8.1.3. sklearn.cluster.KMeans

class sklearn.cluster.KMeans(k=8, init='k-means++', n_init=10, max_iter=300, tol=0.0001, precompute_distances=True, verbose=0, random_state=None, copy_x=True)

K-Means clustering

Parameters :

k : int, optional, default: 8

The number of clusters to form as well as the number of centroids to generate.

max_iter : int

Maximum number of iterations of the k-means algorithm for a single run.

n_init: int, optional, 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 init is an 2d array, it is used as a seed for the centroids

precompute_distances : boolean

Precompute distances (faster but takes more memory).

tol: float, optional default: 1e-4 :

Relative tolerance w.r.t. 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.

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.

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.

Attributes

cluster_centers_: array, [n_clusters, n_features]	Coordinates of cluster centers
labels_:	Labels of each point
inertia_: float	The value of the inertia criterion associated with the chosen partition.

Methods

fit(X[, y])	Compute k-means
predict(X)	Predict the closest cluster each sample in X belongs to.
score(X)	Opposite of the value of X on the K-means objective.
set_params(**params)	Set the parameters of the estimator.
transform(X[, y])	Transform the data to a cluster-distance space

__init__(k=8, init='k-means++', n_init=10, max_iter=300, tol=0.0001, precompute_distances=True, verbose=0, random_state=None, copy_x=True)

fit(X, y=None)

Compute k-means

predict(X)

Predict the closest cluster each sample in X belongs to.

In the vector quantization literature, cluster_centers_ is called the code book and each value returned by predict is the index of the closest code in the code book.

Parameters :

X: {array-like, sparse matrix}, shape = [n_samples, n_features] :

New data to predict.

Returns :

Y : array, shape [n_samples,]

Index of the closest center each sample belongs to.

score(X)

Opposite of the value of X on the K-means objective.

Parameters :

X: {array-like, sparse matrix}, shape = [n_samples, n_features] :

New data.

Returns :

score: float :

Opposite of the value of X on the K-means objective.

set_params(**params)

Set the parameters of the estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns :self :

transform(X, y=None)

Transform the data to a cluster-distance space

In the new space, each dimension is the distance to the cluster centers. Note that even if X is sparse, the array returned by transform will typically be dense.

Parameters :

X: {array-like, sparse matrix}, shape = [n_samples, n_features] :

New data to transform.

Returns :

X_new : array, shape [n_samples, k]

X transformed in the new space.