REVIEW OF ANT METHODS AND PROPOSED MODIFIED ANT METHOD FOR FUZZY CLUSTERING

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1 REVIEW OF ANT METHODS AND PROPOSED MODIFIED ANT METHOD FOR FUZZY CLUSTERING ABSTRACT M. NANDHINI Department of Mathematics, NPR Arts and Science college, India Fuzzy clustering techniques work well with dataset and it discovers effectively the available structure in the real world database. But the standard fuzzy clustering techniques have disadvantages in clustering to large and more general database. Hence in this paper we tries to identify new fuzzy clustering algorithm. The very important problem in fuzzy clustering is assigning initial centers, there are many methods have been already invented for supporting the fuzzy clustering algorithms. Mainly ants based fuzzy clustering algorithms work well with data clustering. This paper review carefully the drawbacks in existed ants method and it invents new modified ant methods. Further this paper implements the proposed methods with two dimensional database and it proves that the proposed methods are effective in clustering in the real world database by comparing the results with standard exited methods. [1] INTRODUCTION The notification of this paper is to find some meaningful Fuzzy clustering algorithm in order to cluster the real world data set into available meaningful groups in the data. It provides us to understand the clustering techniques and it s helpful to do research in the area of fuzzy clustering in the real world data analysis. Cluster analysis has been a fundamental research area in data analysis and pattern recognition. Clustering plays an important role in unsupervised learning technique. Fuzzy set theory was introduced by Lotfi Askar Zadeh (born feb ). He is an mathematician, computer scientist, artifical intelligent researchers, electrical engineer and he has also worked as a Professor emeritus of computer science at the university of california Berkely. It is an extension of classical set theory. Classical set theory allows the membership of the objects in a set in binary terms of a bivalent condition. It denotes that whether the object belong to a cluster or not. But Fuzzy sets are the functions that map each member in a set to a real number in [0,1] to indicate the degree of membership of that member. Fuzzy logic plays major role in pattern recognition. The utility of fuzzy logic is also well established in the design of automatic controllers. Mainly in the aviation industry because of high degrees of non-linearity, uncertainty and complexity of the aerospace systems and the involvement of human be- gins, fuzzy logic based methodologies which is used the design of flight control systems. M. NANDHINI 1

2 In 1939 the cluster analysis was first formalized by Tryon based on group of different algorithm and methods of grouping a similar object into respective categories. The main aim of the clustering is to find the proper and well separated clusters of the objects [1]. [2] REVIEW OF ANT METHODS AND PROPOSED MODIFIED ANT METHOD Ant colonies, plays a major role in research area of swarm intelligence studies, has been fully investigated and applied in many real life fields during these recent years [2]. Ant colonies have the characteristic of self organization, self adaptation, parallel computing, flexibility, no need of priori information etc. Ant colony clustering algorithms is helpful in solving clustering problems. There are two kinds of Ant colony method for clustering namely foraging and pilling model. Foraging model is based on ant colony optimization. The ant colonies searches the shortest paths between their nest and food source. Pilling model is inspired by the ant colonies in clustering their corpses and sorting their larvae. In this chapter first we review ant algorithms based on pilling model in terms of its merits and demerits in supporting to cluster techniques have reasonable initial cluster center. To rectify this demerits we provide a new modified Ant Algorithm for selecting cluster centers of fuzzy clustering algorithm. 2.1 Self organization Self-organization is a process of attraction and repulsion in which the internal organization of a system normally an open system which continuously interacts with its environment while maintaining its state increases in complexity without being guided or managed by an outside source [3]. Self-organization is a form of Stigmergy [4]. It is a process of indirect coordination between the agents or action. The principle is that trace left in the environment by an action induces the performance of a next action by the same agent or by a different agent. In that way, subsequently actions tend to strengthen and build on each other, leading to the spontaneous emergence of coherent, apparently systematic activity. It produces complex, seemingly intelligent structures, there is no need for any planning before, it is not controlled by any internal or external agents and also there is no direct communication between the agents. As such it supports the efficient cooper- ating (collaboration) between the agents, which lack any memory, intelligence or even individual awareness of each other. It was first observed in social insects. In 1959 the French biologist Pierre Paul Grasse introduced the concept of "stigmergy" to refer the termite behavior. For example, ant exchange their information by leaving out the pheromone smell deposited along the path from nest to food. Ant develop different path way from food to nest, it collectively form a complex network trail like structure. When ant comes out from the nest in search of food, it releases pheromone smell on its path of the trail from food to nest. The network of trails functions as a shared external memory for the ant colony. In computer science, this general method has been applied in a variety of techniques called ant colony optimization which search for the solutions to complex problems by depositing "virtual pheromone" along trails promising. M. NANDHINI 2

