### abstract ###
This paper introduces a model based upon games on an evolving network, and develops three clustering algorithms according to it
In the clustering algorithms, data points for clustering are regarded as players who can make decisions in games
On the network describing relationships among data points, an edge-removing-and-rewiring (ERR) function is employed to explore in a neighborhood of a data point, which removes edges connecting to neighbors with small payoffs, and creates new edges to neighbors with larger payoffs
As such, the connections among data points vary over time
During the evolution of network, some strategies are spread in the network
As a consequence, clusters are formed automatically, in which data points with the same evolutionarily stable strategy are collected as a cluster, so the number of evolutionarily stable strategies indicates the number of clusters
Moreover, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the comparison with other algorithms also provides an indication of the effectiveness of the proposed algorithms \\ \\  Keywords : Unsupervised learning, data clustering, evolutionary game theory, evolutionarily stable strategy
### introduction ###
Cluster analysis is an important branch of Pattern Recognition, which is widely used in many fields such as pattern analysis, data mining, information retrieval and image segmentation
For the past thirty years, many excellent clustering algorithms have been presented, say,  K -means  CITATION , C4 5~ CITATION , support vector clustering (SVC)  CITATION , spectral clustering~ CITATION , etc , in which the data points for clustering are fixed, and various functions are designed to find separating hyperplanes
In recent years, however, a significant change has been made
Some researchers thought about that why not those data points could move by themselves, just like agents or something, and collect together automatically
Therefore, following their ideas, they created a few exciting algorithms  CITATION , in which data points move in space according to certain simple local rules preset in advance
Game theory came into being with the book named "Theory of Games and Economic Behavior" by John von Neumann and Oskar Morgenstern  CITATION  in 1940
In this period, Cooperative Game was widely studied
Till 1950's, John Nash published two well-known papers to present the theory of non-cooperative game, in which he proposed the concept of Nash equilibrium, and proved the existence of equilibrium in a finite non-cooperative game  CITATION
Although non-cooperative game was established on the rigorous mathematics, it required that players in a game must be perfect rational or even hyper-rational
If this assumption could not hold, the Nash equilibrium might not be reached sometimes
On the other hand, evolutionary game theory  CITATION  stems from the researches in biology which are to analyze the conflict and cooperation between animals or plants
It differs from classical game theory by focusing on the dynamics of strategy change more than the properties of strategy equilibria, and does not require perfect rational players
Besides, an important concept, evolutionarily stable strategy  CITATION , in evolutionary game theory was defined and introduced by John Maynard Smith and George R
Price in 1973, which was often used to explain the evolution of social behavior in animals
To the best of our knowledge, the problem of data clustering has not been investigated based on evolutionary game theory
So, if data points in a dataset are considered as players in games, could clusters be formed automatically by playing games among them
This is the question that we attempt to answer
In our clustering algorithm, each player hopes to maximize his own payoff, so he constantly adjusts his strategies by observing neighbors' payoffs
In the course of strategies evolving, some strategies are spread in the network of players
Finally, some parts will be formed automatically in each of which the same strategy is used
According to different strategies played, data points in the dataset can be naturally collected as several different clusters
The remainder of this paper is organized as follows: Section 2 introduces some basic concepts and methods about the evolutionary game theory and evolutionary game on graph
In Section 3, the model based upon games on evolving network is proposed and described specifically
Section 4 gives three algorithms based on this model, and the algorithms are elaborated and analyzed in detail
Section 5 introduces those datasets used in the experiments briefly, and then demonstrates experimental results of the algorithms
Further, the relationship between the number of clusters and the number of nearest neighbors is discussed, and three edge-removing-and-rewiring (ERR) functions employed in the clustering algorithms are compared
The conclusion is given in Section 6
