## 4 Data Aggregation
### Temporal  
In some applications such as environment monitoring, only the variation of physical parameters may be required, while in proactive clustering protocols including LEACH-like algorithms, a comprehensive picture of the entire sensing area in each round is provided by the sensor nodes. Therefore, the paper [53] presents a new reactive energy-efficient protocol called Threshold sensitive Energy Efficient sensor Network protocol (TEEN), which defines two Hard Threshold (H\({}_{\mathrm{T}}\)) and Soft Threshold (S\({}_{\mathrm{v}}\)) values to control triggering of data transmission and to exploit the temporal coherency of sensor readings to suppress data redundancy and reducing energy consumption. In this scheme, each node continuously senses the environment, but it switches on its transmitter to send the sensed data only when the sensed value satisfies two conditions. First, if the current value of the sensed attribute is greater than the hard threshold; and second, if the sensed value differs from the prior record by an amount equal or greater than the soft threshold. Thus, H\({}_{\mathrm{T}}\) reduces number of transmissions by confining the desired value of the sensed attribute; and S\({}_{\mathrm{T}}\) eliminates transmissions of the sensed data when there is minute or no change in the sensed value. By pursuing a hierarchical approach along with the use of data centric mechanism, TEEN is highly responsive to sudden changes in the sensed attributes which is an important feature for time-critical applications. However, the drawback of the method is in situations that the thresholds are not reached and so user may not get any data from network. To address the aforementioned issue in TEEN and also increase the control level of the user over the network performance, the same authors of the TEEN algorithm proposed Adaptive Periodic Threshold-sensitive Energy Efficient Sensor Network Protocol (APTEEN) [114] as an extension to TEEN. In the proposed algorithm, the best features of proactive and reactive networks are combined and a hybrid protocol is presented which sends data in adjustable time intervals while it still responds to sudden changes in attribute values. To implement the protocol, CHs broadcast a count time (T\({}_{\mathrm{C}}\)) in addition to the threshold values to the sensor nodes, which defines the maximum periods between two successive reports by a node; and if a node is not triggered to send data by exceeding the threshold values, it sends the sensed data every T\({}_{\mathrm{C}}\) intervals. Although, due to additional complexity in implementation and further data transmissions, APTEEN's performance in terms of energy dissipation and network lifetime is less than TEEN, it provides additional flexibility and a more complete picture of the network. A prediction-based data aggregation algorithm is presented in [115] to reduce redundant data transmission. The main objective of the algorithm is to provide a prediction mechanism of data series and to minimize data transmission overhead due to temporal data correlation. To achieve an acceptable level of accuracy, the protocol uses the combination of two data aggregation models: Gray-Model-based Data Aggregation (GMDA) [116] for its merits in quick modeling with a few data items and Kalman-Filter-based Data Aggregation (KFDA) because of its merits in processing data series of noisy measurements [117]. Therefore, Combined Grey model and Kalman Filter Data Aggregation (CoGKDA) can provide high prediction accuracy and more adaptability and scalability to dynamic changes in the distribution of sensed data. The algorithm is based on the synchronization of the prediction data series in the sensor node and the sink node. In other words, at the initial stage according to the level accuracy expected by the user, the sink node broadcasts the acceptable prediction error threshold and cumulative error threshold (accumulation of the error in continuous prediction) to all sensor nodes.