# Mining Evolution Patterns from Complex Trajectory Structures—A Case Study of Mesoscale Eddies in the South China Sea

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Data Sets

_{w}is the spatial standard deviation of W. We compared the eddy identification results and found that the HD method outperformed the OW and the SSH method in correctly identifying mesoscale ocean eddies in the SCS [20].

#### 2.2. Mining Periodic Pattern from Complex Trajectories

#### 2.2.1. Translation of a Complex Trajectory to a Symbol Sequence

**v**was used to represent a linear structure in which all points are not involved in any splitting or merging events. The letter

**s**was used to represent a splitting structure in which an eddy splits into two or even more structures. The letter

**m**was used to represent a merging structure in which two or more eddies merge. Lastly, the letter

**w**was used to represent a structure in which multiple points join together and then split right away.

**vssmv**and

**mwmv**, respectively.

**w**, then

**s**, then

**m**, and the linear structure

**v**would be given the lowest priority.

#### 2.2.2. The Largest and Most Frequent Pattern (LFP)

_{i}represents the i-th trajectory, which consists of m points.

_{j}represents the jth point along a trajectory. A trajectory point is represented as:

_{j}and Y

_{j}represent its spatial position, T

_{j}the time of motion, and P

_{type}represents the type of a point which represents an eddy’s specific behavior at T

_{j}over its evolution progress. P

_{type}could be a(an) starting, ending, splitting, merging, merge–split point, or common point. Any non-starting, ending, splitting, merging, split–merge points are defined as common points in this study.

_{i}is translated into a sequence of symbols, it can be expressed as

_{k}represents the type of structural change (i.e., those represented with v, s, m, and w in Figure 3a) and the data items in the sequence. The data items are arranged in a chronological order and accordingly the complex trajectories set CTD is translated into a CTS data set, which was stored in the sequence database CTSD.

**Definition**

**1.**

**Definition**

**2.**

_{1}, Pt

_{2}… Pt

_{a}>). The LFP was defined as the sequence in S with a sequence length L

_{T}and the frequency (f), as expressed below:

_{T}represents the length of the active period of the largest and most frequent sequences S, and f refers to the number of S in the CTSD.

#### 2.2.3. Mining the LFPs Using the PPSE Method

**S**.

## 3. Results

#### 3.1. The LFP Analysis

**S**, the length of the active cycle

**L**for the sequence

_{T}**S**, the number of trajectories, as well as the percentage of trajectories. The percentage is calculated as the proportion of the trajectories in the sequence

**S**in relation to the total number of trajectories within that specific cluster.

#### 3.2. Periodic Pattern Discovery

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**A flow chart showing the major components of the periodic pattern mining of structural evolution (PPSE) method.

**Figure 3.**The letters represent different behaviors of an eddy (

**a**) and the translation results (sequence of symbols) of two complex trajectories (

**b**).

**Figure 5.**Clustering results of complex trajectories of anticyclonic eddies (AE) (

**a**) and cyclonic eddies (CE) (

**b**) in the South China Sea (SCS) using the global similarity measuring algorithm for complex trajectories (GSMCT) proposed by Wang et al. [31].

**Figure 6.**The LFPs for the structural evolution of AE (

**a**) and CE (

**b**) in the SCS based on the PPSE algorithm.

**Figure 9.**The maximum (represented with circles) and annual average velocity (represented with lines) of the currents in the migration channels (R1-R7).

**Table 1.**The largest and most frequent patterns (LFPs) of the trajectory structures of AE and CE in the SCS.

Space area (Pattern) | AE | CE |
---|---|---|

Northern cluster: LFP 1 | <vmvmv, 90, 52(62%)> | <vmv, 60, 84(63%)> |

Central cluster: LFP 2 | <vmv, 60, 228(59%)> | <vmv, 60, 250(60%)> |

Southeast of Vietnam:LFP 3 | <vmvsvmsvsv, 150, 33(75%)> | <vmvsvmvsv, 120, 26(57%)> |

Southern cluster: LFP 4 | <vmsv, 60, 70(55%)> | <vmvmv, 90, 78(59%)> |

LFP | AE Mobile channel R: cycle years | CE Mobile channel R: cycle years |
---|---|---|

LFP 1 | R1 (21 years): 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2011, 2012, 2013, 2015, 2016R2 (20 years): 1993, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2005, 2006, 2007, 2008, 2011, 2012, 2013, 2014, 2015, 2016 | R1 (23 years): 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 |

LFP 2 | R4 (22 years): 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, | R2 (20 years): 1993, 1994, 1995, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2016R6 (19 years): 1993, 1994, 1996, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, |

LFP 3 | R3 (17 years): 1994, 1995, 1996, 1997, 1998, 2000, 2001, 2004, 2005, 2007, 2008, 2009, 2012, 2013, 2014, 2015, 2016 | R3 (17 years): 1993, 1994, 1995, 1996, 1997, 2000, 2001, 2002, 2003, 2006, 2008, 2009, 2010, 2012, 2013, 2014, 2016 |

LFP 4 | R5 (22 years): 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 | R7 (24 years): 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 |

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**MDPI and ACS Style**

Wang, H.; Du, Y.; Yi, J.; Wang, N.; Liang, F. Mining Evolution Patterns from Complex Trajectory Structures—A Case Study of Mesoscale Eddies in the South China Sea. *ISPRS Int. J. Geo-Inf.* **2020**, *9*, 441.
https://doi.org/10.3390/ijgi9070441

**AMA Style**

Wang H, Du Y, Yi J, Wang N, Liang F. Mining Evolution Patterns from Complex Trajectory Structures—A Case Study of Mesoscale Eddies in the South China Sea. *ISPRS International Journal of Geo-Information*. 2020; 9(7):441.
https://doi.org/10.3390/ijgi9070441

**Chicago/Turabian Style**

Wang, Huimeng, Yunyan Du, Jiawei Yi, Nan Wang, and Fuyuan Liang. 2020. "Mining Evolution Patterns from Complex Trajectory Structures—A Case Study of Mesoscale Eddies in the South China Sea" *ISPRS International Journal of Geo-Information* 9, no. 7: 441.
https://doi.org/10.3390/ijgi9070441