Efficient Cluster Head Selection Using Naïve Bayes

Efficient Cluster Head Selection Using Naïve Bayes Classifier for Wireless Sensor Networks Vahid Jafarizadeh1, Amin Keshavarzi2, Tajedin Derikvand3

Abstract Data mining and approaches based on it have always been of approaches that have been considered in solving problems in the field of computer, but on some issues, this approach has been neglected. The area of wireless sensor networks (WSN) and specifically the issue of optimal determining of the cluster head node are of these issues. To solve the problem of optimal determining of the cluster head node, Naïve Bayes that is the subset of data mining techniques is used in this paper. The results obtained after simulation of the presented algorithm show that the efficiency of this algorithm is significantly higher compared with other approaches that have so far been used to solve this problem, and thus it can be said that using this algorithm will lead to improved outcomes of solving this problem.

Keywords

WSN, cluster head, Naïve Bayes, classification, data mining.

1 Introduction WSNs have many Challenges and open issues yet, such as topology [26], [30], [39], protocols [24], [29], security [28], [31], routing [23], [32], [35], [41] data [18], [33] and etc. [34], [36], [40], [42] Energy Efficiency is the most important Problem in WSNs, that is considered as yet [18], [19], [23], [24], [25], [26], [27]. Clustering nodes in WSNs is among the most important measures taken to reduce and optimize energy consumption [37] because if it is set that a few hundred or even several thousand nodes simultaneously and continuously send information from environment to the base station, a lot of problems such as a waste of bandwidth, the occurrence of congestion, and error increase and so on occur in the network, all of which ultimately lead to a waste of energy consumption and thus reduce the lifetime of the network. Thus, the idea of clustering nodes in the network was offered to avoid this problem. After clustering nodes in the network, nodes inside each network (the number of which is not a large number compared to the total number of network nodes) receive information from the environment and send it to one of the nodes in that cluster called cluster head. After receiving the information of all nodes that are members of the cluster, cluster head aggregates and sometimes compress this information [18], [19], [20], [21], [22], [38] and sends it to Base station or Sink. Existence of cluster head brings about the reduction in the number of communications set on the network and thereby reduces power consumption and extends the life of the WSN.

 Amin Keshavarzi [email protected] 1

Department of Computer Engeenering, Marvdasht Branch, Islamic Azad University, Marvasht, Iran Department of Computer Engeenering, Marvdasht Branch, Islamic Azad University, Marvasht, Iran 3 Department of Mathematics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran 2

As the algorithm used for clustering is important and effective in energy consumption, proper selecting of cluster head is also important to reduce the energy consumption of the network. Methods used to select the cluster head node are divided into two categories: the first category are the ways introduced with clustering algorithms; in fact, in this group of methods right way, the main purpose is offering clustering algorithm, but beside this clustering algorithm, a procedure is presented for selection of cluster head node that is not optimal in most cases. The second category includes the methods that solely focus on selecting the Cluster Head node. The methods of this category offer algorithms that, in most cases, only provide the selection of cluster head in a cluster, regardless of the clustering algorithm (regardless of clustering method). It is obvious that the output of these algorithms is more often efficient in practice compared with the first method. Most of the algorithms of the second set use optimization problem solution methods based on artificial intelligence techniques and analytical methods to determine the best solution. It is worth noting that accurate determination of the number and location of optimal cluster head is of NP problems, so in this problem obtaining near to optimal solutions is pursued. In this paper, will try on representing a new method based on Naïve Base to determine the Cluster Head Node in WSN which enables us to produce better outputs regarding to other methods in the same category; in other words using this method, Network Lifetime will rise highly in compare to the other methods. The rest of the paper is organized as follows. In Section 2, some of the prior successful works that each one has used a different approach, have been introduced. We discuss how to create dataset in detail. Section 4 is assigned to the explanation of simulating the proposed method. In the next section, the values of constants used in the simulation are explained. Section 6 is for evaluating the output of the proposed method. And final sections are related to conclusion and future works. 2 Related works As mentioned in the previous section, the aim of some of the presented algorithms to select a cluster head node is clustering and have implicitly introduced a procedure for selecting the node of cluster head. The most famous of these algorithms in the field is LEACH algorithm [1]. In addition to this one, some algorithm like PEGASIS [2] and HEED [3] are of other algorithms introduced in this category. In addition to the methods mentioned, other methods have been introduced for this purpose, and in some cases have also been used [4], for example, an efficient method introduced is by employing a coordinator. In [5] a static algorithm has been used that provides a near-optimal solution. In [6] an algorithm is introduced whose base is calculation of a linear function for the node, and this function sets the remaining energy of the node as the basis for its work. In [7] a hierarchical cluster analysis is used to select cluster head. But most of the above methods do not offer optimal solutions because of using of linear functions or not considering the dynamic conditions of the network and or not considering the possibility of adding new factors, and only in some special cases have good outputs. Thus, the importance of the second group methods get more evident because in second group methods, some models are presented that are made based on training from network data. Therefore, their outputs will be acceptable and appropriate in different networks with different conditions. In the second category methods some general approaches such as evolutionary algorithms, data mining and fuzzy systems are used, for example, in [8] and [9] genetic algorithm, in [10] ant colony algorithm, and in [11] the decision tree are used and in [12] , [13] , [14] and [15] fuzzy system designed to select the cluster head node is used.