3 2.2 Self organization map A self organization map is an artificial network [5] which consists of a set of inters connected units, each of which has its own weight factor. One trained using unsupervised learning it produces a representation of a set of high dimension samples in which similar samples are cluster together and remaining are pushed away from each other as much as possible. The first self organization map algorithm was formalized in [6], and the popularity of the more advanced SOM method is growing at a steady pace. The SOM is useful for clustering and visualizing high dimen- sional data into simple geometric relationship on a low dimensional display. SOM is a tool in exploratory phase of data mining [7]. It projects input space on prototypes of a low dimensional regular grid that can be effectively utilized to visualize and explore properties of the data. It is especially suit- able for data survey because it has prominent visualization properties. [3] REVIEW OF ANT METHOD Cluster analysis plays an important role in handling many factors like cri- terion functions, algorithms and initial conditions, and effective similarity measures, and common clustering technique can handle all kinds of cluster structures(shapes, size, and density). They found that by using preprocessing data can improve the quality of clusters [8]. Commonly clustering algorithms are scalability, finding the clusters arbitrary shape, capacity to deal with data types, noise and outliers, insensitivity to input records, incorporation of user defined constraints, interpretability, and usability, to determine the input parameters. Nowadays the researchers introduce many clustering algorithm but no one algorithm is not suitable for all types of items. This is the main reason for getting a large number of drawbacks. Recently researchers found an algorithm which is based on nature inspired method for clustering. Ant based clustering techniques is a nature inspired method. They found that it had been successful in solving clustering problems. So the researcher community gives more important to this method. Because these methods are specifically applicable to exploratory data analysis and also there are still many investigation to perform on this field. The researchers give attention to improve its performance, stability rate of convergence, robustness speed and other factors that allow us to apply these methods in real life applications. It does not focus mainly on strict modeling of the natural process, it merely focuses on using the best way to improve the convergence and accuracy of these in many techniques. This method has benefits in many way such as self organization, flexibility, robustness, no requirement of prior information and decentralization. Ant based clustering sorting was first introduced by Denebourg et.al in 1991 [2], [8], [9], [10] he explained the pheromone of corpse clustering and larval sorting behavior of ants. Denebourg was the first person introduced the larval sorting and corpse cleaning items by using group of real works robotics. His model is called as Basic Model or BM. [4] PROPOSED MODIFIED ANT METHOD Presently, the clustering techniques have choosen the centers by random man- ner which affects the results of find results. To rectify this problem we use the Ant based clustering method to get the good initial cluster M. NANDHINI 3

4 centers. Nowadays many researchers published a lot of research work based on Ant clustering method in recent years. In this paper we particularly discuss about Fuzzy ant clustering method which was proposed by Mr.Kanade and O.Hall in 2004 [11]. This algorithm is used to create initial raw clusters and they are refined by using Fuzzy C-Means algorithm. This algorithm consists of two stage process. In the first stage, data objects are randomly scattered on a 2D space and initially ants moves the individual data object to form a heaps. Then the centroids of these heaps are considered as the initial cluster centers and these clusters are refined by using Fuzzy C-Means algorithm. In the second stage the objects obtained from the Fuzzy C-Means algo- rithm are hardened according to the maximum membership criterion to form a new heaps. These newly formed heaps in first stage are then sometimes moves and merged by the ants. Then we obtain the final clusters and these clusters are also refined by using the Fuzzy C-Means algorithm. Even though his method is good to obtain the initial cluster centers, it is very much sensitive to the parameters. So we prefer some modification in formulas to get the result better than above algorithm, while the probability of ant picking up an item or dropping down an item. The general outline of the ant based algorithm used in this study was proposed in [11]. Initially the data items are randomly scattered on a discrete 2D space board. The board can be considered a matrix of p ÃU p cells. The matrix is toroidal which allows the ants to travel from one end of a board to another end easily. The size of the board is dependent on the number of items. We have used a board of pãup such that p 2 = 4q where q is the total number of objects to be clustered. Likewise q/3 the ants are also randomly scattered throughout the board, where q is the total number of items to be clustered. The ants form heaps by clustering the data items. A heap may be a collection of two items or more than two items. A heap is spatially located in a single cell. The main ant based clustering algorithm is given as below. 1. Randomly place the ants on the board and also randomly place items on the 2D board at mostone per cell. 2. Repeat. 3. For each ant Do. 3.1 Move the ant. M. NANDHINI 4

