KMeans

Incremental k-means.

The most common way to implement batch k-means is to use Lloyd's algorithm, which consists in assigning all the data points to a set of cluster centers and then moving the centers accordingly. This requires multiple passes over the data and thus isn't applicable in a streaming setting.

In this implementation we start by finding the cluster that is closest to the current observation. We then move the cluster's central position towards the new observation. The halflife parameter determines by how much to move the cluster toward the new observation. You will get better results if you scale your data appropriately.

Parameters

• n_clusters – defaults to 5

  Maximum number of clusters to assign.

• halflife – defaults to 0.5

  Amount by which to move the cluster centers, a reasonable value if between 0 and 1.

• mu – defaults to 0

  Mean of the normal distribution used to instantiate cluster positions.

• sigma – defaults to 1

  Standard deviation of the normal distribution used to instantiate cluster positions.

• p – defaults to 2

  Power parameter for the Minkowski metric. When p=1, this corresponds to the Manhattan distance, while p=2 corresponds to the Euclidean distance.

• seed (int) – defaults to None

  Random seed used for generating initial centroid positions.

Attributes

• centers (dict)

  Central positions of each cluster.

Examples

In the following example the cluster assignments are exactly the same as when using sklearn's batch implementation. However changing the halflife parameter will produce different outputs.

>>> from river import cluster
>>> from river import stream

>>> X = [
...     [1, 2],
...     [1, 4],
...     [1, 0],
...     [-4, 2],
...     [-4, 4],
...     [-4, 0]
... ]

>>> k_means = cluster.KMeans(n_clusters=2, halflife=0.1, sigma=3, seed=42)

>>> for i, (x, _) in enumerate(stream.iter_array(X)):
...     k_means = k_means.learn_one(x)
...     print(f'{X[i]} is assigned to cluster {k_means.predict_one(x)}')
[1, 2] is assigned to cluster 1
[1, 4] is assigned to cluster 1
[1, 0] is assigned to cluster 0
[-4, 2] is assigned to cluster 1
[-4, 4] is assigned to cluster 1
[-4, 0] is assigned to cluster 0

>>> k_means.predict_one({0: 0, 1: 0})
0

>>> k_means.predict_one({0: 4, 1: 4})
1

Methods

learn_one

Update the model with a set of features x.

Parameters

• x (dict)

Returns

Clusterer: self

learn_predict_one

Equivalent to k_means.learn_one(x).predict_one(x), but faster.

Parameters

• x

predict_one

Predicts the cluster number for a set of features x.

Parameters

• x (dict)

Returns

int: A cluster number.

References

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1. Sequential k-Means Clustering ↩

2. Sculley, D., 2010, April. Web-scale k-means clustering. In Proceedings of the 19th international conference on World wide web (pp. 1177-1178 ↩