2017 Taiwan and Japan Conference on Circuits and Systems
Okayama Convention Center, Okayama, Japan. August 21-23, 2017

Investigation of a New Clustering Method used
Modified Firefly Algorithm for K-Means Clustering
Masaki TakeuchiThomas Ott

Dept. of Electrical
Zurich University
and Electronic Eng.,of Applied Sciences
thomas.ott@zhaw.ch
Tokushima University
2-1 Minami-Josanjima,Tokushima, 770–8506, Japan
masaki@ee.tokushima-u.ac.jp

Haruna Matsushita

Yoko Uwate and Yoshifumi Nishio

Dept. of Electronics
Dept. of Electricaland Info. Eng.,and Electronic Eng.,
Kagawa University
Tokushima University
2217-20 Hayashi-cho,
2-1 Minami-Josanjima,Takamatsu, Kagawa,Tokushima, 770–8506, Japan761–0396, Japan{ uwate , nishio }@ee.tokushima-u.ac.jp
haruna@eng.kagawa-u.ac.jp

S UMMARYClustering is a popular data analysis technique used for data analysis, image analysis, data mining and the other fields ofscience and engineering. The goal of clustering is to find homogeneous groups of data points in a data set. Each group is calleda cluster and is characterized by the fact that objects belonging to the same group are more similar than objects belonging todifferent groups. One of the most famous clustering methods is the K-means algorithm. It is used if the number of clusters is
known and the clusters tend to be spherical. The goal of this method is to find K cluster centers and assign each object to theclosest cluster center such that the sum of the squared distances between the objects and the corresponding cluster centers isminimal. This means that the K-means clustering problem is an optimization problem.
Senthilnath et al.[1] proposed an algorithm that used the firefly algorithm for K-means clustering (KMFA). Numericalexperiments have indicated that this algorithm is more efficient algorithm than the standard algorithm or other optimization
heuristics. The firefly algorithm (FA) has been proposed by Yang in 2007 and is based on the idealized behavior of the flashing
characteristics of fireflies[2], [3], [4]. FA is an efficient optimization algorithm because it has a deterministic component anda random component. Almost all algorithms having only the deterministic component are local search algorithms, for which
there is a risk of being trapped in a local optimum. However, the random component makes it possible to escape from such alocal optimum.
In this study, we propose a new clustering method that combines K-means clustering and improved firefly algorithm (KMIFA).
We modify the random component of FA to suit our concept. In KMIFA, at the beginning of the search, all fireflies movewith a relatively strong random influence. Hence, they can more easily escape from local optima. As the number of iterations
increases, the firefly tends to converge. We compare the conventional K-means algorithm, the previous Senthilnath’s study
KMFA and our proposed algorithm KMIFA using several data models that have several spherical clusters. These experiments
indicate that our algorithm is more efficient than the other algorithms.
R EFERENCES[1] J. Senthilnath, S.N. Omkar and V. Mani, “Clustering using Firefly Algorithm: Performance Study”, Swarm and Evolutionary Computation 1, pp. 164–171,
2011.
[2] X.S. Yang, Nature-Inspired Metaheuristic Algorithms Second Edition, Luniver Press, 2010.
[3] S. Lukasik and S. Zak, “Firefly Algorithm for Continuous Constrained Optimization Tasks”, Computational Collective Intelligence, Semantic Web, Social
Networks and Multiagent Systems, Vol. 5796 of the Series Lecture Notes in Computer Science, pp. 97–106, 2009.
[4] H. Matsushita, “Firefly Algorithm with Dynamically Changing Connections”, Proceedings of International Symposium on Nonlinear Theory and its
Application (NOLTA’14), pp. 906–909, 2014.

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