5 3.2 If the ant does not lift any item then if there is an item in the 8 neighboring cells of the ant, the ant possibly picks up the items. 3.3 Else the ant possibly drops a carried item, by looking at the 8 neighboring cells around it. 4. Until the termination condition holds. When picking up an item or dropping down an item, themovement of the ant is not completely random. Initially the ant moves in a direction randomly then the ant follows the same direction with a probability p direction, otherwise it create a new direction randomly. Picking up an Object M. NANDHINI 5

6 When an ant is not lifting any item, then its try to find for possible item to pick up by examining the eight neighboring cells around its present position. suppose an ant found an item or heap then it has a probability to pick up an item depending on the number of items present in a heap.consider three ways to pick an item namely: single item, a heap containing two items and a heap containing more than two items. If a single item is present then an ant has more probability to pick up an item by using the condition is given as follows. d(ant,x) < P load In the second case, if a heap containing two items then ant destroys that heap and finding a minimum distance between ant and items in that heap H by using the equation is given as below, Then ant pick up the item and it is denoted as p destroy. In last case a heap contain more than two items then ant pickup an item from the heap only if, maxd(ant,xi)dmean(h) > Tremove Then ant pick up the dissimilar item and is denoted as T remove. The Second Stage In the ant based algorithm if an item is a bad fit to a heap then it can take a large amount of time for it to be moved to form a better heap/cluster. So we used ant based algorithms which is based on stochastic principles in combination with Fuzzy C means algorithm as the deterministic algorithm. Fuzzy c-means require good initializations, which can be provided by ant based algorithm. The algorithm used is given as follows, 1. Randomly scatter the items on the 2D board 2. Initialize the ants with random position, and random direction 3. For N iterations Do 3.1 For each ant Do Move the ant If the ant is carrying an item Y it then possibly drop down the item Y else Possibly pick up an item Y. 4. Use the cluster centers obtained in step 3 to initialize cluster centers for the Fuzzy C Meansalgorithm 5. Cluster the data using the Fuzzy C Means algorithm 6. Harden the data obtained from the Fuzzy C means algorithm, using the maximum membershipcriterion, to form new heaps 7. Repeat steps 1-6 by considering each heap as a single item. In this ants are very sensitive to the threshold parameters for deciding when to merge the heaps. So we felt that this modification is not enough for merging the heaps. so we again introduce some changes in our proposed modified algorithm. In the first stage the algorithm is same for picking up an item. We did some changes in dropping down an item. consider three cases namely: a cell has no item, single item present and a cell contain a heap. M. NANDHINI 6

7 If two heaps H 1 and H 2 are clustered together, then it form only one heap H 3 and it cannot be separated any more. The numbers of heaps either decreases or remain constant as the number of iterations increase. The Fuzzy C Means algorithm is then used to cluster the data using the cluster centers obtained from the second stage of the ant based algorithm as an initialization. The algorithm used is given as follows, 1. Randomly scatter the items on the 2D board 2. Initialize the ants with random position, and random direction 3. For N iterations Do 3.1 For each ant Do Move the ant If the ant is carrying an item Y it then possibly drop down the item Y else Possibly pick up an item Y. 4. Use the cluster centers obtained in step 3 to initialize cluster centers for the Fuzzy C Meansalgorithm 5. Cluster the data using the Fuzzy C Means algorithm 6. Harden the data obtained from the Fuzzy C means algorithm, using the maximum membershipcriterion, to form new heaps 7. Repeat steps 1-6 by considering each heap as a single item. These modification gives better result when compared to earlier one. We performed sensitivity analysis on the controlling parameters and especially we focus on setting the T create for heap threshold parameters. [5] REVIEW ABOUT ANT ALGORITHM We discuss about review of some ant based clustering model. Deneubourg introduce the Basic Model concept for the probability of picking and dropping an item. The main disadvantage of this algorithm is, it does not convergence quickly and also the number of clusters is often too high. After that Lumer and Faieta modified this version and he present the LF model by using dissimilarity based evaluation of the local density. In this each ant has a short term memory to recall only few number of location in which it has visited last. Gutowitz introduce the complex seeking ant method which would sense the complexity in their neighborhood. This method would speed up the con- vergence time. After that Monmarche presented Antclass method, in this method we should concentrate on ant meet on the cell and could exchange the items. Ramos and Merelo presented a Acluster method. It is used in ex- ploratory data analysis and for data retrieval problems. In this they discuss mainly about short term memory and also artificial types of ant. It does not need any information such as the number of classes and number of partition. Vizine and others did three main changes in Lumer and Faieta model to improve the progressive vision, cooling scheme, and pheromone sensitivity. Using this algorithm we get the correct number of clusters and convergence into a good solution. Later Kanade introduce the fuzzy ant as a clustering concept in this he produce two algorithm. Using Fuzzy ant algorithm we get the number of clusters and best initial cluster centers. The main drawback of this is using more number of controlling parameters and it is very sensitive to this algorithm. But in second algorithm Fuzzy ant clustering with cen- troid method, it has less sensitivity parameters. Using fuzzy ant algorithm we get the number of clusters and the result is given to second algorithm. The main disadvantage on setting parameters T createforloop, is that very sen- sitive to the algorithm, random M. NANDHINI 7

