:mod:`heat.cluster.kmedians`
============================
.. py:module:: heat.cluster.kmedians

.. autoapi-nested-parse::

   Module Implementing the Kmedians Algorithm



Module Contents
---------------


.. py:class:: KMedians(n_clusters: int = 8, init: Union[str, heat.core.dndarray.DNDarray] = 'random', max_iter: int = 300, tol: float = 0.0001, random_state: int = None)

   Bases: :class:`heat.cluster._kcluster._KCluster`

   K-Medians clustering algorithm [1].
   Uses the Manhattan (City-block, :math:`L_1`) metric for distance calculations

   :param n_clusters: The number of clusters to form as well as the number of centroids to generate.
   :type n_clusters: int, optional, default: 8
   :param init:
                Method for initialization:

                     - ‘k-medians++’ : selects initial cluster centers for the clustering in a smart way to speed up convergence [2].
                     - ‘random’: choose k observations (rows) at random from data for the initial centroids.
                     - 'batchparallel': initialize by using the batch parallel algorithm (see BatchParallelKMedians for more information).
                     - DNDarray: gives the initial centers, should be of Shape = (n_clusters, n_features)
   :type init: str or DNDarray, default: ‘random’
   :param max_iter: Maximum number of iterations of the k-means algorithm for a single run.
   :type max_iter: int, default: 300
   :param tol: Relative tolerance with regards to inertia to declare convergence.
   :type tol: float, default: 1e-4
   :param random_state: Determines random number generation for centroid initialization.
   :type random_state: int

   .. rubric:: References

   [1] Hakimi, S., and O. Kariv. "An algorithmic approach to network location problems II: The p-medians." SIAM Journal on Applied Mathematics 37.3 (1979): 539-560.


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   .. method:: _update_centroids(x: heat.core.dndarray.DNDarray, matching_centroids: heat.core.dndarray.DNDarray)

      Compute coordinates of new centroid as median of the data points in ``x`` that are assigned to it

      :param x: Input data
      :type x: DNDarray
      :param matching_centroids: Array filled with indeces ``i`` indicating to which cluster ``ci`` each sample point in x is assigned
      :type matching_centroids: DNDarray


   .. method:: fit(x: heat.core.dndarray.DNDarray, oversampling: float = 2, iter_multiplier: float = 1)

      Computes the centroid of a k-medians clustering.

      :param x: Training instances to cluster. Shape = (n_samples, n_features)
      :type x: DNDarray
      :param oversampling: oversampling factor used in the k-means|| initializiation of centroids
      :type oversampling: float
      :param iter_multiplier: factor that increases the number of iterations used in the initialization of centroids
      :type iter_multiplier: float