Trans RINA, Vol 157, Part A3, Intl J Maritime Eng, Jul-Sep 2015
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Prior probability of hypothesis H Prior probability of training data E Probability of H given E Probability of E given H
3.2 NAÏVE BAYESIAN CLASSIFIER The naïve Bayesian classifier works as follows: 1.
(1)
In this paper, we focus on learning the BNs from data without the support of human knowledge. The AIS reporting data are used for the purpose of our research. When learning the BNs from data, an assumption has to be made so that
there is a fundamental process that
follows a probability distribution. Hence, it is possible to represent the fundamental probability distribution with the BNs.
4.
Let E be a training set of samples, each with class labels. There are k classes, C1, C2, …, Ck. Each sample is represented by an n-dimensional vector, E = {E1, E2, … En}, depicting n measured values of the n attributes, A1, A2, …, An, respectively.
2. Given a sample E, the classifier will predict that E belongs to the class that has the highest posteriori probability, conditioned on E. E is predicted to belong to class Ci if and only if
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Thus, we find the class that maximizes P(Ci|E). The class Ci for which P(Ci|E) is maximized is called as the maximum posteriori hypothesis. By the Bayes’ theorem
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3. Maximize P(E|Ci)P(Ci) as P(E) is constant
4. In order to reduce the computational process in evaluating P(E|Ci)P(Ci), the naïve assumption of class conditional
independence is made. This
presumes that the values of the attributes are conditionally independent of one another, given the class label of the sample. Mathematically, this means that
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The probabilities P(E1|Ci), P(E2|Ci), …, P(En|Ci) can be easily estimated from the training set.
3.2 BNS-BASED APPROACHES TO ANOMALY DETECTION
According to [7], the BNs can be learnt from:
1) Domain experts’ knowledge; 2) Data set; or 3) Combination of the two.
Figure 1. Flowchart of the simulation process
In this paper, we use the visual analysis method for the detection of vessels anomaly behaviour. For small data sets, the visual analysis approach will produce a very good result. However, when the data set is too large to be captured by human analysis, the result will fail [35]. The design process of the overall anomaly detection process can be organized into the following step:
1. Categorize data, separate and label into two sets, normal tracks and anomaly tracks data 2. Randomized normal tracks data
A-148 ©2015: The Royal Institution of Naval Architects | (3) (2) SIMULATION
As illustrated in Figure 1, the simulation begins with the cleaning of the AIS raw data and the assigning of each record to separate tracks based on the Maritime Mobile Service Identity (MMSI). The next
step is the
interpolation process which will improve the accuracy of the anomaly detection. This process interpolates each row’s value into the nearest three minutes interval and eliminates duplicated data.
The data are categorized into normal and anomaly tracks data. Each group of tracking data will be randomized and divided into two groups using hold-out process. Hold-out is the process in which data is divided into two parts; the first part is reserved for the testing process, and the second is reserved for the training process. The last step is the BNs classification.
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