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Application of Teaching-Learning-Based Optimization Algorithm on

Cluster Analysis

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ABSTRACT

Cluster analysis has received attention in many scientific fields. The purpose of clustering analysis is to

detect group data points, which are close to one another. One of the most widely used techniques for

clustering is the K-means algorithm. The performance of K-means algorithm which converges to numerous

local minima depends highly on initial cluster centers. In order to overcome local optima problem lots of

studies done in clustering. A population-based method called Teaching-Learning-Based-Optimization

(TLBO) is proposed to solve the clustering problem. TLBO is a robust and effective search algorithm. The

most salient advantage of this algorithm is that it does not require the tuning of any kind of controlling

parameters. The efficiency of the proposed algorithm is studied by testing on several data sets. Numerical

results show that the proposed evolutionary optimization algorithm is robust and suitable for data

clustering.

INTRODUCTION

One of the most important techniques of unsupervised classification is clustering. In clustering objects

with the same attributes will be grouped in a same cluster. Clustering techniques can be classified in to

major classes: hierarchical and partitional. The hierarchical clustering can be divided into agglomerative

and divisive. In hierarchical clustering n objects will be grouped into k clusters by minimizing some

measure of dissimilarity in each group and maximizing the dissimilarity of different groups [1, 2, 3 and 4]

In this paper our focus is on partitional clustering, and in particular the K-means algorithm that is one of the

most efficient clustering algorithms. However, the K-means algorithm suffers from several drawbacks [5].

The objective function of the K-means algorithm may contain several local optima because it is not convex.

Therefore the outcome of K-means algorithm heavily depends on the initial solution [6]. To overcome

these shortcomings recently many algorithms have been developed based on evolutionary algorithms like

GA, TS, PSO and SA [7, 8, 9, 10, 11, 12 and 13]. But problem is that most of these evolutionary algorithms

are very slow to find optimal solution.

TLBO Algorithm

The TLBO algorithm is a newly developed meta-heuristic optimization algorithm [17]. It is a

population-based optimization algorithm that is modelled based on the transfer of knowledge to the

classroom environment, where learners first gain knowledge from a teacher (Teacher Phase) and then from

fellow-students (Learner Phase). The structure of the proposed algorithm can be explicated as follows:

Teacher phase: In this phase the solution nominations are randomly distributed throughout the search

space. Thus, the best solution will be selected amongst all and will interact the knowledge with other

candidates. Elaborately, since a teacher, who is the most skilled person about the objective in the

population, influences the student’s deed to take part some pre-planned aim. It is desired that the teacher

augments the mean of his or her class information level depending on his or her experience. The teacher,

thus, will put maximum effort into training his or her learners, but learners will acquire information

according to the worthiness of training delivered by a teacher and the worthiness of learners in the class.

Experimental results

The efficiency of the TLBO algorithm on clustering has been tested on several well known datasets

such as: four artificial data sets and six real-life data sets and compared with the ACO, PSO, SA and Kmeans

algorithms [14, 15 and 16]. In stochastic algorithms the effectiveness highly depends on the initial

solutions. To overcome these drawback each algorithms performed 100 times individually with randomly

generated initial solutions. The simulations are performed on a Core i7 2.7 GHz computer with 4 GB RAM

memory. The software is developed using MATLAB 7.13.

Conclusion

The clustering analysis is a very important technique and has attracted much attention of many

researchers in different areas. The K-means algorithm one of the most efficient clustering method and is

very simple that has been applied to many engineering problems. This paper has applied a newly developed

TLBO algorithm for solving the clustering problem. The proposed algorithm has been implemented and

tested on several artificial and well known real, the result illustrate that the proposed TLBO optimization

algorithm can be considered as a viable and an efficient heuristic to find optimal or near optimal solutions

for clustering problems of allocating N objects to k clusters. The experimental results indicate that the

proposed optimization algorithm is at least comparable to the other algorithms in terms of function

evaluations and standard deviations.