# Approximate Sensory Data Collection: A Survey
## 5 Other Works  
For the convenience of reading the main advantages and disadvantages of the approximate data collection algorithms belonging to the three aforementioned categories are summarized in Table 1. Besides the aforementioned algorithms, there are some other approximate data collection works in WSNs. The work in [55] discussed how to adjust the compression rate adaptively during data collection. Since a large compression rate can reduce communication cost but increase computation cost, it is important to find a trade-off. The authors of [55] proposed an algorithm for this problem. It is assumed that the data entropy of every node is available, and the lower bound \(L_{i}\) of compression rate for node \(i\) satisfies \(L_{i}=\frac{H_{i}}{i}\), where \(H_{i}\) is the data entropy of node \(i\). It is also assumed that \(L_{i}\geq L_{j}\) if node \(j\) is on the path from \(i\) to the sink. Based on such assumptions, each node \(i\) computes the energy costs for communication and computation, respectively, during transmission. If the computation cost is larger, \begin{table}
\begin{tabular}{c c c} \hline
**Algorithms** & **Properties** & **Advantages** & **Disadvantages** \\ \hline \multirow{8}{*}{Model Based Algorithms} & & (1) The mathematical model are usually too ideal \\  & (1) The spatial and temporal correlations among sensory data are considered & (2) Lots of in-network communication are involved to determine parameters of prediction models and guarantee the consistence between local and global models \\  & (2) Only a partial of sensory values need to be transmitted & (3) The algorithm has the fixed error bound and cannot be adjusted automatically \\ \hline \multirow{8}{*}{Compressed-Sensing Based Algorithms} & & (1) The compression ratio can be controlled according to users’ requirements (2) Efficient when the sensory data matrix are sparse & (1) The assumption is strong and the sparsity of sensory data is very hard to be obtained \\  & (1) The transmission cost is extremely small & (2) All algorithms have the fixed global information loss rate \\  & (2) Sufficiently consider the users’ requirement and only transmit the valuable sensory data & (3) The centralized algorithms cost too much to transmit the bases, while the distributed one also have redundant information since the bases are not orthogonal \\ \hline \multirow{8}{*}{Query-Driven Algorithms} & & (1) The algorithms are only designed for the specific kind of queries \\  & (1) The transmission cost is extremely small & (2) They do not consider the correlations among the sensory data and cannot support to recover the original sensory data \\ \cline{1-1}  & (2) Sufficiently consider the users’ requirement and only transmit the valuable sensory data & (3) The kernel information of the sensory data is not preserved \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \cline{1-1}  & & \\ \end{tabular}
\end{table} 
Table 1: Comparisons among different approximate data collection algorithms. then the compression rate of node \(i\) is reduced to \(L_{i}\). Otherwise, it keeps the same compression rate as its child. The problems of the above algorithm are as follows. First, the assumptions are too strict for WSNs, e.g., the data entropy of an internal node in a spanning tree not only depends on its own sensory values, but also depends on the data received from its child nodes; thus, it is hard to obtain the data entropy in advance. Meanwhile, the assumption on the lower bound of compression rate seems unconvincing since there does not exist any theoretical analysis to guarantee its correctness. Third, the algorithm only considers the compression problem on one path, which is not practical for WSNs since a network is usually organized as a tree. Finally, the algorithm cannot recover data with the information loss rate satisfying an arbitrary user-specified precision requirement.