The package provides a powerful set of tools for fast, optimal, and reproducible univariate clustering by dynamic programming. It is practical to cluster millions of sample points into a few clusters in seconds using a single core on a typical desktop computer. It solves four types of problem, including univariate \(k\)-means, \(k\)-median, \(k\)-segments, and multi-channel weighted \(k\)-means. Dynamic programming is used to minimize the (weighted) sum of within-cluster distances using respective metrics. Its advantage over heuristic clustering in efficiency and accuracy is increasingly pronounced as the number of clusters \(k\) increases. Weighted \(k\)-means can also optimally segment time series to perform peak calling. An auxiliary function generates histograms that are adaptive to patterns in data. The package is used to identify dysregulated genomic zones in human cancers (Song and Zhong, 2020) <10.1093/bioinformatics/btaa613>.

The Ckmeans.1d.dp algorithm clusters (weighted) univariate data given by a numeric vector \(x\) into \(k\) groups by dynamic programming (Wang and Song, 2011) <doi:10.32614/RJ-2011-015> (Song and Zhong, 2020) <10.1093/bioinformatics/btaa613>. It guarantees the optimality of clustering—the total of within-cluster sums of squares is always the minimum given the number of clusters \(k\). In contrast, heuristic univariate clustering algorithms may be non-optimal or inconsistent from run to run. As unequal non-negative weights are supported for each point, the algorithm can also segment a time course using the time points as input and the values at each time point as weight. Utilizing the optimal clusters, a function can generate histograms adaptive to patterns in data.

Excluding the time for sorting \(x\), the default weighted univariate clustering algorithm takes a runtime of \(O(kn)\) (Song and Zhong, 2020) <10.1093/bioinformatics/btaa613>, linear in both sample size \(n\) and the number of clusters \(k\), using a new divide-and-conquer strategy based on a theoretical result on matrix search (Aggarwal et al., 1987) <doi:10.1007/BF01840359> implemented via a novel in-place search space reduction method (Song and Zhong, 2020) <10.1093/bioinformatics/btaa613>. The space complexity is \(O(kn)\). This method is numerically stable.

This package provides a powerful alternative to heuristic clustering and also new functionality for weighted clustering, segmentation, and peak calling with guaranteed optimality.

`install.packages("Ckmeans.1d.dp")`