MiniBatchDPMeans

Parameters

n_clustersint, default=1

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

init{‘k-means++’, ‘random’}, callable or array-like of shape (n_clusters, n_features), default=’k-means++’

Method for initialization:

‘k-means++’ : selects initial cluster centroids for deterministic initialization using sampling based on an empirical probability distribution of the points’ contribution to the overall inertia. This technique speeds up convergence. The algorithm implemented is “greedy k-means++”. It differs from the vanilla k-means++ by making several trials at each sampling step and choosing the best centroid among them.

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

If an array is passed, it should be of shape (n_clusters, n_features) and gives the initial centers.

If a callable is passed, it should take arguments X, n_clusters and a random state and return an initialization.

max_iterint, default=100

Maximum number of iterations over the complete dataset before stopping independently of any early stopping criterion heuristics.

batch_sizeint, default=1024

Size of the mini batches. For faster computations, you can set the batch_size greater than 256 * number of cores to enable parallelism on all cores.

verboseint, default=0

Verbosity mode.

compute_labelsbool, default=True

Compute label assignment and inertia for the complete dataset once the minibatch optimization has converged in fit.

random_stateint, RandomState instance or None, default=None

Determines random number generation for centroid initialization and random reassignment. Use an int to make the randomness deterministic. See Glossary.

tolfloat, default=0.0

Control early stopping based on the relative center changes as measured by a smoothed, variance-normalized of the mean center squared position changes.

max_no_improvementint, default=10

Control early stopping based on the consecutive number of mini batches that does not yield an improvement on the smoothed inertia.

init_sizeint, default=None

Number of samples to randomly sample for speeding up the initialization (sometimes at the expense of accuracy): the only algorithm is initialized by running a batch DPMeans on a random subset of the data. This needs to be larger than n_clusters.

n_initint, default=3

Number of random initializations that are tried. The algorithm is only run once, using the best of the n_init initializations as measured by inertia.

reassignment_ratiofloat, default=0.01

Control the fraction of the maximum number of counts for a center to be reassigned. A higher value means that low count centers are more easily reassigned, which means that the model will take longer to converge, but should converge in a better clustering.

deltafloat, default=1.0

Parameter controlling the number of clusters in the DP-means algorithm. A higher value will lead to fewer clusters.

Attributes

cluster_centers_ndarray of shape (n_clusters, n_features)

Coordinates of cluster centers.

labels_ndarray of shape (n_samples,)

Labels of each point (if compute_labels is set to True).

inertia_float

The value of the inertia criterion associated with the chosen partition if compute_labels is set to True. If compute_labels is set to False, it’s an approximation of the inertia based on an exponentially weighted average of the batch inertiae. The inertia is defined as the sum of square distances of samples to their cluster center, weighted by the sample weights if provided.

n_iter_int

Number of iterations over the full dataset.

n_features_in_int

Number of features seen during fit.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

DPMeans : The full batch version of DP-Means clustering.

KMeansThe classic implementation of the clustering method based on the

Lloyd’s algorithm. It consumes the whole set of input data at each iteration.

When there are too few points in the dataset, some centers may be duplicated, which means that a proper clustering in terms of the number of requesting clusters and the number of returned clusters will not always match. One solution is to set reassignment_ratio=0, which prevents reassignments of clusters that are too small.

>>> from pdc_dp_means import MiniBatchDPMeans
>>> import numpy as np
>>> X = np.array([[1, 2], [1, 4], [1, 0],
...               [4, 2], [4, 0], [4, 4],
...               [4, 5], [0, 1], [2, 2],
...               [3, 2], [5, 5], [1, -1]])
>>> # manually fit on batches
>>> dpmeans = MiniBatchDPMeans(n_clusters=1,
...                            random_state=0,
...                            batch_size=6,
...                            n_init=3,
...                            delta=1.0)
>>> dpmeans = dpmeans.partial_fit(X[0:6,:])
>>> dpmeans = dpmeans.partial_fit(X[6:12,:])
>>> dpmeans.cluster_centers_
array([[3.375, 3.  ],
    [0.75 , 0.5 ]])
>>> dpmeans.predict([[0, 0], [4, 4]])
array([1, 0], dtype=int32)
>>> # fit on the whole data
>>> dpmeans = MiniBatchDPMeans(n_clusters=1,
...                            random_state=0,
...                            batch_size=6,
...                            max_iter=10,
...                            n_init=3,
...                            delta=1.0).fit(X)
>>> dpmeans.cluster_centers_
array([[3.55102041, 2.48979592],
    [1.06896552, 1.        ]])
>>> dpmeans.predict([[0, 0], [4, 4]])
array([1, 0], dtype=int32)

API

class pdc_dp_means.MiniBatchDPMeans(n_clusters=1, *, init='k-means++', max_iter=100, batch_size=1024, verbose=0, compute_labels=True, random_state=None, tol=0.0, max_no_improvement=10, init_size=None, n_init=3, reassignment_ratio=0.01, delta=1.0)

Bases: KMeans

Parameters

n_clustersint, default=1

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

init{‘k-means++’, ‘random’}, callable or array-like of shape (n_clusters, n_features), default=’k-means++’

Method for initialization:

‘k-means++’ : selects initial cluster centroids for deterministic initialization using sampling based on an empirical probability distribution of the points’ contribution to the overall inertia. This technique speeds up convergence. The algorithm implemented is “greedy k-means++”. It differs from the vanilla k-means++ by making several trials at each sampling step and choosing the best centroid among them.

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

If an array is passed, it should be of shape (n_clusters, n_features) and gives the initial centers.

