## 3 Traffic Model and Knowledge Discovery
### Learning Performance and Traffic Entropy  
The learning performance of TREAD methodology was analyzed in terms of the ratio between the number of AIS messages mapped into the extracted system of routes and the number of processed positioning messages. Figure 9 shows the learning results on 50-day ground based data over the Strait of Gibraltar and the North Adriatic Sea and satellite-based data over the Indian Ocean as introduced by Figures 3b, 5a and 8, respectively. After a common preliminary phase when the system constructs the entry/exit and stationary point objects, the learning accuracy performance stabilizes at different levels, depending on traffic density and constraints. Thus, the more the traffic is constrained or regulated, the more accurate the unsupervised learning results. The extremely high traffic density and rigid routing system allowed the Strait of Gibraltar to be learned relatively quickly and consistently, capturing up to 95% of the processed messages. Lower accuracy performance can be seen in the North Adriatic Sea, where, despite the relatively constrained traffic, there are opportunities for many routes to be followed within the time window. As a result, only 70% of the traffic is learned. This aspect is even more pronounced in the Indian Ocean, where merely 40% of the traffic can be clustered, due to a lack of traffic constraints over a large area combined with the low update rates of satellite-based AIS data.  
Figure 8: Three-month satellite AIS positioning data over the Indian Ocean (**a**); superposition of detected routes (**b**). Two of them are further analyzed in terms of spatial (**c** and **e**) and travel times distribution (**d** and **f**).  
The curves in Figure 9 represent the portion of the information that contributes to the historical traffic pattern model _versus_ the amount of processed information. The amount of information that does not contribute to the traffic knowledge discovery is discarded. There is a certain point of diminishing returns, or an upper threshold, for the number of data points, which are included into the learned system of routes, beyond which the additional data do not provide further useful information to the historical route system. The traffic pattern knowledge discovery process can therefore be linked to the notion of entropy, which measures the degree of disorder in a system. Information Theory entropy is widely employed to predict human mobility, Asynchronous Transfer Mode (ATM) traffic streams and cellular network traffic [40]. Entropy clearly provides a measure of the extent to which the traffic can be predicted on the basis of the historical patterns over the area. Within this framework, entropy can be used to quantify the information gain that the derived traffic patterns will provide for prediction [41]. In geographical clustering studies, the notion of entropy has been suggested in [42] and recently applied to detect abnormal activities in video surveillance in [43]. As a consequence, the detection of potential anomalies can be linked to the traffic entropy: the capability to successfully recognize low-likelihood behaviors is enhanced in areas where the traffic patterns are highly regular and, therefore, the associated level of disorder is low.  
Thus, while the learning rate depends on the traffic density, the end state knowledge discovery performance is affected by the different levels of traffic entropy over the area of interest and will vary from region to region.  
Figure 9: Portion of AIS messages captured by the learned system of routes over the reported areas of interest.