Probabilistic Data Aggregation in Information-based Clustered Sensor Network

Abstract

Efficient data aggregation helps in achieving maximum performance for complex interactive and sensing applications. In our proposed work, we have considered a heterogeneous sensor network which is partitioned into clusters. Each cluster is further divided into smaller information-based groups (also called similar groups) by the local processing center (LPC). The LPC acts as a cluster head and computes the probabilistic similarity of sensors by exploiting resemblance in the pattern of their sensed data. It further schedules the active and sleep duration of sensor nodes, such that only single node from every group remains active to participate in the aggregation cycle. The LPC gathers multi-characteristic dataset from the active clustered nodes and processes them by using probabilistic aggregation model. The proposed model normalizes the multi-characteristic data for deriving relative weights of each of the characteristic attribute. Finally, the aggregated information is transmitted to the global processing center. Our protocol is evaluated with wide range of performance metrics which includes aggregation gain, information accuracy, aggregation miss ratio, network lifetime and energy consumption.

Appendix A: Dissimilarity Coefficient

The dissimilarity coefficient is a function to measure differences between two entities. Our proposed clustering and aggregation method uses the coefficient to detect the amount of dissimilarity existing in the sensed dataset gathered by pair of sensor nodes.

$$\begin{aligned} {\upbeta }\left( \hbox {P}_{\mathrm{i}=\mathrm{q}},\hbox {P}_{{\mathrm{i}=\hbox {r}}} \right) =\hbox {H}\left( \frac{1}{2}\hbox {P}_{\mathrm{i}=\mathrm{q}} +\frac{1}{2}\hbox {P}_{\mathrm{i}=\mathrm{r}} \right) -\frac{1}{2}\left[ \hbox {H}\left( {\hbox {P}_{{\mathrm{i}=\hbox {q}}}} \right) +\hbox {H}\left( \hbox {P}_{\mathrm{i}=\hbox {r}} \right) \right] \end{aligned}$$

(32)

The dissimilarity coefficient is computed on every row entities that refer to the datasets sensed by cluster members. On simplifying the above equation, we get:

$$\begin{aligned} {\upbeta }\left( {\hbox {P}_{\mathrm{i}=\hbox {q}}}, \hbox {P}_{\mathrm{i}=\hbox {r}} \right)&= -\sum _{\mathrm{j}=1}^{\updelta } \frac{\hbox {p}_\mathrm{q, j}^{\uppsi } +\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } }{2}\log \left( {\frac{\hbox {p}_\mathrm{q, j}^{\uppsi } +\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } }{2}} \right) \nonumber \\&+\frac{1}{2}\sum _{\mathrm{j}=1}^{\updelta } \hbox {p}_\mathrm{q, j}^{\uppsi } \log \left( {\hbox {p}_\mathrm{q, j}^{\uppsi } } \right) +\frac{1}{2}\sum _{\mathrm{j}=1}^{\updelta } \hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } \log \left( {\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } } \right) \end{aligned}$$

(33)

$$\begin{aligned}&= \frac{1}{2}\log 2\sum _{\mathrm{j}=1}^{\updelta } \left( {\hbox {p}_\mathrm{q, j}^{\uppsi } +\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } } \right) -\frac{1}{2}\sum _{\mathrm{j}=1}^{\updelta } \hbox {p}_\mathrm{q, j}^{\uppsi } \log \left( {\hbox {p}_\mathrm{q, j}^{\uppsi } +\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } } \right) \nonumber \\&-\frac{1}{2} \sum _{\mathrm{j}=1}^{\updelta } \hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } \log \left( {\hbox {p}_\mathrm{q, j}^{\uppsi } +\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } } \right) +\frac{1}{2}\sum _{\mathrm{j}=1}^{\updelta } \hbox {p}_\mathrm{q, j}^{\uppsi } \log \left( {\hbox {p}_\mathrm{q, j}^{\uppsi } } \right) \nonumber \\&+\frac{1}{2}\sum _{\mathrm{j}=1}^{\updelta } \hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } \log \left( {\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } } \right) \end{aligned}$$

(34)

$$\begin{aligned}&= 1-\frac{1}{2}\mathop \sum \limits _{\mathrm{j}=1}^{\updelta } \hbox {p}_\mathrm{q, j}^{\uppsi } \left[ {\log \left( {\hbox {p}_\mathrm{q, j}^{\uppsi } +\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } } \right) -\log \hbox {p}_\mathrm{q, j}^{\uppsi } } \right] \nonumber \\&-\frac{1}{2}\mathop \sum \limits _{\mathrm{j}=1}^{\updelta } \hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } \left[ {\log \left( {\hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } +\hbox {p}_\mathrm{q, j}^{\uppsi } } \right) -\log \hbox {p}_{\mathrm{r},\hbox {j}}^{\uppsi } } \right] \end{aligned}$$

(35)

Moreover, the coefficient of dissimilarity satisfies following important properties:

$$\begin{aligned}&0\le {\upbeta }\left( {\hbox {P}_{\mathrm{i}=\hbox {q}}}, \hbox {P}_{\mathrm{i}=\hbox {r}} \right) \le 1\end{aligned}$$

(36)

$$\begin{aligned}&{\upbeta }\left( {\hbox {P}_{\mathrm{i}=\hbox {q}}}, \hbox {P}_{\mathrm{i}=\hbox {q}} \right) =0\end{aligned}$$

(37)

$$\begin{aligned}&{\upbeta }\left( {\hbox {P}_{\mathrm{i}=\hbox {q}}}, \hbox {P}_{\mathrm{i}=\hbox {r}} \right) ={\upbeta }\left( {\hbox {P}_{\mathrm{i}=\hbox {r}}}, \hbox {P}_{\mathrm{i}=\hbox {q}} \right) \end{aligned}$$

(38)