C++ fast hierarchical clustering algorithms

This is a simplified C++ interface to the fast implementations of hierarchical clustering by Daniel Müllner. The original library with interfaces to R and Python can be found on danifold.net and is described in:

Daniel Müllner: "fastcluster: Fast Hierarchical, Agglomerative Clustering Routines for R and Python." Journal of Statistical Software 53, no. 9, pp. 1-18 (2013)

Daniel Müllner has compared the performance of different hierarchical clustering algorithms and implemented the fastest of them in C++ with R and Python interfaces. Whilst these interfaces are described in the above journal article, direct use of the underlying C++ functions is tricky and undocumented. To simplify this, I have written a C++ interface that hides the intricacies of the internal output formats behind a single function (hclust_fast) and provides two simple functions for the actual partitioning step (cutree_k and cutree_cdist).

How to call the library

The interface for the basic clustering algorithms requires a condensed distance matrix, which is the upper triangle (without the diagonal elements) of the full distance matrix. Here is an example for its construction where n is the number of observables x:

double* distmat = new double[(n*(n-1))/2];
int k,i,j;
for (i=k=0; i<n; i++) {
  for (j=i+1; j<n; j++) {
    // compute distance between observables i and j  
    distmat[k] = distance(x[i], x[j]);
    k++;
  }
}

The actual clustering is done by the function hclust_fast, which supports four methods for defining a cluster distance from individual distances (see fastcluster.h for a description of the methods):

int* merge = new int[2*(n-1)];
double* height = new double[n-1];
hclust_fast(n, distmat, HCLUST_METHOD_SINGLE, merge, height);

height is filled with the cluster distance for each step. This can be useful for automatically determining the clustering break point, e.g, with the "elbow method". merge contains the dendrogram in the encoding of the R function hclust. Fortunately, you do not need to understand this encoding, because there are two function for further processing the output:

int* labels = new int[n];
// partitioning into nclust clusters
cutree_k(n, merge, nclust, labels);
// stop clustering at step with custer distance >= cdist
cutree_cdist(npoints, merge, height, cdist, labels);

labels[i] is filled with the cluster label of observable x[i]. Cluster labels start at zero. Final note: do not forget to free the memory after you are done with the variables:

delete[] distmat;
delete[] merge;
delete[] height;
delete[] labels;

How to compile the library

For using the library, the following source files are needed:

• fastcluster_dm.cpp, fastcluster_R_dm.cpp
  This is the original code by Daniel Müllner, which is included by fastcluster.cpp and therefore need not be compiled to object code

• fastcluster.[h|cpp]
  This is the simplified C++ interface and fastcluster.cpp is the only file that must be compiled.

A simple demo is implemented in demo.cpp, which can be compiled and run with

make
./hclust-demo -m complete lines.csv

It creates two clusters of line segments such that the segment angle between line segments of different clusters have a maximum (cosine) dissimilarity. For visualizing the result, plotresult.r can be used as follows (requires R to be installed):

./hclust-demo -m complete lines.csv | Rscript plotresult.r

Authors & Copyright

• Daniel Müllner, 2011, http://danifold.net

• Christoph Dalitz, 2018-2020, https://lionel.kr.hs-niederrhein.de/~dalitz/data/hclust/

License

This code is provided under a BSD-style license. See the file LICENSE for details.