8 movement of ants and initial placement of ant so we should concentrate on incorporating trail and giving intelligent initialization to the ants. Schockaret and others introduce a fuzzy rule on ant clustering method which is named as fuzzy if then rules. In this they introduce intelligent ant they decide themselves for picking or dropping one item or a heap. This is applied to web search clustering and also it gives a best result. It is robust, simple, and easy to use. Urszula Boryczka introduce ant based clustering algorithm. He did a slight adjustment in LF model and BM model to improve the quality of clustering and space separation between clusters on the grid. It is used to find out the different kinds of data which can be divided into clusters of the hardly anticipated shapes on the grid cells. It is used to improve their convergence speed and also it deals with outliers in data sets.from this we conclude that we should concentrate on ant should exchange the items, convergence speed. It should work in large data sets and also in high dimensional space. To reduce the controlling parameters in order to avoid the sensitivity and outliers in data set. We should give importance to the pheromone updating rules with huge database. If we give special attention to this drawback, then it is very useful to apply these methods in real life application. [6] CONCLUSION In this paper, we have invented new ant based fuzzy clustering technique for real world data clustering problems. This paper examined ant algorithm thoroughly and identified the merits and demerits of the existed algorithm. In order to overcome the drawback in the existed method we have proposed an ant algorithm based on fuzzy clustering which are capable to work with large data base and general shaped data base. From the experimental study of this paper, we have shown that the proposed algorithm takes very less iteration to complete the process of algorithm in clustering the dataset. Our proposed algorithm have been taken few seconds to complete the process of algorithm. REFERENCES [1] Cluster Analysis: Basic concets and Algorithms-CSE USER HOME.. kumar/dmbook/ch8.pdf [2] Gong Zhe, Li Dan, An Baoyr, Ou Yangxi, Ci Wei, Niu Xinxin, Xin Yang, An analysis of Ant colony Clustering Methods: Mod- els, Algorithms and Applications, International Journal of Advance- ments in computing Technology(IJACT) vol 3, no. 11, dec 2011,Doi: /ijat.vol3.issue [3] Self- Organisation web address: organisation-defined/ [4] Stigmery web address: [5] Grant Strong, Minglun Gong, Similarity-based image organisation and browsing using multi resolution self organisation map, Image and vision on computing 2011, M. NANDHINI 8

9 [6] Teuvo Kohonen Fellow, Erkki Oja Olli Simula, Ari visa, and Jari Kan- gas, Engineering Applications of the self organisation map, proceed- ings of the IEEE vol:84, No.1o, oct [7] Juha Vesanto and Esa Alhoniemi, student member IEEE, Clustering of the self- orangisation map IEEE TRANSACTION ON NEURAL NETWORKS, VOL 11, No.3, May [8] O. A. Mohamed jafar and R. Sivakumar,Ant-Based Clustering Algo rithms: A Brief Survey ",International Journal of computer Theory and Engineering Vol. 2, No. 5, October, [9] Mi Aranha, claus de castro, A Survey on using Ant-Based Techniques for clustering 56343, [10] J.-L. Deneubourg, S. Gross, N. Franks, A. Sendova-Franks, C. Detrain and L. Chretien, The dynamics of collective sorting: Robot-like ants and ant-like robots, In Proceedings of the First International Conference on Simulation of Adaptive Behavior: From Animals to Animats, Cambridge, MA, MIT Press, 1991, pp [11] Dissertation of Parag M.Kanade,Fuzzy ants as a clustering concept, (2004) Graduate School Thesis and Dissertations paper 1104, University of South Florida (USF) M. NANDHINI 9