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ISO-SPLIT is an efficient clustering algorithm that handles an unknown number of unimodal clusters in low to moderate dimension, without any user-adjustable parameters. It is based on repeated tests for unimodality---using isotonic regression and a modified Hartigan dip test---applied to 1D projections of pairs of putative clusters. It handles well non-Gaussian clusters of widely varying densities and populations, and in such settings has been shown to outperform K-means variants, Gaussian mixture models, and density-based methods.

This repository contains an efficient single-threaded implementation in C++, with a MATLAB/MEX interface.

It was invented and coded by Jeremy Magland, with contributions to the algorithm and tests by Alex Barnett, at SCDA/Flatiron Institute.

(C) Jeremy Magland 2015-2018.

Dependencies and compilation

For now, C++ and MATLAB codes are together, and MATLAB is a dependency.

In MATLAB, from the repository's root directory, do:

cd matlab
cd ..

You should get a plot showing three correctly-clustered point clouds.


Here is a simple equal-population isotropic Gaussian demo with 100000 points in MATLAB. Make sure that the matlab directory is in your MATLAB path:

d = 20;                                              % number of dimensions
n = 1e4;                                             % points per cluster
K = 10;                                              % number of clusters
rng(1);                                              % fix the seed
X = randn(d,K*n) + 2.0*kron(randn(d,K),ones(1,n));   % N=K*n points in d dims
L = isosplit5_mex(X);                                % cluster: takes 2 sec
k = mode(reshape(L,[n,K]),1);                        % get gross labeling
fprintf('gross label errors: %d\n',sum(sort(k)-(1:K)))
fprintf('number of points misclassified: %d\n',sum(L~=kron(k,ones(1,n))))

The outputs should be 0 and 14. The reader (once they have parsed the last three lines of code above) should conclude that the number of clusters was correctly found, and that 14 out of 100000 points were misclassified.

Further usage and tests

This repo also contains a hybrid MATLAB/C++ implementation (isosplit5) which still uses C++/MEX for the isocut (and jisotonic) stages. The interface allows control of various algorithm parameters (see help isosplit5). This code is about 10x slower than the pure C++ version (isosplit5_mex), on an i7 laptop. To use this, do compile_mex_isocut5. Then, running isosplit5 with no arguments does a simple 2D self-test of both the hybrid and the pure C++ versions, and produces the above picture.


"Unimodal clustering using isotonic regression: ISO-SPLIT," J. F. Magland and A. H. Barnett. technical report (2016). stat.ME/1508.04841v2

"A fully automated approach to spike sorting," J. E. Chung, J. F. Magland, A. H. Barnett, V. M. Tolosa, A. C. Tooker, K. Y. L ee, K. G. Shah, S. H. Felix, L. M. Frank, L. F. Greengard. NEURON 95(6) 1381–1394 (2017)

To do

  • calling from C++ demo
  • separate the src and matlab directories
  • openmp
  • python wrapper
  • more impressive pic/demos


ISO-SPLIT clustering (stand-alone version)



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