# An Internet of Things Approach for Extracting Featured Data Using AIS Database: An Application Based on the Viewpoint of Connected Ships

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## Abstract

**:**

## 1. Introduction

## 2. A Proposed Approach

#### 2.1. Step 1: Feature Extraction

_{min}and the maximum mean of SOG is v

_{max}, the range of mean of SOG is equally divided into L parts. Then, ${y}_{i}^{j}$ denotes the frequency or the number of times that the mean of SOG being equal to Value i for Class j, with i = 1, 2, …, L, j = 1, 2, …, m. Then, the total number of data samples for class j can be present as ${Q}^{j}={\displaystyle {\sum}_{i=1}^{L}{y}_{i}^{j}}$. As shown in Table 1.

#### 2.2. Step 2: Likelihood Modelling

#### 2.3. Step 3: Conjunctive Inference

_{i}is represented as a random set and profiled by a Belief Distribution (BD) as follows:

_{i}, representing that the evidence points to proposition $\theta $, which can be any subset of $\Theta $ or any element of $P(\Theta )$ except for the empty set, to the degree of ${p}_{\theta ,i}$, referred to as probability or degree of belief in general. $\left(\theta ,{p}_{\theta ,i}\right)$ is referred to as a focal element of e

_{i}, if ${p}_{\theta ,i}>0$. In this occasion, ${p}_{\theta ,i}$ is exactly coming from the probabilities obtained from the quantified characterized distributions of different classification, given by Equations (2) and (3).

_{i}, denoted by r

_{i}, which represents the ability of the evidence, where e

_{i}is generated, to provide a correct assessment or solution for a given problem [21]. The reliability of a piece of evidence is the inherent property of the evidence, and in the ER framework it measures the degree of support for, or opposition to, a proposition given that the evidence points to the proposition. In other words, the unreliability of a piece of evidence sets a bound within which another piece of evidence can play a role in support for, and opposition against, different propositions. On the other hand, evidence e

_{i}can also be associated with a weight, denoted by w

_{i}. The weight of a piece of evidence shares the same definition as that of its reliability [22]. When different pieces of evidence are acquired from different sources, or measured in different ways, the weight of evidence can be used to reflect its relative importance in comparison with other evidence and determined according to who uses the evidence.

_{i}with both the weight and reliability of e

_{i}taken into account, defined as follows:

_{i}denotes for weight, and r

_{i}denotes reliability. ${m}_{\theta ,i}$ is the degree of support for proposition θ from evidence i, which is given by ${m}_{\theta ,i}={w}_{i}{p}_{\theta ,i}$, with ${p}_{\theta ,i}$ being the degree of belief that evidence i points to θ. As described previously, ${p}_{\theta ,i}$ can be obtained using Table 1, Equations (2) and (3) $P(\Theta )$ is the power set of the frame of discernment Θ that contains all mutually exclusive hypotheses in question. It is worth mentioning that $P(\Theta )$ is treated as an independent element in the ER rule [22].

_{i}= 1 for any i, the ER rule reduces to Dempster’s rule. Evidences given by AIS are not fully reliable, so r

_{i}< 1. The combination of two pieces of evidence e

_{1}and e

_{2}(defined in Equation (4)) will be conducted as follows:

_{1}and e

_{2}into consideration. Yang et al. [23] proved that the belief distribution here is equivalent to the probability in Bayesian rule if belief is assigned to singleton states only and ${p}_{i}^{\theta}$ is calculated by Equation (4). Therefore, the ER rule can be used to obtain the probability of an AIS data cell indicates to which classification, by using the mean and variance of SOG, COG extracted from the AIS data, respectively.

