## 4 The Structure Fidelity Data Collection Framework
### Data Collection  
Once clusters are formed and active sensors serving as samplers to collect data are selected, no-sampler nodes enter the energy-efficient sleep mode without much degradation of structure fidelity. Note that with a fixed number of sampler nodes determined throughout the data collection phase, it is possible that the fidelity is not always superior to the preset threshold. In essence, the phenomenon that WSN is sensing is in a constant state of flux and continual change. Even an anomaly may occur in a particular time slot, for example a sudden flood, forest fire or earthquake involved in the event detection problem. More likely, the intra-cluster nodes relationships may imperceptibly change due to the slight and gradual changes in environment. Such the observation on temperature and humidity is clearly affected by seasonal changes. These changes can lead to the negative effects on the performance of our data collection framework. The first is that the nodes in a cluster no longer have a close spatial correlation. Furthermore, sensor nodes have a different sort for the data deviation compared to previous data, which would further affect the quality of cluster head and sampler nodes selection. We define the global parameter denoted by \(T_{d}\) as the period of data collection and \(T_{l}\) (_i.e._, \(M\)) as the period of learning. The setting of \(T_{d}\) is mainly for consideration of two aspects. On the one hand, the sampler nodes consume more energy compared to the sleeping nodes, since they carry out the task of sensing and report the readings. The cluster head node has additional responsibility for collecting the data from all sampler nodes in the cluster and forwarding them to the sink. In this case, energy dissipation is not balanced especially for the large number of sampler nodes. Moreover, the spatial correlation of nodes may change with the change of sensor readings. As a result, the nodes scheduling scheme fails to keep stability in a long run. Consequently, the value of \(T_{d}\) should be small enough to balance the energy consumption and maintain the correlation between different nodes. On the other hand, too small value of \(T_{d}\) can not result in a substantial saving in energy consumption. Its value is expected to be much large than the learning period \(T_{l}\). Thus, the data collection period should be dynamically adjusted to maintain the stability of correlation structure in the cluster in response to environmental changes. In order to deal with the dynamics, a feasible solution to adaptively adjust the data collection period is that the cluster head node broadcast a \"relaxning\" message to all member nodes when the drastic deterioration in sensor readings happen. In our nodes scheduling scheme, what we are most concerned is any trend changes occurred in the monitored field. Therefore, we define a metric to approximately measure the cluster trend based on the sensor time sequences. **Definition 2**. : _Two sensor nodes are isotonic if there is \(\frac{m_{1}}{m}>t\) for their time sequences \(\{x_{1},x_{2},\cdots,x_{m}\}\) and \(\{y_{1},y_{2},\cdots,y_{m}\}\), where \(m_{1}\) is the number of pairs \((x_{i},y_{i})\) in the time sequences that satisfy \((x_{i}-x_{i-1})(y_{i}-y_{i-1})\geq 0\), \(2\leq i\leq m\)._  
**Definition 3**. : _The cluster trend is deteriorating if any two nodes in the cluster are not isotonic._  
According to Definition 2, the isotonicity means that the value of a senor will increase/decrease with the value of another correlated senor increase/decrease in most of the time. As a more precise indicator to highlight the impact of sensor readings' change on data structure, the isotonicity is different from the former Pearson's coefficient, which roughly classifies the sensor nodes from the perspective of linear relation and thus more suitable to be used at the time of cluster launch. The value of \(t\) depend on the requirement of the application at hand.