Vessel Trajectory Similarity Measure Based on Deep Convolutional Autoencoder

Dynamic time warping(DTW) distance is the most effective similarity measurement methods in time-series data mining area. Because of the high computational complexity of DTW, it is not suitable for huge amounts of data. Thus, some DTW distance lower bound methods are proposed, which can improve the efficiency of DTW distance calculation. In this paper, we summarized the existing lower bound of DTW method and then proposed a closely related field with the application and exacted Lower Bounding distance measure with Segmentation(eLBS). Experiment results show that this method meet the need of non-omission.

The similarity between a pair of time series, i.e., sequences of indexed values in time order, is often estimated by the dynamic time warping (DTW) distance, instead of any in the well-studied family of measures including the longest common subsequence (LCS) length and the edit distance. Although it may seem as if the DTW and the LCS(-like) measures are essentially different, we reveal that the DTW distance can be represented by the longest increasing subsequence (LIS) length of a sequence of integers, which is the LCS length between the integer sequence and itself sorted. For a given pair of time series of n integers between zero and c, we propose an integer sequence that represents any substring-substring DTW distance as its band-substring LIS length. The length of the produced integer sequence is O(c⁴ n²) or O(c² n²) depending on the variant of the DTW distance used, both of which can be translated to O(n²) for constant cost functions. To demonstrate that techniques developed under the LCS(-like) measures are directly applicable to analysis of time series via our reduction of DTW to LIS, we present time-efficient algorithms for DTW-related problems utilizing the semi-local sequence comparison technique developed for LCS-related problems.

The similarity between a pair of time series, i.e., sequences of indexed values in time order, is often estimated by the dynamic time warping (DTW) distance, instead of any in the well-studied family of measures including the longest common subsequence (LCS) length and the edit distance. Although it may seem as if the DTW and the LCS(-like) measures are essentially different, we reveal that the DTW distance can be represented by the longest increasing subsequence (LIS) length of a sequence of integers, which is the LCS length between the integer sequence and itself sorted. For a given pair of time series of length n such that the dissimilarity between any elements is an integer between zero and c, we propose an integer sequence that represents any substring-substring DTW distance as its band-substring LIS length. The length of the produced integer sequence is O(c n^2), which can be translated to O(n^2) for constant dissimilarity functions. To demonstrate that techniques developed under the LCS(-like) measures are directly applicable to analysis of time series via our reduction of DTW to LIS, we present time-efficient algorithms for DTW-related problems utilizing the semi-local sequence comparison technique developed for LCS-related problems.

Identification of crops is an important topic in the agricultural domain. Hyperspectral remote sensing data are very useful for crop feature extraction and classification. Remote sensing data is an unstructured data and Convolutional Neural Network (CNN) can work on unstructured data efficiently. This paper presents an evaluation of CNN for crop classification using the Indian Pines standard dataset obtained from the AVIRIS sensor and the study area dataset obtained from the EO-1hyperion sensor. Optimized CNN has been tuned by training the model on different parameters. It has been compared with two classification algorithms: Deep Neural Network (DNN) and Convolutional Autoencoder. According to the test results, the proposed optimized CNN model provided better results as compared to the other two methods. CNN has given 97 ± 0.58% overall accuracy for the Indian Pines standard dataset and 78 ± 2.43% for our study area dataset.

Many researchers have been attracted towards searching of similar moving objects' trajectories due to their myriad applications. Similarity of trajectories is determined mainly by closeness or shape parameters. Closeness is measured by distance measures like Dynamic Time Warping (DTW), Edit Distance with Real Penalty (ERP), Edit Distance with Real Sequence (EDR) and Longest Common Subsequence (LCSS). These edit distance measures support scaling and translation property, but do not support rotation invariant property. Rotation Invariant (RI) distance measure supports all three properties and hence it is considered to be superior compared to other edit distance measures. However, it has two main drawbacks. The first one is, RI does not compares trajectories based on the shape. The second drawback is, RI is not robust to noise and hence produces poor results. In order to eliminate drawbacks faced by existing measures, in this paper, we have proposed Polygon Based Distance (PBD) measure to compare trajectories for similarity. Our proposed PBD distance measure supports scaling and translation properties like other measures. The main advantages of PBD distance measure are, it is invariant of rotation, it compares the trajectories based on the shape and it is robust to noise. We have performed experimental study on real time and synthetic datasets. The average accuracy of DTW is 21.67, RI is 35 and PBD is 58.33. Since PBD measure compares the trajectories based on shape and is robust to noise, its accuracy is higher compared to DTW and RI distance measures.