#### 2.4. Step 4: Nonlinear Optimization

_{j}is the number of samples for class j. Let ${S}_{j}^{k}$ denotes the sample k in class j, where k = 1, 2, …, N

_{j}. ${p}_{{\theta}_{j},e}\left({S}_{j}^{k},{w}^{T}\right)$ denotes the probability to proposition ${\theta}_{j}$, where ${\theta}_{j}$ indicates to the class j. ${p}_{{\theta}_{j},e}\left({S}_{j}^{k},{w}^{T}\right)$ is obtained by the conjunctive reasoning process using the ER rule. Thus, for each judgment on the sample ${S}_{j}^{k}$, the deviation can be presents as 1 − ${p}_{{\theta}_{j},e}\left({S}_{j}^{k},{w}^{T}\right)$. All of the probability ${p}_{{\theta}_{j},e}\left({S}_{j}^{k},{w}^{T}\right)$ share the same weight vector

**w**

^{T}= {w

_{1}, w

_{2}, w

_{3}, w

_{4}}, which denotes the weight coefficients of mean of SOG, variance of SOG, mean of COG, variance of COG, respectively. Hence, the global accuracy or sum of inferred probabilities that have been assigned to the correct propositions is presented as,

^{T}should make Equation (10) minimum. Therefore, the optimization formulation can be presented as,

## 3. A Case Study

#### 3.1. Step 1: Statistical Analysis of the Attributes from Verified AIS Data

#### 3.2. Step 2: Belief Distribution by Likelihood

#### 3.3. Step 3: Evidence Combination

^{T}= {w

_{1}, w

_{2}, w

_{3}, w

_{4}} = {0.7244, 0.7244, 0.7244, 0.7244}. Classification results of the verified samples with initial weight coefficient are presented in Table 2.

#### 3.4. Step 4: Non-Linear Optimization of Evidential Weights

^{T}* = {w

_{1}, w

_{2}, w

_{3}, w

_{4}} = {0.45, 0.45, 0.45, 0.55}. In this occasion, w

^{T}* is used as the weight vector for the verified samples. The obtained results are presented in Table 3.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**The directions of vessels in the intersection waterway, Wuhan, China. The black lines with arrows in (

