# Approximate Sensory Data Collection: A Survey
## 2 Model-Based Approximate Data Collection Algorithms
### The Algorithms  
The initial work in [6] proposed a statistics prediction model based on multivariate Gaussian distribution towards historical sensory data. Sensory data with larger estimation confidence do not need to be transmitted to the sink. This work also considers how to design a query plan to optimize resource consumption. However, it does not consider network dynamics and still requires a large amount of historical data to guarantee performance. Meanwhile, the model cannot detect abnormal events since it relies on historical data. Another probabilistic model was proposed in [7]. According to the temporal and spatial correlations of sensory data, local and global probabilistic prediction models are respectively built at the sensor nodes and sink. If a node finds that the current sensory value can be estimated by the local model with high probability, it will not send the value to the sink and the sensory value will be estimated according to the global prediction model. An energy efficient \(k\)-coverage algorithms based on probability driven mechanism is proposed by [8] in wireless sensor networks, besides, the problems of how to schedule the low-energy nodes, how to balance the energy consumption and optimize the network resource was also considered. However, it will lead to the extra energy consumption for maintaining the probabilistic model in the network, meanwhile, such model is also a little ideal and cannot describe the complicate relationship among sensory data accurately. A spatial-correlation based data collection algorithm was designed in [9]. A network is divided into clusters and sub-clusters periodically such that the sensory data in one sub-cluster are similar and highly spatially correlated. During the data collection process, only a partial amount of data needs to be collected, while other non-transmitted data in the same sub-cluster can be estimated by the Multivariate Gaussian model. However, the model incurs huge energy consumption due to the necessity of frequently updating the sensory data required by the Multivariate Gaussian model. It also seems too strict to assume that sensory data follow the Multivariate Gaussian Distribution. In [10], similarly, a network is divided into clusters. Instead of Gaussian Distribution, a linear regression model is adopted to describe the temporal correlation of sensory data from a node, and a correlation graph is utilized to depict the spatial correlation of different nodes in a cluster. Only representative nodes of each cluster selected from the minimum dominant set are responsible for reporting data to the sink. Similar to [9], the efficiency and effectiveness of the algorithm depends on the variance of sensory data. If sensory values vary frequently, the models become invalid quickly. The work in [11] proposed an approximate data collection algorithm in wearable sensor networks utilizing the temporal and spatial correlations among sensory data. The algorithm has two parts. The first part is to determine the transmission order offline, where history data and linear regression are used to analyze the correlations among different sensors. Then, a weighted directed graph is constructed according to the correlations, and the topology order of the weighted directed graph is used to determine the transmission order of different sensors. The second part is to forward sensory data based on the transmission order. Each node overhears the sensory values from the sensors with higher priorities, calculates the difference between its values and the overheard ones, and only reports the difference to the sink. The computation cost for determining transmission order is high and the delay of data collection is unacceptable for large-scale networks; thus, the algorithm is only suitable for small-scale networks. A flexible framework for mobile data collection is proposed by [12] in health care applications. Such a framework supports the model-based data collection techniques; however, the detailed algorithms were not provided.