We have proposed a model based upon flocking on a complex network, and then developed two clustering algorithms on the basis of it. In the algorithms, firstly a \textit{k}-nearest neighbor (knn) graph as a weighted and directed graph is produced among all data points in a dataset each of which is regarded as an agent who can move in space, and then a time-varying complex network is created by adding long-range links for each data point. Furthermore, each data point is not only acted by its \textit{k} nearest neighbors but also \textit{r} long-range neighbors through fields established in space by them together, so it will take a step along the direction of the vector sum of all fields. It is more important that these long-range links provides some hidden information for each data point when it moves and at the same time accelerate its speed converging to a center. As they move in space according to the proposed model, data points that belong to the same class are located at a same position gradually, whereas those that belong to different classes are away from one another. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the rates of convergence of clustering algorithms are fast enough. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.
Deep Dive into A New Clustering Algorithm Based Upon Flocking On Complex Network.
We have proposed a model based upon flocking on a complex network, and then developed two clustering algorithms on the basis of it. In the algorithms, firstly a \textit{k}-nearest neighbor (knn) graph as a weighted and directed graph is produced among all data points in a dataset each of which is regarded as an agent who can move in space, and then a time-varying complex network is created by adding long-range links for each data point. Furthermore, each data point is not only acted by its \textit{k} nearest neighbors but also \textit{r} long-range neighbors through fields established in space by them together, so it will take a step along the direction of the vector sum of all fields. It is more important that these long-range links provides some hidden information for each data point when it moves and at the same time accelerate its speed converging to a center. As they move in space according to the proposed model, data points that belong to the same class are located at a same posi
Data clustering is a widely investigated problem in Pattern Recognition. For the past forty years, a lot of excellent algorithms for clustering have been presented from those that put the emphasis on cluster centers and boundaries, say, K -means [1], support vector clustering (SVC) [2], to current particle swarm optimization (PSO) based [3], ant-based [4], and flocking-based [5] algorithms for clustering. Observing the history of clustering algorithms, we can notice that a significant change has been made, which may be considered as two stages. First, with fixed data points, we utilized various functions to find complex curve planes in order to cluster or classify data points; second, till the past few years, some pioneers thought about that why not those data points could move in themselves, just like agents or whatever, and collect together automatically. Therefore, following their ideas, they create a few exciting algorithms [3,4,5], in which data points moves in a whole space according to certain simple local rules preset in advance.
Flocking is a form of collective behavior among animals like birds, bees and fishes, which is to realize a group objective by interacting between individuals [6]. In the last ten years, many researchers with different backgrounds, ranging from physics, biology to computer sciences and sociology, are involved in this field in order to explore the mechanism of emergence of flocking with local interactions [7]. Certainly, flocking is also widely used in engineering applications, for example, self-assembly of connected mobile networks, massive distributed sensing using mobile sensor networks in an environment, etc. In particularly, flocking is applied to perform military missions as well, such as reconnaissance, surveillance, and combat using cooperative unmanned aerial vehicles.
To the best of our knowledge, flocking has begun to become an emerging method applied to the problem of data clustering. So, if data points for clustering are considered as a flock of agents who can move in space by local interactions, then could they collect together as separating parts automatically like the emergence of flocking? This is the question that we attempt to answer in this paper. In the proposed algorithms, the relationship among data points is represented by a time-varying complex network, on which data points interacts with its neighbors by a local potential function. Furthermore, each data point takes one step proportional to the magnitude of actions that it experiences along the direction of the actions. As data points move in space constantly, we can observe that they may gather together gradually and form some clusters automatically at last in the experiments. The remainder of this paper is organized as follows: Section 2 introduces some concepts and important parameters about the complex network theory briefly, and then reviews some related work about clustering algorithms based on flocking. Section 3 elaborates the proposed model of flocking on a complex network. Section 4 describes two clustering algorithms based on the model, in which the effects of long-range connections are analyzed in detail. Section 5 discusses the relation between the number of clusters and the number of nearest neighbors, and the rates of convergence of two algorithms. Section 6 introduces those datasets used in the experiments briefly, and then compares experimental results of the proposed algorithms with other clustering algorithms. The conclusion is given in Section 7.
There exist various networks or structures in the real world that we live [8], for example, the topology of food webs [9], electrical power grids, cellular and metabolic networks [10], the World-Wide Web [11], the neural network of the nematode worm [12], coauthorship and citation networks of scientists [13][14]. How to describe these networks in the real world is an issue that has puzzled researchers for about two hundred years. In the first one hundred years or so, the regular graph, say lattices in a two-dimensional plane, was applied to represent the relationship among factors in a real system. Till the end of 1950’s, two Hungarian mathematicians, Paul Erdös and Alfréd Rényi, presented a random graph model or ER model. In the next forty years, it was believed by many researchers that the ER model was an optimum model to describe those real systems [15,16]. In 1998, however, a significant breakthrough was made. Duncan J. Watts and Steven H. Strogatz [17] proposed a small-world network model (WS model) which is a new type of network between a regular lattice network and a random graph. This made researchers realize that most of real-world networks were neither purely regular networks nor purely random networks, but they were networks with statistical features that differed from two previously mentioned networks, so this new type of network was named Complex Network. WS model may well exhibit two features in a great number of social n
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