**a**–

**f**) present the directions for vessels in different routes. (

**a**) The direction 1 of vessels go downstream from Han River to lower reaches of Yangtze River; (

**b**) The direction 2 of vessels go downstream from Han River to upper reaches of Yangtze River; (

**c**) The direction 3 of vessels go upstream from Yangtze River to Han River; (

**d**) The direction 4 of vessels go upstream of Yangtze River, (

**e**) The direction 5 of vessels go downstream from Yangtze River to Han River; (

**f**) The direction 6 of vessels go downstream of Yangtze River.

**Figure 3.**Frequency distributions of mean of SOG for vessels in different directions. (

**a**) The frequency distribution of vessels in direction 1; (

**b**) The frequency distribution of vessels in direction 2; (

**c**) The frequency distribution of vessels in direction 3; (

**d**) The frequency distribution of vessels in direction 4; (

**e**) The frequency distribution of vessels in direction 5; (

**f**) The frequency distribution of vessels in direction 6.

**Figure 4.**Frequency distribution of variance of SOG for vessels in different directions. (

**a**) The frequency distribution of vessels in direction 1; (

**b**) The frequency distribution of vessels in direction 2; (

**c**) The frequency distribution of vessels in direction 3; (

**d**) The frequency distribution of vessels in direction 4; (

**e**) The frequency distribution of vessels in direction 5; (

**f**) The frequency distribution of vessels in direction 6.

**Figure 5.**Frequency distribution of mean of COG for vessels in different directions. (

**a**) The frequency distribution of vessels in direction 1; (

**b**) The frequency distribution of vessels in direction 2; (

**c**) The frequency distribution of vessels in direction 3; (

**d**) The frequency distribution of vessels in direction 4; (

**e**) The frequency distribution of vessels in direction 5; (

**f**) The frequency distribution of vessels in direction 6.

**Figure 6.**Frequency distribution of variance of COG for vessels in different directions. (

**a**) The frequency distribution of vessels in direction 1; (

**b**) The frequency distribution of vessels in direction 2; (

**c**) The frequency distribution of vessels in direction 3; (

**d**) The frequency distribution of vessels in direction 4; (

**e**) The frequency distribution of vessels in direction 5; (

**f**) The frequency distribution of vessels in direction 6.

**Figure 7.**Likelihood distribution of the four attributes. (

**a**) The distribution of likelihood for attribute mean of SOG; (

**b**) The distribution of likelihood for attribute variance of SOG; (

**c**) The distribution of likelihood for attribute mean of COG; (

**d**) The distribution of likelihood for attribute variance of COG.

Classification | Verified Sample Attribute Distribution Value | Total | ||||
---|---|---|---|---|---|---|

Value 1 | … | Value i | … | Value L | ||

Class (1) | ${y}_{1}^{1}$ | … | ${y}_{i}^{1}$ | … | ${y}_{L}^{1}$ | ${Q}^{1}={\displaystyle {\sum}_{i=1}^{L}{y}_{i}^{1}}$ |

Class (2) | ${y}_{1}^{2}$ | … | ${y}_{i}^{2}$ | … | ${y}_{L}^{2}$ | ${Q}^{2}={\displaystyle {\sum}_{i=1}^{L}{y}_{i}^{2}}$ |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

Class (j) | ${y}_{1}^{j}$ | … | ${y}_{i}^{j}$ | … | ${y}_{L}^{j}$ | ${Q}^{j}={\displaystyle {\sum}_{i=1}^{L}{y}_{i}^{j}}$ |

⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |

Class (m) | ${y}_{1}^{m}$ | … | ${y}_{i}^{m}$ | … | ${y}_{L}^{m}$ | ${Q}^{m}={\displaystyle {\sum}_{i=1}^{L}{y}_{i}^{m}}$ |

Directions | Total | Correct Classification | Incorrect Classification | Accuracy |
---|---|---|---|---|

Direction 1 | 698 | 692 | 6 | 99.14% |

Direction 2 | 812 | 758 | 54 | 93.35% |

Direction 3 | 693 | 692 | 1 | 99.86% |

Direction 4 | 6230 | 6220 | 10 | 99.84% |

Direction 5 | 755 | 616 | 139 | 81.59% |

Direction 6 | 8535 | 8535 | 0 | 100% |

Overall | 17,723 | 17,513 | 210 | 98.82% |

Directions | Total | Correct Classification | Incorrect Classification | Accuracy |
---|---|---|---|---|

Direction 1 | 698 | 691 | 7 | 99% |

Direction 2 | 812 | 772 | 40 | 95.07% |

Direction 3 | 693 | 692 | 1 | 99.86% |

Direction 4 | 6230 | 6221 | 9 | 99.86% |

Direction 5 | 755 | 623 | 132 | 82.52% |

Direction 6 | 8535 | 8535 | 0 | 100% |

Overall | 17,723 | 17,534 | 189 | 98.93% |

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**MDPI and ACS Style**

He, W.; Li, Z.; Malekian, R.; Liu, X.; Duan, Z.
An Internet of Things Approach for Extracting Featured Data Using AIS Database: An Application Based on the Viewpoint of Connected Ships. *Symmetry* **2017**, *9*, 186.
https://doi.org/10.3390/sym9090186

**AMA Style**

He W, Li Z, Malekian R, Liu X, Duan Z.
An Internet of Things Approach for Extracting Featured Data Using AIS Database: An Application Based on the Viewpoint of Connected Ships. *Symmetry*. 2017; 9(9):186.
https://doi.org/10.3390/sym9090186

**Chicago/Turabian Style**

He, Wei, Zhixiong Li, Reza Malekian, Xinglong Liu, and Zhihe Duan.
2017. "An Internet of Things Approach for Extracting Featured Data Using AIS Database: An Application Based on the Viewpoint of Connected Ships" *Symmetry* 9, no. 9: 186.
https://doi.org/10.3390/sym9090186