First, we investigate the impact of the two storage strategies. We set the value of min_sup to be 15, α to be 0.01, β to be 6, C to be 3, δ to be 0.6, σ to be 10, to be 0.7, ε to be 0.5 and each CH can store 30 emission tree nodes. Figure 20 shows the object missing rate in the level 0 cluster at which the sink is located. With the clustering strategy 1, the sink node has to maintain the emission tree nodes for 3 levels so the memory space is insufficient for each level and the emission tree growing is limited. Hence, the missing rate increases when the number of objects increases. However, clustering strategy 2 is a load balance clustering approach and the sink will have more sufficient memory space for the emission tree training at different levels.
In the next experiment, we let the CH can store 500 emission tree nodes. Figure 21 shows the average number of level 1 emission tree nodes for each object in the sink. It can be seen that clustering strategy 2 is better than clustering strategy 1 since the sink can have more sufficient memory space to store more level 1 emission tree nodes.
To observe the impact of locality parameter C on the prediction hit rate of our scheme,
0 2 4 6 8 10
5 10 15
Number of Objects Average number of Lv1 emission tree nodes in Lv2 CH
Strategy 1 Strategy 2
Figure 21: The level 1 emission tree nodes in the level 2 CH
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
0.5 1 1.5 2 2.5 3 3.5
C
Prediction Hit Rate
α = 0.1 α = 0.05 α = 0.01
Figure 22: The impact of locality parameter on the prediction hit rate
we set min_sup to be 15, β to be 6, δ to be 0.6, σ to be 10, to be 0.7, ε to be 0.5, each CH can store 500 emission tree nodes, α to be 0.01, 0.05 and 0.1 respectively. Figure 22 shows the average prediction hit rate in each level 0 cluster. It can be seen that the prediction hit rate tends to increase as the value of C increases. The reason is that if C is high, the object tends to stay in the current cluster so that the CH can get much more moving records for mining more quickly and the CH would seldom make incorrect predictions when the object leaves its current level 0 cluster.
Next, we conduct the experiments to see the impact of α on prediction hit rate. We set
0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84
0.01 0.05 0.1 0.15 α
Prediction Hit Rate
MinSup = 15, β= 6 MinSup = 25, β= 6 MinSup = 35, β= 6
Figure 23: The impact of α for emission tree node maturity verification
β to be 6, min_sup to be 15, 25, and 35 respectively. The experimental results are shown in Figure 23. It can be seen that the prediction hit rate decreases as the value of α increases.
Since a lower α means that a CH needs more moving records to let the probability variation of a tree node between two successive updates ≤ α. And more updates in a node means that the probability distribution in the node is more stable and close to the real probability distribution.
To conduct the experiments of another emission tree node maturity verification parameter β, we set α to be 0.01, min_sup to be 15, 25, and 35. Figure 24 shows the experimental results.
We can conclude that the value of β should not be too small or too big. If the emission tree training in a CH just gets start, it is possible that the probability difference is very small when the CH receives the same record for a few times. If β is very small, we may make incorrect decision that the node is mature. If β is big, then the appropriate nodes can not be used for prediction as soon as possible. From Figure 23 and Figure 24, it can be seen that the major factor of maturity verification is α.
Now, we observe the impact of the probability threshold for prediction on prediction hit rate. Figure 25 shows the experiment results of the average level 0 CH prediction hit rate with various probability threshold. A low threshold means that the CH will predict more sensors
0.65 0.7 0.75 0.8 0.85
1 2 3 4 5 6 7 8 9 10 11 12 β
Prediction Hit Rate MinSup = 15, α=
0.01
MinSup = 25, α=
0.01
MinSup = 35, α=
0.01
Figure 24: The impact of β for emission tree node maturity verification
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.1 0.2 0.3 0.4 0.5
Probability Threshold
Prediction Hit Rate
α= 0.01 α= 0.05 α= 0.1
Figure 25: The impact of the probability threshold for prediction
as the next position so the prediction hit rate will be higher. A high threshold has low hit rate due to the reason that there may be no sensor with probability which is higher than or equal to the threshold so the CH won’t predict any sensor as the next position.
Finally, we conduct the experiments of the phase verification for two strategies. For the experiments, we set δ to be 0.5, 0.6, 0.7, σ to be 10 and the object number to be 7. In strategy1, a CH simply estimates the average hit rate and the average prediction hit numbers of all objects. If the average hit rate ≥ δ and the average hit numbers ≥ σ, then the CH will turn into prediction phase. The experimental results of strategy 1 is shown in Figure 26. It can be
0 1 2 3 4 5 6 7 8
4000 8000 12000 16000 20000 Time
Number of Lv0 CH in Prediction Phase δ= 0.5,σ= 10
δ= 0.6,σ= 10 δ= 0.7,σ= 10
Figure 26: The experimental result of phase verification strategy1
0 5 10 15 20
100 200 300 400 500 Time
Number of Lv0 CH in Prediction Phase
δ= 0.5,σ= 10 δ= 0.6,σ= 10 δ= 0.7,σ= 10 δ= 0.8,σ= 10
Figure 27: The experimental results of phase verification strategy2
seen that it is hard for CHs turning into prediction phase. The reason is that there may be some clusters in which only a few objects are often present so the average hit rate and the average hit numbers will tends to descend. To solve the problem, strategy 2 uses the weighted average hit rate and weighted hit numbers. Let the weighted average hit rate be wavg(hit_rate) and the weighted hit numbers be wavg(hit_num). Then wavg(hit_rate) = Phit_ratePw i∗wi
i and
wavg(hit_num) =
Phit_numP i∗wi
wi ,where wi is the number of times which Obji is in the cluster.
Figure 27 shows the experimental results of strategy 2. As shown in the figure, using strategy 2, the CHs can turn into prediction phase much faster than using strategy 1.
5 Conclusions
In this paper, based on the fact that the movements of the tracked objects generally reflect periodic behaviors, we proposed a heterogeneous tracking model, called HTM, to efficiently mine object moving patterns and track objects. Specifically, since the movements of objects have the feature of dependencies, we explored variable memory Markov to mine object moving patterns. Furthermore, due to the hierarchical feature of HTM, multi-resolution object moving patterns are provided. In light of object moving patterns, our proposed HTM is able to accurately predict the movements of objects and thus reduces the energy consumption for object tracking. Explicitly, HTM consists two phases: data collection and mining phase and prediction phase. In data collection and mining phase, all sensors will turn on and monitor the whole sensing region to collect movements of objects. Once collecting sufficient movements of objects, sensor nodes will be in prediction phase. In prediction phases, sensor nodes turn to sleep modes so as to save energy consumption. Only selected sensor nodes will be activated to track objects according to the object moving patterns. Moreover, due to the storage constraint on sensor nodes, we devised two storage strategies to build HTM. Performance of the proposed HTM was analyzed and sensitivity analysis on several design parameters was conducted. Simulation results showed that HTM is able to not only effectively mine object moving patterns but also efficiently track objects.
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