When a single-phase grounding fault occurs in a resonant grounding system, the determination of the fault location remains a significant challenge due to the small fault current and the instability of the grounding arc. In order to solve the problem of low protection sensitivity when a high-resistance grounding fault occurs in a resonant grounding system, this paper proposes a fault location method based on the combination of dynamic time warping (DTW) distance and fuzzy C-means (FCM) clustering. By analyzing the characteristics of the zero-sequence current upstream and downstream of the fault point when a single-phase grounding fault occurs in the resonant grounding system, it is concluded that the waveform similarity on both sides of the fault point is low. DTW distance can be used to measure the similarity of two time series, and has the characteristics of good fault tolerance and synchronization error tolerance. According to the rule that the DTW value of faulty section is much larger than that of nonfaulty sections, FCM clustering is used to classify the DTW value of each section. The membership degree matrix and cluster centers are obtained. In the membership degree matrix, the section corresponding to the data in a class of their own is the faulty section, and all other data correspond to the nonfaulty section; otherwise, it is a fault occurring at the end of the line. The simulation results of MATLAB/Simulink and the field data test show that the method can accurately locate the faulty section.

Synchronized spontaneous low frequency fluctuations of the so called BOLD signal, as measured by functional Magnetic Resonance Imaging (fMRI), are known to represent the functional connections of different brain areas. Dynamic Time Warping (DTW) distance can be used as a similarity measure between BOLD signals of brain regions as an alternative of the traditionally used correlation coefficient and the usage of the DTW algorithm has further advantages: beside the DTW distance, the algorithm generates the warping path, i.e. the time-delay function between the compared two time-series. In this paper, we propose to use the relative length of the warping path as classification feature and demonstrate that the warping path itself carries important information when classifying patients according to cannabis addiction. We discuss biomedical relevance of our findings as well.

A trajectory is a sequence of observations in time and space, for examples, the path formed by maritime vessels, orbital debris, or aircraft. It is important to track and reconstruct vessel trajectories using the Automated Identification System (AIS) data in real-world applications for maritime navigation safety. In this project, we use the National Science Foundation (NSF)'s Algorithms for Threat Detection program (ATD) 2019 Challenge AIS data to develop novel trajectory reconstruction method. Given a sequence of N unlabeled timestamped observations Χ={x1,x2,...,xN}, the goal is to track trajectories by clustering the AIS points with predicted positions using the information from the true trajectories Χ. It is a natural way to connect the observed point xî with the closest point that is estimated by using the location, time, speed, and angle information from a set of the points under consideration xi ∀ i ∈ {1, 2, …, N}. The introduced method is an unsupervised clustering-based method that does not train a supervised model which may incur a significant computational cost, so it leads to a real-time, reliable, and accurate trajectory reconstruction method. Our experimental results show that the proposed method successfully clusters vessel trajectories.

In a cloud environment, resources should be acquired quickly and automatically released at runtime. Traditional trajectory data partitions, indexing and query processing techniques are extended, so that they can take advantage of the cloud of large clusters of highly parallel processing capabilities. There are ways with trajectory data in the cloud database query processing. The advanced sensing techniques available today caused the existence of many types of trajectory datasets whose study can form a strong basis for decision making regarding a data context. Trajectory data generally includes trajectory classification, trajectory clustering, and trajectory associations and so on. All these tools need trajectory similarity measures to get comparisons in trajectory data. Some of the popular existing methods of trajectory similarity include Euclidean distance, semantic distance and there near variants. Each variant of these techniques exhibits notable differences in measurement of similarity and computational difficulty. This paper targeted to deal with this situation with the goal of lower computational efforts in trajectory similarity computations. A two‐phase trajectory similarity measure is defined. The first phase does point level analysis of trajectory points representing all trajectories and the following phase use the analysis to find the similarities. Using a hybrid similarity framework, new means for trajectory clustering and trajectory query processing are developed. From trajectory analysis followed by trajectory clustering, evaluation of cluster quality and processing of trajectory query are undertaken in this paper in different ways from the existing methods. All the proposed developments are tested with trajectory datasets with multiple attributes and the results are more favour to proposed framework than the existing ones.

Research on Automatic Identification System (AIS) anomalies has largely focused on vessel trajectories and kinematics, while identifier validity is often assumed. This study fills that gap by using the nine-digit Maritime Mobile Service Identity (MMSI) to build a rules-first baseline for anomaly classification. Validation rules are derived from ITU-R M.585-9 and operational guidance (USCG NA VCEN, AMSA), covering format constraints, category and prefix patterns, and MID ranges. The same rules are applied to two public data sources (Global Fishing Watch and NOAA/Access AIS). The pipeline assigns per-record labels for validity, category, and diagnostic notes, and defines a taxonomy of identity anomalies: invalid format, misclassification or misuse, MID and policy inconsistencies, and spatiotemporal “cloned MMSI” detected via overlap tests when positions are available. Results indicate that identity screening reduces noise, highlights priority cases, and produces cleaner inputs for downstream behavioral models without relying on speed or trajectories. Contributions include a reproducible MMSI rule set, an anomaly taxonomy, and a per-source evaluation protocol to avoid misleading generalizations. The approach is transparent, computationally efficient, and easy to integrate as a first-stage filter in maritime analytics pipelines.

