kmeans1d

A Python library with an implementation of k-means clustering on 1D data, based on the algorithm from Xiaolin (1991), as presented by Gronlund et al. (2017, Section 2.2).

Globally optimal k-means clustering is NP-hard for multi-dimensional data. Lloyd's algorithm is a popular approach for finding a locally optimal solution. For 1-dimensional data, there are polynomial time algorithms. The algorithm implemented here is an O(kn + n log n) dynamic programming algorithm for finding the globally optimal k clusters for n 1D data points.

The code is written in C++, and wrapped with Python.

Requirements

kmeans1d supports Python 3.x.

Installation

kmeans1d is available on PyPI, the Python Package Index.

$ pip3 install kmeans1d

Example Usage

import kmeans1d

x = [4.0, 4.1, 4.2, -50, 200.2, 200.4, 200.9, 80, 100, 102]
k = 4

clusters, centroids = kmeans1d.cluster(x, k)

print(clusters)   # [1, 1, 1, 0, 3, 3, 3, 2, 2, 2]
print(centroids)  # [-50.0, 4.1, 94.0, 200.5]

Tests

Tests are in tests/.

# Run tests
$ python3 -m unittest discover tests -v

Development

The underlying C++ code can be built in-place, outside the context of pip. This requires Python development tools for building Python modules (e.g., the python3-dev package on Ubuntu). gcc, clang, and MSVC have been tested.

$ python3 setup.py build_ext --inplace

The packages GitHub action can be manually triggered (Actions > packages > Run workflow) to build wheels and a source distribution.

License

The code in this repository has an MIT License.

See LICENSE.

References

[1] Wu, Xiaolin. "Optimal Quantization by Matrix Searching." Journal of Algorithms 12, no. 4 (December 1, 1991): 663

[2] Gronlund, Allan, Kasper Green Larsen, Alexander Mathiasen, Jesper Sindahl Nielsen, Stefan Schneider, and Mingzhou Song. "Fast Exact K-Means, k-Medians and Bregman Divergence Clustering in 1D." ArXiv:1701.07204 [Cs], January 25, 2017. http://arxiv.org/abs/1701.07204.