribution. Generally, if .. math:: |Y_i - \mu| > 3 \cdot \sigma \, \text{,} the data point is considered outside the region of interest. :math:`\mu` is the mean distribution, :math:`Y_i` is :math:`i`\ th element of :math:`Y` and :math:`\sigma` denotes the standard deviation. Note that :math:`\mu \pm 3\sigma` contains :math:`99.7%` data under the assumption of normal distribution. .. rubric:: Input Parameters +----------------------------+------------------------------------------------+----------------------------------------+--------------------------------------------------+---------+ | Parameter | Type | Constraint | Description | Remarks | +============================+================================================+========================================+==================================================+=========+ | :math:`Y` | :math:`Y \in \mathbb R^N` | :math:`N \in \mathbb{N}` | Input data sequence of length :math:`N` | | +----------------------------+------------------------------------------------+----------------------------------------+--------------------------------------------------+---------+ | :math:`\mu` | :math:`\mu \in \mathbb{R}` | | Mean distribution of :math:`Y` | | +----------------------------+------------------------------------------------+----------------------------------------+--------------------------------------------------+---------+ | :math:`\sigma` | :math:`\sigma\in \mathbb{R}` | | Standard deviation of :math:`Y` | | +----------------------------+------------------------------------------------+----------------------------------------+--------------------------------------------------+---------+ .. rubric:: Output Parameters +----------------------------+----------------------------------------------------+------------+-------------------------------------------------------------------------------------------+---------+ | Parameter | Type | Constraint | Description | Remarks | +============================+====================================================+============+===========================================================================================+=========+ | :math:`\hat{Y}` | :math:`\hat{Y} \in \mathbb R^N` | | Values in the :math:`Y` list which are outside the region of interest are marked | | +----------------------------+----------------------------------------------------+------------+-------------------------------------------------------------------------------------------+---------+ .. rubric:: Tool Support * :doc:`/Tools/MatlabTool/index` For details refer to the online documentation of the function `'mle' `__. .. rubric:: Single Steps using the Algorithm * :doc:`/DataPreprocessing/DataCleaning/OutlierDetection/OutlierDetectionWithMaximumLikelihood/index` .. rubric:: References - J.\ Han, M. Kamber and J. Pei, Data Mining - Concepts and Techniques, 3rd ed., Amsterdam: Morgan Kaufmann Publishers, 2012.