## 7 SMEP Algorithms
### AuxDataQueue Compression Algorithm
#### 9.1.2 Comparison Target Methods

For comparison with other methods, we have chosen five compression methods, i.e., _winavg, delta, CQP, 2 MC_, and SMEP. We have applied their own methods to each sample in compression. We have applied a simple line interpolation to decompression and recovery in the SMEP method. We have not applied other interpolations such as two- or three-point spline interpolation, since we had used these interpolation methods but their average error rates were higher in each sample than average error rates by the line interpolation. #### 9.1.3 Performance Evaluation Measure

For performance evaluation, we use the average error rate defined as the below:

**Definition 22**. : _Let \(M\) and \(S^{0}=S_{o,o},S_{0,1},\ \cdots,\ S_{0,n-1}\) be a compression method and a ground sensor data sequence, respectively. Given a compressed sensor data sequence of \(S_{0}\), \(S^{c}=S_{c,o},S_{c,1},\ \cdots,\ S_{c,m}\), let \(S^{\prime}=S^{\prime}_{0,0},\ S^{\prime}_{0,1},\ \cdots,\ S^{\prime}_{0,n-1}\) be a decompressed and recovered sensor data sequence of \(S_{c}\). Then, the average error rate (AER) \(E_{M,S^{c}}\) of \(S^{c}\) with respect to \(S^{0}\) in the compression method \(M\) is defined as_

\[E_{M,S_{c}}=\frac{\sum_{i=1}^{i=n}\left|S^{\prime}_{0,i}-S_{0,i}\right|}{\frac {\sum_{i=1}^{i=n}\left|S_{0,i}\right|}{n}}=\frac{\sum_{i=1}^{i=n}\left|S^{ \prime}_{0,i}-S_{0,i}\right|}{\sum_{i=1}^{i=n}\left|S_{0,i}\right|}\]

From the above definition, note that an average error rate means an average ratio of the average difference value between the recovered sensor data and the original sensor data with respect to the average original sensor data value. #### 9.1.4 Experimental Tool and Method

We have used MATLAB R2014a as an experimental tool. With this tool, we have experimented with four compression methods per sample, while increasing the number of compressions one-by-one. With our experimental results, we have analyzed and evaluated our SMEP method, comparing it with other methods. ### Experiments, Experimental Results and Analysis

In wireless sensor network literatures only a few methods for reducing the sensor data loss during communication failure have been proposed while a lot of the methods for reducing the number of sensor data transmissions with energy efficiency purpose have been mostly presented. They are _winavg, delta, CQP_ and _2 MC_ methods as they have been briefly discussed in Section 2 and among the the \begin{table}
\begin{tabular}{c c} \hline \hline
**Categories** & **Experimental Environments and Performance Evaluation Measure** \\ \hline Sensor Data Sets & Relative Humidity, Air Temperature, Underwater pH, Underwater Temperature \\ \hline \multirow{4}{*}{Samples and Sizes} & consecutive 129 sensor data sequence extracted from each set, 25, 41, 73, 93 and 97 \\  & consecutive sensor data corresponding to 1-0-0-0, 2-0-0, 3-0-0, 3-2-2, and 3-0-0 \\  & _Zones_ patterns, respectively, where _m-n-o-p Zones_ pattern means _Zones[0]=m, Zones[1]=n, Zones[2]=o, and Zones[3]=p_. \\ \hline Experimental Tool & MATLAB R2014a \\ \hline Recovery Method & linear interpolation \\ \hline Comparison Targets & _winavg, delta, CQP, 2 MC,_ and _SMEP_ methods \\ \hline Evaluation Measure & the average error rate (AER) \(E_{M,S_{c}}=\frac{\sum_{i=1}^{i=n}\left|S^{\prime}_{0,i}-S_{0,i}\right|}{\sum _{i=1}^{i=n}\left|S_{0,i}\right|}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental environments and performance evaluation measure. winavg_ and _delta_ methods are other's works. In this section we show experimental results comparing the SMEP method with _winavg_, _delta_, _CQP_ and _2 MC_ methods. We performed experiments for two categories of analysis: the AER analysis in round compressions and the AER analysis in _Zones_ value patterns. In Sections 9.2.1 and 9.2.2, we present the above two categories of experiments, their experimental results, and the analysis on them, respectively.