## 5 STCDRR Protocol
### Eliminating Temporal Data Redundancy at Source Level  
1. Assume that the root node observes the homogeneous (or identical) input estimate when the discerning neighborhood changes periodically or the time slot (\(j\)) is minimal. For reduction in dimensions, the juncture recognizes the identical data measurements. 2. These duplicate data are eliminated using the JACCARD similarity [36] match function. The _match_ function between two data measures is defined as \[match\big{(}m_{ij}\,,\ m_{jk}\big{)}=\left\{ \begin{array}{rl}1\text{ if }\|m_{ij}-m_{jk}\|\leq\delta\\ 0,\ \text{ otherwise}\end{array} \right.\] (2)  
Equation (2), describes the mathematical formulation of the _match_ function. Here, the threshold value is dependent on the type of application. The _match_ function returns 1 for redundant data which means the two data values are similar. 1. The poundage of the input estimate is denoted by \(wt\) which is the numeral of the successive phenomenon of the identical or same measurement in the same set. 2. After the accomplishment of the time interval, the root node converts the native vector of input estimates into a set accommodating the dissimilar input estimate as derived in Equation (3), \[X_{i}=\left\{\left(x_{i1},wt_{i1}\right),\left(x_{i2},wt_{i2}\right),\ldots, \ \left(x_{ik},wt_{ik}\right)\right\}\] (3) where \(k\leq t\). 3. The weighted cardinality of \(X_{i}\) can be denoted as \(|X_{i}|\) which is the grand total of all the input estimates in \(X_{i}\) which can be denoted as described in Equation (4). \[wt(X_{i})=\sum_{j=1}^{|X_{i}|}wt\big{(}m_{ij}\big{)}=t\] (4)  
Algorithm 1 proposes the source level data redundancy reduction temporally using the JACCARD similarity index. ```
Input: new data measurement\({}_{ij}\), Output: reduced dataset with unique values Require: Existing data measurement value \(M_{i}(m_{i1},m_{i2},\ldots,m_{in})\) in time period \(T\) Ensure: to forage homogeneous values in \(M_{i}\) Start: \(for\ i=1:n\) \(\{\) for\(j=2:n+1\) \(\{\) \(\) \(\) \(\) \(\)



data vectors along with their weights to each aggregator node. To eliminate the data redundancy among the collected data set implementation of the correlation coefficient technique method is a suitable solution. In this paper, we have used Pearson's Correlation Coefficient method to discover the highly correlated input set [37]. Thus, discarding the unwanted similar data set, only the relevant non-redundant data sets are forwarded to the sink node. A lesser number of transmissions can effectively reduce the overall energy consumption enhancing the network lifetime. An overview of Pearson's Correlation Coefficient (\(\rho\)) method. 1. This technique is a covariance measurement of the correlation degree between two input set estimates. Sensor data sets associated with their weights can be evaluated using this technique. Its value varies from \(-1\) to \(1\). A negative correlation exists when the data set results in the value of \(-1\). Getting a resulting value of \(0\) means there is no correlation. The positive correlation is derived when a value of \(1\) is obtained among two input sets. 2. We can formulate this correlation function for two sensor input sets and along with their weights as follows: \[\rho X_{i},Y_{j}=\frac{cov\big{(}X_{i},Y_{j};wt\big{)}}{\sqrt{cov(X_{i},X_{i} ;wt)cov\big{(}Y_{j},Y_{j};wt\big{)}}}\] (5) \[cov\big{(}X_{i},Y_{j};wt\big{)}=\frac{\sum_{i=1}^{n}wt_{i}(X_{i}-m(X_{i}; wt))\big{(}Y_{j}-m\big{(}Y_{j};wt\big{)}\big{)}}{\sum_{i=1}^{n}wt_{i}}\] (6) \[m(X_{i};wt)=\frac{\sum_{i=1}^{n}wt_{i}X_{i}}{\sum_{i=1}^{n}wt_{i}}\] (7) where, \(cov\big{(}X_{i},Y_{j};wt\big{)}=\) The weighted covariance between \(X_{i}\) and \(Y_{j}\), \(n\) = Gross number of input estimates in every data set, \(m(X_{i};wt)=\) The weighted mean of \(X_{i}\), \(m(Y_{j};wt)=\) The weighted mean of \(Y_{j}\). Equations (5)-(7) describe the mathematical formulation of the Pearson Correlation Coefficient and Covariance and Weighted Mean of two sets, respectively. 3.