Clustering based on the Krill Herd Algorithm with selected validity measures

This paper describes a new approach to metaheuristic-based data clustering by means of Krill Herd Algorithm (KHA). In this work, KHA is used to find centres of the cluster groups. Moreover, the number of clusters is set up at the beginning of the procedure, and during the subsequent iterations of the optimization algorithm, particular solutions are evaluated by selected validity criteria. The proposed clustering algorithm has been numerically verified using twelve data sets taken from the UCI Machine Learning Repository. Additionally, all cases of clustering were compared with the most popular method of k-means, through the Rand Index being applied as a validity measure.

[1]  Kevin Baker,et al.  Classification of radar returns from the ionosphere using neural networks , 1989 .

[2]  Olatz Arbelaitz,et al.  An extensive comparative study of cluster validity indices , 2013, Pattern Recognit..

[3]  Sergio M. Savaresi,et al.  Cluster Selection in Divisive Clustering Algorithms , 2002, SDM.

[4]  Paul Compton,et al.  Inductive knowledge acquisition: a case study , 1987 .

[5]  A. Asuncion,et al.  UCI Machine Learning Repository, University of California, Irvine, School of Information and Computer Sciences , 2007 .

[6]  Sabu M. Thampi,et al.  A Discrete Krill Herd Method with Multilayer Coding Strategy for Flexible Job-Shop Scheduling Problem , 2016 .

[7]  Mohammad Saniee Abadeh,et al.  Breast cancer detection using a multi-objective binary Krill Herd algorithm , 2014, 2014 21th Iranian Conference on Biomedical Engineering (ICBME).

[8]  Lior Rokach,et al.  Clustering Methods , 2005, The Data Mining and Knowledge Discovery Handbook.

[9]  Amir Hossein Gandomi,et al.  Stud krill herd algorithm , 2014, Neurocomputing.

[10]  G. Krishna,et al.  A heuristic clustering algorithm using union of overlapping pattern-cells , 1979, Pattern Recognit..

[11]  Pasi Fränti,et al.  Iterative shrinking method for clustering problems , 2006, Pattern Recognit..

[12]  Miin-Shen Yang.  A survey of fuzzy clustering , 1993 .

[13]  Piotr A. Kowalski,et al.  Data-Driven Fuzzy Modeling and Control with Kernel Density Based Clustering Technique , 2008 .

[14]  William M. Rand,et al.  Objective Criteria for the Evaluation of Clustering Methods , 1971 .

[15]  P. K. Chattopadhyay,et al.  Application of bio-inspired krill herd algorithm to combined heat and power economic dispatch , 2014, 2014 IEEE Innovative Smart Grid Technologies - Asia (ISGT ASIA).

[16]  Jan Paul Siebert,et al.  Vehicle Recognition Using Rule Based Methods , 1987 .

[17]  Janez Demsar,et al.  Statistical Comparisons of Classifiers over Multiple Data Sets , 2006, J. Mach. Learn. Res..

[18]  Amir Hossein Gandomi,et al.  A new improved krill herd algorithm for global numerical optimization , 2014, Neurocomputing.

[19]  T. Caliński,et al.  A dendrite method for cluster analysis , 1974 .

[20]  Donald W. Bouldin,et al.  A Cluster Separation Measure , 1979, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .

[22]  Piotr A. Kowalski,et al.  Experimental Study of Selected Parameters of the Krill Herd Algorithm , 2014, IEEE Conf. on Intelligent Systems.

[23]  S. S. Ravi,et al.  Agglomerative Hierarchical Clustering with Constraints: Theoretical and Empirical Results , 2005, PKDD.

[24]  J. Bezdek,et al.  FCM: The fuzzy c-means clustering algorithm , 1984 .

[25]  F. Malerba,et al.  The Geography of Innovation and Economic Clustering: Some Introductory Notes , 2001 .

[26]  Piotr A. Kowalski,et al.  The column-oriented database partitioning optimization based on the natural computing algorithms , 2015, 2015 Federated Conference on Computer Science and Information Systems (FedCSIS).

[27]  Piotr A. Kowalski,et al.  Training Neural Networks with Krill Herd Algorithm , 2015, Neural Processing Letters.

[28]  Piotr A. Kowalski,et al.  Complete Gradient Clustering Algorithm for Features Analysis of X-Ray Images , 2010 .

[29]  Terrence J. Sejnowski,et al.  Analysis of hidden units in a layered network trained to classify sonar targets , 1988, Neural Networks.

[30]  Charu C. Aggarwal,et al.  Data Clustering: Algorithms and Applications , 2014 .

[31]  Jianping Zhang,et al.  Selecting Typical Instances in Instance-Based Learning , 1992, ML.

[32]  Piotr A. Kowalski,et al.  Interval probabilistic neural network , 2015, Neural Computing and Applications.

[33]  Bin Zhang,et al.  Defining clusters from a hierarchical cluster tree: the Dynamic Tree Cut package for R , 2008, Bioinform..

[34]  Elke Achtert,et al.  Evaluation of Clusterings -- Metrics and Visual Support , 2012, 2012 IEEE 28th International Conference on Data Engineering.

[35]  Malgorzata Charytanowicz,et al.  A Complete Gradient Clustering Algorithm , 2011, AICI.

[36]  Piotr A. Kowalski,et al.  Fuzzy Models Synthesis with Kernel-Density-Based Clustering Algorithm , 2008, 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery.

[37]  Piotr A. Kowalski,et al.  The Complete Gradient Clustering Algorithm: properties in practical applications , 2012 .

[38]  J. Ross Quinlan,et al.  Induction of Decision Trees , 1986, Machine Learning.

[39]  P. Rousseeuw.  Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

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

[41]  Taher Niknam,et al.  An efficient hybrid approach based on PSO, ACO and k-means for cluster analysis , 2010, Appl. Soft Comput..

[42]  Abhay Singh,et al.  Comparative Study of Krill Herd, Firefly and Cuckoo Search Algorithms for Unimodal and Multimodal Optimization , 2014 .

[43]  W. Welch.  Algorithmic complexity: three NP- hard problems in computational statistics , 1982 .

[44]  Radovan R. Bulatović,et al.  Modified Krill Herd (MKH) algorithm and its application in dimensional synthesis of a four-bar linkage , 2016 .

[45]  Chun-Wei Tsai,et al.  Recent Development of Metaheuristics for Clustering , 2013, MUSIC.

[46]  Amir Hossein Alavi,et al.  Krill herd: A new bio-inspired optimization algorithm , 2012 .