k-MS: A novel clustering algorithm based on morphological reconstruction

Abstract This work proposes a clusterization algorithm called k-Morphological Sets (k-MS), based on morphological reconstruction and heuristics. k-MS is faster than the CPU-parallel k-Means in worst case scenarios and produces enhanced visualizations of the dataset as well as very distinct clusterizations. It is also faster than similar clusterization methods that are sensitive to density and shapes such as Mitosis and TRICLUST. In addition, k-MS is deterministic and has an intrinsic sense of maximal clusters that can be created for a given input sample and input parameters, differing from k-Means and other clusterization algorithms. In other words, given a constant k , a structuring element and a dataset, k-MS produces k or less clusters without using random/pseudo-random functions. Finally, the proposed algorithm also provides a straightforward means for removing noise from images or datasets in general.

[1]  Ian H. Witten,et al.  The WEKA data mining software: an update , 2009, SKDD.

[2]  David B. Shmoys,et al.  A Best Possible Heuristic for the k-Center Problem , 1985, Math. Oper. Res..

[3]  Chien-Hsing Chou,et al.  Short Papers , 2001 .

[4]  Leonardo Torok,et al.  A Mobile Game Controller Adapted to the Gameplay and User's Behavior Using Machine Learning , 2015, ICEC.

[5]  Mohammad Hossein Fazel Zarandi,et al.  Relative entropy collaborative fuzzy clustering method , 2015, Pattern Recognit..

[6]  T. Moon.  The expectation-maximization algorithm , 1996, IEEE Signal Process. Mag..

[7]  Fernando Torres Medina,et al.  Vectorial morphological reconstruction for brightness elimination in colour images , 2004, Real Time Imaging.

[8]  Sergei Vassilvitskii,et al.  k-means++: the advantages of careful seeding , 2007, SODA '07.

[9]  Jianhong Wu,et al.  Data clustering - theory, algorithms, and applications , 2007 .

[10]  Reid G. Simmons,et al.  Unsupervised learning of probabilistic models for robot navigation , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[11]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[12]  Marian Cristian Mihaescu,et al.  Using M Tree Data Structure as Unsupervised Classification Method , 2012, Informatica.

[13]  Vipin Kumar,et al.  Chameleon: Hierarchical Clustering Using Dynamic Modeling , 1999, Computer.

[14]  Nikos A. Vlassis,et al.  The global k-means clustering algorithm , 2003, Pattern Recognit..

[15]  Jingsheng Lei,et al.  A clustering ensemble: Two-level-refined co-association matrix with path-based transformation , 2015, Pattern Recognit..

[16]  H WittenIan,et al.  The WEKA data mining software , 2009 .

[17]  Débora C. Muchaluat-Saade,et al.  Hybrid analysis for indicating patients with breast cancer using temperature time series , 2016, Comput. Methods Programs Biomed..

[18]  Andrew McCallum,et al.  Efficient clustering of high-dimensional data sets with application to reference matching , 2000, KDD '00.

[19]  John A. Goldsmith,et al.  Unsupervised Learning of the Morphology of a Natural Language , 2001, CL.

[20]  Ramin Javadi,et al.  Clustering and outlier detection using isoperimetric number of trees , 2013, Pattern Recognit..

[21]  David H. Wolpert,et al.  Coevolutionary free lunches , 2005, IEEE Transactions on Evolutionary Computation.

[22]  Aristides Gionis,et al.  Clustering aggregation , 2005, 21st International Conference on Data Engineering (ICDE'05).

[23]  S. Goswami,et al.  Brain Tumour Detection Using Unsupervised Learning Based Neural Network , 2013, 2013 International Conference on Communication Systems and Network Technologies.

[24]  A. Rama Mohan Reddy,et al.  A fast DBSCAN clustering algorithm by accelerating neighbor searching using Groups method , 2016, Pattern Recognit..

[25]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[26]  Pedro Larrañaga,et al.  An empirical comparison of four initialization methods for the K-Means algorithm , 1999, Pattern Recognit. Lett..

[27]  Henk J. A. M. Heijmans,et al.  Fundamenta Morphologicae Mathematicae , 2000, Fundam. Informaticae.

[28]  Mohamed A. Ismail,et al.  A distance-relatedness dynamic model for clustering high dimensional data of arbitrary shapes and densities , 2009, Pattern Recognit..

[29]  Luc Vincent,et al.  Morphological grayscale reconstruction in image analysis: applications and efficient algorithms , 1993, IEEE Trans. Image Process..

[30]  Meng Wang,et al.  Image clustering based on sparse patch alignment framework , 2014, Pattern Recognit..

[31]  Xudong Jiang,et al.  A multi-prototype clustering algorithm , 2009, Pattern Recognit..

[32]  Rafael C. González,et al.  Digital image processing using MATLAB , 2006 .

[33]  Olga Sourina,et al.  Effective clustering and boundary detection algorithm based on Delaunay triangulation , 2008, Pattern Recognit. Lett..