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For the latest updates as well as for a standalone application capable of reproducing this work please refer to the PhD-additions branch of this repository.

This repository contains the code used to produce the results of the manuscript: An empirical comparison between stochastic and deterministic centroid initialisation for K-Means variations.

Generate manuscript results

To reproduce the results of the paper run nag_init_methods_generate.m which will produce the folder NAG_init_res. This folder will be populated with several files in the format: [modelName]_model_[setNo].mat (for each clustering algorithm a subfolder will be created). Each of these files contains a struct array (rows: initialisation method, columns: number of data sets - default: 40). For stochastic methods multiple values are available based on the repetition of the clustering solution (default: 50).

Struct fields:

  • centers: initial clustering centroids.
  • idx: cluster index of each data point.
  • centroids: final clustering centroids.
  • iterations: number of iterations until convergence (not for Hartigan-Wong).
  • Silh2 & Silh: silhouette index of the clustering solution (Silh2 was used in the manuscript).
  • wcd: within-cluster-distance.
  • bcd: between-cluster-distance.
  • clPur: purity index of the clustering solution.

nag_init_methods_timing.m runs the execution time analysis. It requires the folder NAG_init_res generated by nag_init_methods_generate.m.

The results of nag_init_methods_generate.m and nag_init_methods_timing.m where then used to generate the figures and tables of the manuscript. For the results of a previous version of the manuscript (arXiv: https://arxiv.org/abs/1908.09946) code for plotting is provided, refer to commit 9e9a00

Current dependencies:

The results were produced using MATLAB R2018b with the following toolboxes:

  1. Statistics and Machine Learning Toolbox
  2. Parallel Computing Toolbox (if this toolbox is not available execution is still possible).
  3. The NAG Toolbox for MATLAB to run Hartigan and Wong's K-Means.

Citations for software and datasets that we have used in this project

Datasets

Clustering basic benchmark:

Fränti, Pasi, and Sami Sieranoja. "K-means properties on six clustering benchmark datasets." Applied Intelligence 48.12 (2018): 4743-4759.

Gap models:

Tibshirani, Robert, Guenther Walther, and Trevor Hastie. "Estimating the number of clusters in a data set via the gap statistic." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63.2 (2001): 411-423.

Weighted Gap models (YanYe):

Yan, Mingjin, and Keying Ye. "Determining the number of clusters using the weighted gap statistic." Biometrics 63.4 (2007): 1031-1037.

Brodinova dataset generator:

Brodinová, Šárka, et al. "Robust and sparse k-means clustering for high-dimensional data." Advances in Data Analysis and Classification (2017): 1-28.

MATLAB code was based on the R implementation of the algorithm; package: wrsk

Real datasets

Dua, D. and Graff, C. (2019). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.

Clustering Algorithms

Hartigan-Wong K-Means:

MATLAB's and Python's default K-Means clustering is Lloyd's K-Means (initialized with the K-Means++ method) while R uses Hartigan-Wong' K-Means. Here we use NAG Toolbox for MATLAB Hartigan and Wong's K-Means implementation thus in order to use this algorithm the toolbox is required.

Clustering Initialization

Random:

MacQueen, J. (1967, June). Some methods for classification and analysis of multivariate observations. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability (Vol. 1, No. 14, pp. 281-297).

K-Means++:

Original algorithm is described in the study of Arthur, D., & Vassilvitskii, S. (2007). k-means++: the advantages of careful seeding, p 1027–1035. In SODA'07: proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA..

MATLAB implementation was based on the instructions of the MSDN Magazine Blog: Test Run - K-Means++ Data Clustering

Maximin:

Stochastic version is based on the study of Gonzalez, T. F. (1985). Clustering to minimize the maximum intercluster distance. Theoretical computer science, 38, 293-306..

Deterministic version is based on the study of: Katsavounidis, I., Kuo, C. C. J., & Zhang, Z. (1994). A new initialization technique for generalized Lloyd iteration. IEEE Signal processing letters, 1(10), 144-146..

ROBIN:

Original algorithm (deterministic) is described in the study of Al Hasan, M., Chaoji, V., Salem, S., & Zaki, M. J. (2009). Robust partitional clustering by outlier and density insensitive seeding. Pattern Recognition Letters, 30(11), 994-1002..

MATLAB code was originally based on the R implementation of the algorithm (stochastic version); package: wrsk

Density K-Means++:

Nidheesh, N., KA Abdul Nazeer, and P. M. Ameer. "An enhanced deterministic K-Means clustering algorithm for cancer subtype prediction from gene expression data." Computers in biology and medicine 91 (2017): 213-221.

MATLAB code was based on the R implementation of the algorithm; code: dkmpp_0.1.0

Kaufman:

MATLAB implementation was based on the pseudocode of Pena, J. M., Lozano, J. A., & Larranaga, P. (1999). An empirical comparison of four initialization methods for the k-means algorithm. Pattern recognition letters, 20(10), 1027-1040.