平成 29 年度電気関係学会四国支部連合大会 講演論文集 (2017 愛媛大学)
2017 SHIKOKU-SECTION JOINT CONVENTION RECORD OF THE INSTITUTES OF ELECTRICAL AND RELATED ENGINEERS (EHIME)

15-2
Parameter Setting of K-Means Clustering used
Firefly Algorithm Modified Random Component
Masaki TAKEUCHI1 , Thomas Ott2 , Haruna MATSUSHITA3 ,Yoko UWATE1 and Yoshifumi NISHIO1(Tokushima University1 , Zurich University of Applied Sciences2 , Kagawa University3 )1. Introduction

Table 1: Information about data toy model we usedcluster ideal center object number ball of radius1(50, 50, 70)
15502(20, 20, 40)30
103(20, 80, 40)30104(80, 20, 40)30
105(80, 80, 40)30
10(50, 50, 40)
20
56A clustering is a popular data analysis technique and isused for data mining, image analysis, etc. The goal of clustering is to find cluster, which is homogeneous groups of objects in data set. One of the most famous clustering methods
is K-means algorithm. This algorithm finds K cluster centersand each object is assigned to the closest cluster center. Thismeans the K-means clustering is an optimization problem. Itis well-known that the performance of this algorithm depend
on initial conditions.
In 2011, an algorithm that used Firefly Algorithm for Kmeans clustering (KMFA) was proposed. Firefly Algorithm
is one of the Swarm Intelligence algorithm. In this study, weintroduce a new clustering algorithm that combined K-meansclustering and improved Firefly Algorithm (KMIFA). Numerical experiment indicates KMIFA is more eﬃcient thanK-means algorithm and KMFA.

2. Proposed Method
In KMFA, each firefly contains the positions of all cluster centers. The brightness of each firefly is determined bythe sum of the squared distances between the objects andthe corresponding cluster centers. The less brighter firefly imoves towards the brighter firefly j and is defined byxnew= xi + β(xj − xi ) + αϵ,i(α(t) = α0−4100.9)t/tmax(1)

Figure 1: Comparison of each algorithm.
,(2)

where xi is the position vector of firefly i, β is the attractiveness: attractiveness stared above decrease as their distanceincreases, ϵ is a uniform random number and t is the numberof iteration.
In KMIFA, each firefly has its own value of α(t):(α(t)i = λti

10−40.9)t/tmax.

(3)

We set all initial values of λ to λ0 when initializing the population of fireflies and define the minimum value of λ is 0.
The new parameter λi changes whether the assignment offirefly i change or not:{ tλt+1=iλi − θ (the assignment changes)
λti + θ (otherwise)(4)

where θ is predefined parameter.
In the case of λ >> 0, a firefly moves with a relatively
strong random influence. This makes the firefly easier to escape from a local optimum. In the case of λ = 0, a firefly
does not move randomly, which leads to a faster convergence.
Therefore, the concept of our proposed method is at the beginning of the search, fireflies easily escape from local optima.
Then, as the number of iteration increases, fireflies tend toconverge.

3. Numerical Experiment
We compare K-means algorithm, KMFA and KMIFA using data toy model that is summarized in Tab. 1. In thismodel, the range of each dimension is [0, 100]. The dataobjects were generated randomly around the ideal centers
within each ball of radius. We used all the same data set ineach numerical experiment. We set the number of fireflies
is 20 and tmax is 100. Each experiment was run 500 times
and we compared the success rate of each algorithm, which
the success rate is defined as the fraction of objects that areassigned to the correct center.
Figure 1 shows the graph of the success rate of each algorithm. In the case of θ = 0.1, we obtain the best results at
all setting initial values. Though as the value of θ increases,
the range that we can obtain the better results is graduallyreduced. When the value of θ is less than 0.5, the graph ofKMFA decreases, while the graph of KMIFA increases.

4. Conclusions
In this study, we have introduced a new clustering methodthat utilizes an improved Firefly Algorithm for K-means clustering. Our algorithm is based on the idea that the randomization parameter is changed whether the assignmentchanges or not. Numerical experiment has indicated our proposed method is more eﬃcient method than the conventional
method and another improved method.

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