Rice is a food commodity that is a basic need for Indonesian people. Since the end of 2022, average rice prices in Indonesia have been increasing, breaking the record for the highest price from August to October 2023. The price of rice in each province in Indonesia is different. This can happen because rice center provinces will distribute their rice production to other regions to meet rice needs. The grouping of provinces in Indonesia based on rice prices over time is an interesting thing to research. The analysis method used to group similar objects into groups for time series data is called clustering time series. The distance that can be used to measure the closeness of two-time series is the Dynamic Time Warping (DTW) distance. The clustering analysis used is the single, complete, average, Ward, and median linkage method. The results of the analysis show that time series clustering in provinces in Indonesia based on rice prices is best using median linkage hierarchical clustering. The median linkage method has a cophenetic correlation coefficient value of 0.899064, meaning that clustering using the DTW distance with the median difference is very good. The resulting clusters contained 3 clusters which had different characteristics between the clusters. There are 2 clusters that can be of concern to the government, because there are clusters that have rice prices that have always been high in the last period and there are provincial clusters that have rice prices that are very diverse or can be said to be unstable.

In this paper, we propose an efficient approach that computes the dynamic time warping (DTW) distance in time-series similarity search. The DTW distance is known to offer the high accuracy in similarity search, but it has difficulty in supporting the large database due to its high computational complexity. Recently, FastDTW and FTW have been proposed for efficient computation of DTW distances, but they have still performance limitations. In this paper, we propose a hybrid approach, called HybridFTW, which combines the advantages of both FastDTW and FTW. First, HybridFTW takes the advantage of FastDTW that provides fast computation through the limitation of allowable ranges. We call these allowable ranges dynamic (warping) bands, which reduce the computation spaces on the fly, and we reanalyze previous FastDTW and FTW in the viewpoint of static and dynamic bands. Second, HybridFTW also takes the advantage of FTW that exploits the early abandon effect by using the segment-based tight lower bound. To maximize the synergy of combining two methods, we obtain the dynamic band of FastDTW during the process of computing the lower bound in FTW. Using HybridFTW, we next propose range search and k-NN search algorithms and prove their correctness through formal theorems. Experimental results on real and synthetic data sets show that HybridFTW improves the search performance by up to 38 times over FastDTW and by up to 12 times over FTW.

One of the most famous algorithms for time series data clustering is k -means clustering with Euclidean distance as a similarity measure. However, many recent works have shown that Dynamic Time Warping (DTW) distance measure is more suitable for most time series data mining tasks due to its much improved alignment based on shape. Unfortunately, k -means clustering with DTW distance is still not practical since the current averaging functions fail to preserve characteristics of time series data within the cluster. Recently, Shape-based Template Matching Framework (STMF) has been proposed to discover a cluster representative of time series data. However, STMF is very computationally expensive. In this paper, we propose a Shape-based Clustering for Time Series (SCTS) using a novel averaging method called Ranking Shape-based Template Matching Framework (RSTMF), which can average a group of time series effectively but take as much as 400 times less computational time than that of STMF. In addition, our method outperforms other well-known clustering techniques in terms of accuracy and criterion based on known ground truth.

One of the advantages of the kernel methods is that they can deal with various kinds of objects, not necessarily vectorial data with a fixed number of attributes. In this paper, we develop kernels for time series data using dynamic time warping (DTW) distances. Since DTW distances are pseudo distances that do not satisfy the triangle inequality, a kernel matrix based on them is not positive semidefinite, in general. We use semidefinite programming (SDP) to guarantee the positive definiteness of a kernel matrix. We present neighborhood preserving embedding (NPE), an SDP formulation to obtain a kernel matrix that best preserves the local geometry of time series data. We also present an out-of-sample extension (OSE) for NPE. We use two applications, time series classification and time series embedding for similarity search, to validate our approach.

<span lang="EN-US">Automatic identification system (AIS) is a vessel radio navigation equipment that has been determined by international maritime organization (IMO). Historical AIS data can be utilized for anomaly detection, trajectory prediction, and vessel trajectory planning. These benefits can be achieved by identifying the vessel's trajectory pattern through trajectory clustering. However, more effort is needed in trajectory clustering using AIS data due to their large volume and the significant number of deficiencies. In addition, trajectory clustering cannot be directly applied to trajectory data, which also applies to vessel trajectory. Therefore, we propose a trajectory clustering framework by combining douglas peucker (DP), longest common subsequence (LCSS), multi-dimensional scaling (MDS), and density-based spatial clustering of applications with noise (DBSCAN). Our experiments, carried out with AIS data for the Lombok Strait, Indonesia, showed that the trajectory compression with DP significantly accelerates the similarity measurement process. Moreover, we found that the LCSS is the optimal algorithm for similarity measurement of vessel trajectories based on AIS data. We also applied the right combination of MDS and DBSCAN in density-based clustering. The proposed framework can distinguish trajectoriess in different directions, identify the noise, and produce good quality clusters in relatively fast total processing time.</span>