scipy.cluster.vq.

kmeans2#

scipy.cluster.vq.kmeans2(data, k, iter=10, thresh=1e-05, minit='random', missing='warn', check_finite=True, *, rng=None, seed=None)[source] #

Classify a set of observations into k clusters using the k-means algorithm.

The algorithm attempts to minimize the Euclidean distance between observations and centroids. Several initialization methods are included.

Parameters:
datandarray

A ‘M’ by ‘N’ array of ‘M’ observations in ‘N’ dimensions or a length ‘M’ array of ‘M’ 1-D observations.

kint or ndarray

The number of clusters to form as well as the number of centroids to generate. If minit initialization string is ‘matrix’, or if a ndarray is given instead, it is interpreted as initial cluster to use instead.

iterint, optional

Number of iterations of the k-means algorithm to run. Note that this differs in meaning from the iters parameter to the kmeans function.

threshfloat, optional

(not used yet)

minitstr, optional

Method for initialization. Available methods are ‘random’, ‘points’, ‘++’ and ‘matrix’:

‘random’: generate k centroids from a Gaussian with mean and variance estimated from the data.

‘points’: choose k observations (rows) at random from data for the initial centroids.

‘++’: choose k observations accordingly to the kmeans++ method (careful seeding)

‘matrix’: interpret the k parameter as a k by M (or length k array for 1-D data) array of initial centroids.

missingstr, optional

Method to deal with empty clusters. Available methods are ‘warn’ and ‘raise’:

‘warn’: give a warning and continue.

‘raise’: raise an ClusterError and terminate the algorithm.

check_finitebool, optional

Whether to check that the input matrices contain only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs. Default: True

rng{None, int, numpy.random.Generator}, optional

If rng is passed by keyword, types other than numpy.random.Generator are passed to numpy.random.default_rng to instantiate a Generator. If rng is already a Generator instance, then the provided instance is used. Specify rng for repeatable function behavior.

If this argument is passed by position or seed is passed by keyword, legacy behavior for the argument seed applies:

  • If seed is None (or numpy.random), the numpy.random.RandomState singleton is used.

  • If seed is an int, a new RandomState instance is used, seeded with seed.

  • If seed is already a Generator or RandomState instance then that instance is used.

Changed in version 1.15.0: As part of the SPEC-007 transition from use of numpy.random.RandomState to numpy.random.Generator, this keyword was changed from seed to rng. For an interim period, both keywords will continue to work, although only one may be specified at a time. After the interim period, function calls using the seed keyword will emit warnings. The behavior of both seed and rng are outlined above, but only the rng keyword should be used in new code.

Returns:
centroidndarray

A ‘k’ by ‘N’ array of centroids found at the last iteration of k-means.

labelndarray

label[i] is the code or index of the centroid the ith observation is closest to.

See also

kmeans

Notes

kmeans2 has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library

CPU

GPU

NumPy

✅

n/a

CuPy

n/a

⛔

PyTorch

✅

⛔

JAX

⚠️ no JIT

⛔

Dask

⚠️ computes graph

n/a

See Support for the array API standard for more information.

References

[1]

D. Arthur and S. Vassilvitskii, "k-means++: the advantages of careful seeding", Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, 2007.

Examples

>>> fromscipy.cluster.vqimport kmeans2
>>> importmatplotlib.pyplotasplt
>>> importnumpyasnp

Create z, an array with shape (100, 2) containing a mixture of samples from three multivariate normal distributions.

>>> rng = np.random.default_rng()
>>> a = rng.multivariate_normal([0, 6], [[2, 1], [1, 1.5]], size=45)
>>> b = rng.multivariate_normal([2, 0], [[1, -1], [-1, 3]], size=30)
>>> c = rng.multivariate_normal([6, 4], [[5, 0], [0, 1.2]], size=25)
>>> z = np.concatenate((a, b, c))
>>> rng.shuffle(z)

Compute three clusters.

>>> centroid, label = kmeans2(z, 3, minit='points')
>>> centroid
array([[ 2.22274463, -0.61666946], # may vary
 [ 0.54069047, 5.86541444],
 [ 6.73846769, 4.01991898]])

How many points are in each cluster?

>>> counts = np.bincount(label)
>>> counts
array([29, 51, 20]) # may vary

Plot the clusters.

>>> w0 = z[label == 0]
>>> w1 = z[label == 1]
>>> w2 = z[label == 2]
>>> plt.plot(w0[:, 0], w0[:, 1], 'o', alpha=0.5, label='cluster 0')
>>> plt.plot(w1[:, 0], w1[:, 1], 'd', alpha=0.5, label='cluster 1')
>>> plt.plot(w2[:, 0], w2[:, 1], 's', alpha=0.5, label='cluster 2')
>>> plt.plot(centroid[:, 0], centroid[:, 1], 'k*', label='centroids')
>>> plt.axis('equal')
>>> plt.legend(shadow=True)
>>> plt.show()
../../_images/scipy-cluster-vq-kmeans2-1.png
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