3

The proposed algorithm

Our proposed algorithm is based on the Naïve Bayes famous Classifier [16], which is described below: 3.1 Overview Given that our proposed algorithm is of the second type algorithms, it should be noted that this algorithm only performs the choosing of cluster head and clustering operation is not carried out by this algorithm. Clustering can be done by any other algorithms such as LEACH, so at first a number of nodes are considered in a cluster, then one of the nodes of the cluster is selected as cluster head, based on specific parameters:

Base Station

Cluster head

Member Node

Member Node Member Node

Member Node

Figure 1 A model of a clustered network

The parameters that we have used to select cluster consists of the residual energy of each node and the sum of local distance of member nodes to cluster head node. Local distance between two nodes is the Euclidean distance between two nodes [14]: 𝒅 = √(𝒙𝟏 − 𝒙𝟐 )𝟐 + (𝒚𝟏 − 𝒚𝟐 )𝟐

(1)

3.2 Dataset Construction method To build datasets, 100 sensor nodes should be put in a space with specific dimensions like 100 * 100 square meters and the data of these nodes are entered in a matrix as follows:

Table 1 sample of the matrix containing data (a part of matrix)

X-coordinate Y-coordinate The remaining energy level Distance from base station Local Distance Class

Node1

Node2

Node3

95.7

37.8

14.1

48.5

81.1

42.1

1.60

1.06

1.83

45.74

33.43

36.65

5817.10

4630.13

4704.98

-1

-1

-1

Node100 … … … … … …

46.27 50.64 1.95 3.78 3703.19 1

As specified in the matrix, each column of data matrix stores one of the nodes in itself, and each row of the matrix represents one of the attributes of the nodes as follows: First row: represents the length, in other words, if we consider node as an ordered pair (x, y), in this row x value of each node is placed. Second row: indicates the width, in other words, if we consider node attributes as a ordered pair (x, y) to consider, in this row y value of each node is placed. Third row: this row shows the remaining power level of each node. Fourth row: the value placed in the cells of this row is the Euclidean distance of each node to the base station. Fifth row: the sum of local distances from other member nodes is calculated and the obtained results are placed in the houses of these row. Sixth row: This record of the table (the row of the matrix) is the class variable that contains label for each node. In each cell of this row of the matrix, if the node is cluster head, it gets 1, otherwise -1. It is noteworthy that the values of the first and the second rows are generated randomly, the values of the fourth and fifth rows can easily be calculated by using the values of the first and second rows and through formula for calculating the Euclidean distance, values of the third row will be calculable at the beginning of the work of the network with a default value (in our case 2 Jouls) and as network life goes on, in each round, it can be obtained based on what follows. [15]. However, there will be a big problem in labeling (calculating sixth row values). The first idea that can be raised is that at each stage labels are given values based on one of the previous methods (such as genetic algorithms) and it is repeated in each round of the network, but then, after testing idea, it is made clear that in this case the output does not show any improvement. The reason for this can be explained thus that when labels are given values according to a secondary method, in fact it means that our best cases is the second method, so the output of the new algorithm in the best case will be the same as the secondary method, and there will be no improvement, so other methods should be used for labeling and determining the optimal cluster head in each stage.

Another idea that we have used in this paper for our work is as follows: To solve the problem, the best way is to consider a time slice from the network, this time slice will be equal to one round of network. Nodes energy (third row of the matrix) in this round is generated randomly, but at a specified interval (greater than zero). For this purpose, in this time slice, 99 nodes are generated as before except that the energy is randomly generated. But hundredth node should be generated in a way that this node has the label 1, then the rest of the nodes in this round will be labeled as -1. In fact, to ensure that the best mode is considered, in this time slice of the network, an ideal node is added to the network. Now, the question arises: what should be the characteristics of this node? In response to this question, it can be said that in a network, at each round, a node is the best suitable to be the cluster head, it is more appropriate to have higher remaining energy level compared to other nodes and have less total distance than other nodes [8] and [17]. So for 100th node, the (x,y) coordinate and its energy level should be initialized in such a way that these circumstances become possible in each time slice. For this purpose, it is acted as follows: Among other 99 nodes, the maximum amount of residual energy (third row of the matrix) is calculated, this maximum amount has slightly increased and considered as the remaining energy of the hundredth node: If it is assumed that the name of matrix containing nodes information is N, then the hundredth node is the ideal node that should be generated:

𝑗

𝑁𝑖 = 𝑚𝑎𝑥(𝑗, 𝑥𝑖 ) + 𝜀 , 𝑤ℎ𝑒𝑛 𝑘 = 1. . (𝑗 − 1) , 𝑖 = 100 𝑎𝑛𝑑 𝑗 = 3

(2)

The value of ε, according to network conditions, is very small value. Among the other 99 nodes, to minimize the total amount of node distance it is enough that the coordinates of the hundredth node be equal to the average coordinate of other nodes of the network; If we consider the previous assumptions:

𝑗

𝑁𝑖 = 𝑚𝑒𝑎𝑛(𝑗, 𝑥𝑖 ) + 𝜀 , 𝑤ℎ𝑒𝑛 𝑘 = 1. . (𝑗 − 1) , 𝑖 = 100 𝑎𝑛𝑑 𝑗 = 1

𝑗

𝑁𝑖 = 𝑚𝑒𝑎𝑛(𝑗, 𝑥𝑖 ) + 𝜀 , 𝑤ℎ𝑒𝑛 𝑘 = 1. . (𝑗 − 1) , 𝑖 = 100 𝑎𝑛𝑑 𝑗 = 2

(3)

(4)

Here, Relation (3) has the task of calculating the value of x of hundredth node, and Relation (4) has the duty to calculate the value of y of the hundredths node. By doing so, an ideal node is made that it can safely be said that this is the most appropriate node to be the cluster head node in the network, so value of variable class is as 1 for it. Now dataset matrix for a time slice of one network is completed; at this point we are faced with an unbalanced dataset where sampling should be carried out from among the data labeled -1 so that no problems occur in continuation. Now, the data of the must hundredth node (hundredths column of the matrix) along with 9 other nodes (which are randomly selected) must be copied and stored in a new matrix (with 10*6 dimensions). Then, all the above steps (for a time slice with new data) should be repeated until a suitable data set is built for later stages. At the end, an appropriate and validated dataset is built for use in the later stages. 4

Simulation

We created an appropriate dataset in the previous stage, now we can apply the Naïve Bayes classifier on it. We have used MATLAB software for simulation. After training and testing phases, we will have a model. At the start of network work, nodes are randomly dispersed in the environment and energy level of all nodes is equal to 2 Joules. In the first round, the node with lowest total local distance is selected as cluster head and other member nodes send the sensed data received from the environment to this node, after receiving and aggregating data, cluster head node sends it to base station or well. Here, it should be noted that the consumed energy to exchange data for each node should be calculated, and based on that the remaining energy level of nodes be updated: In accordance with [15], the amount of energy lost for member nodes is calculated from the following relation:

𝑻

𝑬𝑻𝑿 (𝒍, 𝒅) = {

𝑿 𝒍 ∗ 𝑬𝒆𝒍𝒆𝒄 + 𝒍 ∗ 𝜺𝒇𝒔 ∗ 𝒅𝟐

𝒍∗

𝑻𝑿 𝑬𝒆𝒍𝒆𝒄

𝟒

+ 𝒍 ∗ 𝜺𝒎𝒑 ∗ 𝒅

, 𝒅 < 𝒅𝟎

(5)

, 𝒅 ≥ 𝒅𝟎

In the above relation, the energy lost for the transmitter node is calculated. d is the Euclidean distance 𝑻

𝑿 between the transmitter and the cluster head node and 𝑬𝒆𝒍𝒆𝒄 and 𝜺𝒇𝒔 and 𝜺𝒎𝒑 and 𝒅𝟎 are fixed values that are determined at the beginning of the life of the network, and 1 the length of the transmitted packet in the network in bits, this amount is fixed during the life of the network and determined from the outset.

Now it's time to calculate the amount of energy wasted in cluster head node, for cluster head node, the amount of energy wasted to get information from a node is calculated from the following relation: 𝑹

𝑿 𝑬𝑹𝑿 (𝒍) = 𝒍 ∗ 𝑬𝒆𝒍𝒆𝒄

(6) 𝑹

𝑿 In the above equation, 𝑬𝒆𝒍𝒆𝒄 is a fixed value determined at the beginning of the life of the network packet, and 1 is the length of the sent packet in bits that is fixed over the network life and determined at onset.

