Ckmeans clustering is an improvement on heuristic-based clustering approaches like Jenks. The algorithm was developed in Haizhou Wang and Mingzhou Song (2011) as a dynamic programming approach to the problem of clustering numeric data into groups with the least within-group sum-of-squared-deviations.
Minimizing the difference within groups – what Wang & Song refer to as
withinss, or within sum-of-squares – means that groups are optimally
homogenous within and the data is split into representative groups.
This is very useful for visualization, where you may want to represent
a continuous variable in discrete color or style groups. This function
can provide groups that emphasize differences between data.
Being a dynamic approach, this algorithm is based on two matrices that store incrementally-computed values for squared deviations and backtracking indexes.
Unlike the original implementation, this implementation does not include any code to automatically determine the optimal number of clusters: this information needs to be explicitly provided.
This is a port (including documentation) of David Schnurr's package https://github.com/schnerd/ckmeans, incorporating some improvements from Bill Mill's Python + Numpy implementation at https://github.com/llimllib/ckmeans.
On an M2 Pro, the algorithm will classify 100k i32 values between 0 and 250 into 7 classes in around 15 ms.
The "matrices" are nested vectors and thus don't have optimal memory layout. In addition, we're not trying to leverage any of the fast linear algebra libraries that might be available if we used e.g. ndarray.
Perhaps some property-based tests