cluster.KMeans¶

class
pai4sk.cluster.
KMeans
(n_clusters=8, max_iter=300, tol=0.0001, verbose=0, random_state=1, precompute_distances='auto', init='kmeans++', n_init=1, algorithm='auto', copy_x=True, n_jobs=None, use_gpu=True)¶ KMeans clustering.
If cudf dataframe is passed as input, then pai4sk will try to use the accelerated KMeans algorithm from cuML. Otherwise, scikitlearn’s KMeans algorithm will be used.
cuML in pai4sk is currently supported only
(a) with python 3.6 and(b) without MPI.If KMeans from cuML is run, then the return values from the APIs will becudf dataframe and cudf Series objects instead of the return types of scikitlearn API.
Parameters:  n_clusters (int, optional, default: 8) – The number of clusters to form as well as the number of centroids to generate.
 init ({'kmeans++', 'random' or an ndarray}) –
Method for initialization, defaults to ‘kmeans++’:
’kmeans++’ : selects initial cluster centers for kmean 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_clusters, n_features) and gives the initial centers.
 n_init (int, default: 10) – Number of time the kmeans 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.
 max_iter (int, default: 300) – Maximum number of iterations of the kmeans algorithm for a single run.
 tol (float, default: 1e4) – Relative tolerance with regards to inertia to declare convergence
 precompute_distances ({'auto', True, False}) –
Precompute distances (faster but takes more memory).
’auto’ : do not precompute distances if n_samples * n_clusters > 12 million. This corresponds to about 100MB overhead per job using double precision.
True : always precompute distances
False : never precompute distances
 verbose (int, default 0) – Verbosity mode.
 random_state (int, RandomState instance or None (default)) – Determines random number generation for centroid initialization. Use an int to make the randomness deterministic. See Glossary.
 copy_x (boolean, optional) – When precomputing distances it is more numerically accurate to center the data first. If copy_x is True (default), then the original data is not modified, ensuring X is Ccontiguous. 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, in this case it will also not ensure that data is Ccontiguous which may cause a significant slowdown.
 n_jobs (int or None, optional (default=None)) –
The number of jobs to use for the computation. This works by computing each of the n_init runs in parallel.
None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors. See Glossary for more details.  algorithm ("auto", "full" or "elkan", "cuml", default="auto") –
Kmeans algorithm to use. The classical EMstyle algorithm is “full”. The “elkan” variation is more efficient by using the triangle inequality, but currently doesn’t support sparse data. “auto” chooses “elkan” for dense data and “full” for sparse data.
If cudf dataframe is passed as input, then if either
(1) algorithm is set to “cuml” or(2) algorithm is “auto”,then pai4sk will try to use kmeans algorithm from RAPIDS cuML.cuML in pai4sk is currently supported only(a) with python 3.6 and(b) without MPI.If KMeans from cuML is run, then the return values of the APIs will be cudf dataframe and cudf Series objects instead of the return types of scikitlearn API.
Variables:  cluster_centers (array, [n_clusters, n_features] or cudf dataframe) – Coordinates of cluster centers. If the algorithm stops before fully
converging (see
tol
andmax_iter
), these will not be consistent withlabels_
. If KMeans from cuML is run, then the return values of some of the APIs will be cudf dataframe and cudf Series objects instead of the return types of scikitlearn API.  labels (array or cudf Series) – Labels of each point
 inertia (float) – Sum of squared distances of samples to their closest cluster center.
 n_iter (int) – Number of iterations run.
 use_gpu (boolean, Default is True) – If True, cuML will use all GPUs. Applicable only for cuML.
Examples
>>> from pai4sk.cluster import KMeans >>> import numpy as np >>> X = np.array([[1, 2], [1, 4], [1, 0], ... [4, 2], [4, 4], [4, 0]]) >>> kmeans = KMeans(n_clusters=2, random_state=0).fit(X) >>> kmeans.labels_ array([0, 0, 0, 1, 1, 1], dtype=int32) >>> kmeans.predict([[0, 0], [4, 4]]) array([0, 1], dtype=int32) >>> kmeans.cluster_centers_ array([[1., 2.], [4., 2.]])
See also
MiniBatchKMeans
 Alternative online implementation that does incremental updates of the centers positions using minibatches. For large scale learning (say n_samples > 10k) MiniBatchKMeans is probably much faster than the default batch implementation.
Notes
The kmeans problem is solved using either Lloyd’s or Elkan’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 kmeans method?’ SoCG2006)
In practice, the kmeans 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.
If the algorithm stops before fully converging (because of
tol
ormax_iter
),labels_
andcluster_centers_
will not be consistent, i.e. thecluster_centers_
will not be the means of the points in each cluster. Also, the estimator will reassignlabels_
after the last iteration to makelabels_
consistent withpredict
on the training set.