As mentioned above, Relation (6) calculates the amount of energy wasted to get data from a node, so in each round, this amount should be multiplied to the number of surviving nodes to calculate the energy waste to receive data from all live nodes of the network.

Then the cluster head node should send data to the base station, which itself reduces the amount of energy of the cluster head. Relation (5) is used, to calculate the amount of wasted energy where d is the Euclidean distance between cluster head nodes and the base station. In addition to these, some energy is wasted in cluster head nodes before sending data to the base station, some energy is also lost for data aggregation, this amount of energy is a fixed number shown with EDA. Given the above, it can be concluded that the wasted energy in cluster head node is:

𝑬𝒅𝒊𝒔 = 𝟗𝟗 ∗ 𝑬𝑹𝑿 (𝒍) + 𝑬𝑻𝑿 (𝒍, 𝒅𝑻𝒐𝑩𝑺 ) + 𝑬𝑫𝑨

(7)

Now, the level of remaining energy of the nodes must be updated according to the following equation, the amount of residual energy of each node at the end of each round will be equal to [10]: 𝑬𝑹𝒆𝒔 = 𝑬 − 𝑬𝒅𝒊𝒔

(8)

In the next rounds, cluster head determines using existing model and Naïve Bayes classifier; and the remaining energy level of the nodes will be updated as before. This process will continue until the death of all nodes (end of network life). 5

The default values and assumptions

In this study, the following values are considered for the constants presented in the previous section: 𝑻

𝑿 𝑬𝒆𝒍𝒆𝒄 = 𝟓𝟎 𝒏𝒋

𝑹

𝑿 𝑬𝒆𝒍𝒆𝒄 = 𝟓𝟎 𝒏𝒋

𝜺𝒇𝒔 = 𝟏𝟎 𝒑𝒋 𝜺𝒎𝒑 = 𝟎. 𝟎𝟎𝟏𝟑 𝒑𝒋 𝒍 = 𝟒𝟎𝟎𝟎 𝒃𝒊𝒕𝒔 𝑬𝑫𝑨 = 𝟓 𝒏𝒋 The amount of d0 is calculated according to the following relation: 𝜺𝒇𝒔

𝒅𝟎 = √ 𝜺

(9)

𝒎𝒑

As specified in the above relation, with respect to the fixed amount of 𝜺𝒇𝒔 and 𝜺𝒎𝒑 , with replacement of values, the constant fixed value d0 can also be achieved as follows: 𝒅𝟎 = √

6

𝜺𝒇𝒔 𝟏𝟎 =√ ≅ 𝟖𝟕. 𝟕𝟏 𝜺𝒎𝒑 𝟎. 𝟎𝟎𝟏𝟑

Performance evaluation

After the implementation of the proposed algorithm in MATLAB, with regard to the previous section assumptions, the results of output were achieved as in the following graph:

Figure 2 The number of live nodes to the number of rounds

The above graph shows the number of live nodes in each round during the life of the sensor network. As Figure 2 shows, the network lifetime (time to start networking until the death of the last node) in our network is a number around 6800 rounds that has good improvement compared with the similar techniques. In the above diagram, the output of the two algorithms is compared with LEACH algorithm based on (proposed) Naïve Bayes:

Figure 3 The number of live nodes to the number of rounds in the proposed and LEACH algorithms

As is seen in Diagram 3, the performance of the proposed algorithm is significantly better. 7

Conclusion

As mentioned, the use of data mining approach to solving the problem of choosing cluster head in wireless sensor networks is rarely taken into consideration, while using subset algorithms of data

mining has several benefits including the flexibility of this algorithm. But more importantly, the use of an algorithm like Naïve Bayes to solve it (as seen) led to better outcomes than the other methods provided in this area. Among the other advantages of using data-mining method is training phase's being separate from the network on which the algorithm is going to be applied; in addition to the rapid increase in output, this point makes it possible to use a made model for multiple networks without spending more time and money. 8

Future works

As mentioned in the previous section, the proposed algorithm has great flexibility through data mining approach in solving the problem, so those interested, in case of having access to the new data, could add new features to the algorithm and bring about development and performance improvements in general or in a particular application. It is also possible that instead of using Naïve Bayes classifier, other conventional algorithms are in data mining to solve this problem. In addition, there are still other techniques to solve this problem that have not been tested in the selection of the optimal cluster of these developed methods Honey-Bee Mating Optimization (HBMO), Firefly Algorithm or Particle Swarm Optimization (PSO) can be mentioned. Those interested can use these techniques to solve problem in the area of cluster head to improve output.

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