# Equal Groups K-Means clustering

"""Equal Groups K-Means clustering utlizing the scikit-learn api and related utilities."""

From: https://github.com/ndanielsen/Same-Size-K-Means/blob/master/clustering/equal_groups.py

And made to work with python3

`_labels_inertia_precompute_dense()`

which follows the steps laid
out in the Elki Same-size k-Means Variation tutorial.
https://elki-project.github.io/tutorial/same-size_k_means
Please note that this implementation only works in scikit-learn 17.X as later
versions having breaking changes to this implementation.
Parameters

"""Equal Groups K-Means clustering
90 percent of this is the Kmeans implmentations with the equal groups logic
located in n_groups : int, optional, default: 8 The number of clusters to form as well as the number of centroids to generate. max_iter : int, default: 300 Maximum number of iterations of the k-means algorithm for a single run. n_init : int, default: 10 Number of time the k-means algorithm will be run with different centroid seeds. The final results will be the best output of n_init consecutive runs in terms of inertia. init : {'k-means++', 'random' or an ndarray} Method for initialization, defaults to 'k-means++': 'k-means++' : selects initial cluster centers for k-mean clustering in a smart way to speed up convergence. See section Notes in k_init for more details. 'random': choose k observations (rows) at random from data for the initial centroids. If an ndarray is passed, it should be of shape (n_groups, n_features) and gives the initial centers. precompute_distances : {'auto', True, False} Precompute distances (faster but takes more memory). 'auto' : do not precompute distances if n_samples * n_groups > 12 million. This corresponds to about 100MB overhead per job using double precision. True : always precompute distances False : never precompute distances tol : float, default: 1e-4 Relative tolerance with regards to inertia to declare convergence random_state : integer or numpy.RandomState, optional The generator used to initialize the centers. If an integer is given, it fixes the seed. Defaults to the global numpy random number generator. verbose : int, default 0 Verbosity mode. copy_x : boolean, default True When pre-computing distances it is more numerically accurate to center the data first. If copy_x is True, then the original data is not modified. If False, the original data is modified, and put back before the function returns, but small numerical differences may be introduced by subtracting and then adding the data mean.

## Attributes

cluster_centers_ : array, [n_groups, n_features] Coordinates of cluster centers labels_ : Labels of each point inertia_ : float Sum of distances of samples to their closest cluster center.

## Notes

## The k-means problem is solved using Lloyd's algorithm. The average complexity is given by O(k n T), were n is the number of samples and T is the number of iteration. The worst case complexity is given by O(n^(k+2/p)) with n = n_samples, p = n_features. (D. Arthur and S. Vassilvitskii, 'How slow is the k-means method?' SoCG2006) In practice, the k-means algorithm is very fast (one of the fastest clustering algorithms available), but it falls in local minima. That's why it can be useful to restart it several times. See also

MiniBatchKMeans: Alternative online implementation that does incremental updates of the centers positions using mini-batches. For large scale learning (say n_samples > 10k) MiniBatchKMeans is probably much faster to than the default batch implementation. """