A Python package for optimal 1D k-means clustering
A Python library with an implementation of k-means clustering on 1D data, based on the algorithm in (Xiaolin 1991), as presented in section 2.2 of (Gronlund et al., 2017).
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 a 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.
kmeans1d supports Python 3.x.
kmeans1d is available on PyPI, the Python Package Index.
$ pip3 install kmeans1d
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]
The code in this repository has an MIT License.
 Wu, Xiaolin. "Optimal Quantization by Matrix Searching." Journal of Algorithms 12, no. 4 (December 1, 1991): 663
 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.
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