If a callable is passed, it should take arguments X, n_clusters and a random state and return an initialization.

max_iterint, default=100

Maximum number of iterations over the complete dataset before stopping independently of any early stopping criterion heuristics.

batch_sizeint, default=1024

Size of the mini batches. For faster computations, you can set the batch_size greater than 256 * number of cores to enable parallelism on all cores.

verboseint, default=0

Verbosity mode.

compute_labelsbool, default=True

Compute label assignment and inertia for the complete dataset once the minibatch optimization has converged in fit.

random_stateint, RandomState instance or None, default=None

Determines random number generation for centroid initialization and random reassignment. Use an int to make the randomness deterministic. See Glossary.

tolfloat, default=0.0

Control early stopping based on the relative center changes as measured by a smoothed, variance-normalized of the mean center squared position changes.

max_no_improvementint, default=10

Control early stopping based on the consecutive number of mini batches that does not yield an improvement on the smoothed inertia.

init_sizeint, default=None

Number of samples to randomly sample for speeding up the initialization (sometimes at the expense of accuracy): the only algorithm is initialized by running a batch DPMeans on a random subset of the data. This needs to be larger than n_clusters.

n_initint, default=3

Number of random initializations that are tried. The algorithm is only run once, using the best of the n_init initializations as measured by inertia.

reassignment_ratiofloat, default=0.01

Control the fraction of the maximum number of counts for a center to be reassigned. A higher value means that low count centers are more easily reassigned, which means that the model will take longer to converge, but should converge in a better clustering.

deltafloat, default=1.0

Parameter controlling the number of clusters in the DP-means algorithm. A higher value will lead to fewer clusters.

Attributes

cluster_centers_ndarray of shape (n_clusters, n_features)

Coordinates of cluster centers.

labels_ndarray of shape (n_samples,)

Labels of each point (if compute_labels is set to True).

inertia_float

The value of the inertia criterion associated with the chosen partition if compute_labels is set to True. If compute_labels is set to False, it’s an approximation of the inertia based on an exponentially weighted average of the batch inertiae. The inertia is defined as the sum of square distances of samples to their cluster center, weighted by the sample weights if provided.

n_iter_int

Number of iterations over the full dataset.

n_features_in_int

Number of features seen during fit.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

DPMeans : The full batch version of DP-Means clustering.

KMeansThe classic implementation of the clustering method based on the

Lloyd’s algorithm. It consumes the whole set of input data at each iteration.

When there are too few points in the dataset, some centers may be duplicated, which means that a proper clustering in terms of the number of requesting clusters and the number of returned clusters will not always match. One solution is to set reassignment_ratio=0, which prevents reassignments of clusters that are too small.

>>> from pdc_dp_means import MiniBatchDPMeans
>>> import numpy as np
>>> X = np.array([[1, 2], [1, 4], [1, 0],
...               [4, 2], [4, 0], [4, 4],
...               [4, 5], [0, 1], [2, 2],
...               [3, 2], [5, 5], [1, -1]])
>>> # manually fit on batches
>>> dpmeans = MiniBatchDPMeans(n_clusters=1,
...                            random_state=0,
...                            batch_size=6,
...                            n_init=3,
...                            delta=1.0)
>>> dpmeans = dpmeans.partial_fit(X[0:6,:])
>>> dpmeans = dpmeans.partial_fit(X[6:12,:])
>>> dpmeans.cluster_centers_
array([[3.375, 3.  ],
    [0.75 , 0.5 ]])
>>> dpmeans.predict([[0, 0], [4, 4]])
array([1, 0], dtype=int32)
>>> # fit on the whole data
>>> dpmeans = MiniBatchDPMeans(n_clusters=1,
...                            random_state=0,
...                            batch_size=6,
...                            max_iter=10,
...                            n_init=3,
...                            delta=1.0).fit(X)
>>> dpmeans.cluster_centers_
array([[3.55102041, 2.48979592],
    [1.06896552, 1.        ]])
>>> dpmeans.predict([[0, 0], [4, 4]])
array([1, 0], dtype=int32)

fit(X, y=None, sample_weight=None)

Compute the centroids on X by chunking it into mini-batches.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features)

Training instances to cluster. It must be noted that the data will be converted to C ordering, which will cause a memory copy if the given data is not C-contiguous. If a sparse matrix is passed, a copy will be made if it’s not in CSR format.

yIgnored

Not used, present here for API consistency by convention.

sample_weightarray-like of shape (n_samples,), default=None

The weights for each observation in X. If None, all observations are assigned equal weight.

New in version 0.20.

Returns

selfobject

Fitted estimator.

partial_fit(X, y=None, sample_weight=None)

Update k means estimate on a single mini-batch X.

Parameters

X{array-like, sparse matrix} of shape (n_samples, n_features)

Training instances to cluster. It must be noted that the data will be converted to C ordering, which will cause a memory copy if the given data is not C-contiguous. If a sparse matrix is passed, a copy will be made if it’s not in CSR format.

yIgnored

Not used, present here for API consistency by convention.

sample_weightarray-like of shape (n_samples,), default=None

The weights for each observation in X. If None, all observations are assigned equal weight.

Returns

selfobject

Return updated estimator.

predict(X, sample_weight=None)

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} of shape (n_samples, n_features)

New data to predict.

sample_weightarray-like of shape (n_samples,), default=None

The weights for each observation in X. If None, all observations are assigned equal weight.

Returns

labelsndarray of shape (n_samples,)

Index of the cluster each sample belongs to.