# Analyzing Data Reduction Techniques: An Experimental Perspective
## 6 Experimental Evaluation Metrics  
In the experimental evaluation, we used the following metrics to assess the performance of each algorithm on each dataset: original size, final size, percentage variance, execution time, and processing time per megabyte (MB). Besides these metrics, we also used mean squared error to evaluate the K-Means algorithm. These metrics are presented below. \begin{table}
\begin{tabular}{l l} \hline
**Data Reduction Techniques Categories** & **Examples of Data Reduction Algorithms** \\ \hline \multirow{3}{*}{Lossless Data Compression Algorithms} & **Delta Encoding 1, BZip2 1,** Huffman Encoding, \\  & Run-Length Encoding, Lempel-Ziv Compression \\  & (LZ77, LZ78, LZW) \\ \multirow{3}{*}{Lossy Data Compression Algorithms} & **Random Projection 1, Quantization 1,** Discrete \\  & Cosine Transform, Wavelet Compression, Cartesian \\ \multirow{3}{*}{Parametric Numerosity Data Reduction} & **Linear Regression 1,** Principal Component \\  & **Analysis 1,** Random Forest, Support Vector \\ \multirow{3}{*}{Non-Parametric Numerosity Data} & Machines, Gaussian Regression, Log–Linear Models \\ \cline{1-1}  & **K-Means 1, Simple Random Sampling 1,** DBSCAN, \\ \cline{1-1}  & Mean-Shift, OPTICS \\ \hline \end{tabular}
\end{table} 
Table 2: Examples of data reduction algorithms by taxonomic category. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Type** & **Name** & **Size (MB)** & \begin{tabular}{c} **Number of** \\ **Lines** & **Columns** \\ \end{tabular} \\ \hline \multirow{3}{*}{\begin{tabular}{c} Temporal, \\ Numeric \\ \end{tabular} } & \multicolumn{2}{c}{\begin{tabular}{c} Daily Minimum \\ Temperatures in Melbourne \\ Electric Production \\ Monthly Beer Production \\ in Austria \\ \end{tabular} } & 0.0558 & 3650 & 2 \\ \cline{1-1}  & \begin{tabular}{c} Daily Minimum \\ Temperatures in Melbourne \\ Electric Production \\ Monthly Beer Production \\ in Austria \\ \end{tabular} & 0.0730 & 397 & 2 \\ \cline{1-1}  & \begin{tabular}{c} Accelerometer \\ Smoke Detection \\ \end{tabular} & 0.0690 & 476 & 2 \\ \hline \multirow{3}{*}{\begin{tabular}{c} Numeric \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} Accelerometer \\ Smoke Detection \\ \end{tabular} } & 3.7000 & 153,000 & 5 \\ \cline{1-1}  &
\begin{tabular}{c} Smoke Detection \\ \end{tabular} & 5.8000 & 62,631 & 15 \\ \hline \multicolumn{1}{c}{Temporal, Text} & \multicolumn{2}{c}{IoT Temperatures} & 6.7000 & 97,606 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overview of dataset characteristics. To evaluate the performance, we measured the execution time that the algorithm took to process the data. The _execution time_ is the subtraction of the end time from the start time and registered in milliseconds (ms):  
\[Execution\ time\ (\text{ms})=end\ time\ (\text{ms})-start\ time\ (\text{ms}) \tag{1}\]  
To evaluate effectiveness, we used several measures depending on the type of algorithm we were using. For the numerosity data reduction algorithms, we used the mean squared error (_MSE_), a frequent metric used to evaluate the accuracy of a predictive model, by measuring the average squared differences between the predicted values and actual values. The formula for calculating the mean squared error is as follows:  
\[MSE=\frac{1}{n}{\sum_{i=1}^{n}}\big{(}Y_{i}-\hat{Y}_{i}\big{)}^{2} \tag{2}\]  
where \(n\) is the number of data points, \(Y_{i}\) represents the actual value for the \(i\)th data point, and \(\hat{Y}_{i}\) represents the predicted value for the \(i\)th data point. To calculate the MSE, we take the squared difference between each predicted and actual value, sum these squared differences for all data points, and then divide by the total number of data points. The result provides the average squared error between the predicted and actual values, with lower values indicating better model performance.