Vessel Trafic Flow Forecasting (VTFF) is vital for maritime harbor supervision, safety management and collision avoidance. Previous works approach the VTFF problem from two diferent perspectives: a) directly - by predicting the future trafic based on sequence analysis of historical trafic flow,and b) indirectly - by estimating the future trafic based on future vessel locations produced by vessel route forecasting algorithms. In this work, we introduce the Unified Approach for VTFF (UA-VTFF) method by taking advantage of both the indirect and direct paradigms. Our method, in order to predict the future vessel trafic flow in a time horizon of up to 30 min for a specific space, utilizes the results of the indirect paradigm by feeding them into a model that approaches the VTFF problem directly. UA-VTFF is validated over real Automatic Identification System (AIS) data and compared to baseline methods with quite promising results.
[
Maritime tracfi information systems can monitor ves- problem from two diferent perspectives [ 11]: a)
indisel trafic in sea waters. Although such commercial sys- rect - as a Vessel Route Forecasting (VRF) application
tems often provide proactive trafic management, their via employing predicted vessels locations in the future,
forecasting capability is based mainly on linear predic- and b) direct - as a flow sequence forecasting problem.
tion methods [
Over the last decade, Machine Learning (ML) based avoidance [12], a longer prediction time horizon in finer
techniques have attracted research interest to develop granularity is necessary.
trafic-related models for the maritime industry as ML In the indirect VTFF case, it is obvious that the
methods are very efective in modeling nonlinear plants method’s performance depends on the prediction
per[
In the direct VTFF case, the method’s performance future trafic. They employed seasonal autoregressive depends on the feature vector included in the sequential integrated moving average (SARIMA) and NN models to forecasting model. The ML algorithms that were imple- predict long-term container vessel trafic at the whole mented in [11] focused on the trafic of each spatial grid area of the Rajaee port in Iran. The experimental results cell on previous timestamps disregarding the trafic that showed that the NN outperforms the SARIMA models. occurs in neighbor-surrounding grid cells on previous In [24] a combined prediction framework based on timestamps. Hence, in this work we enhance the feature wavelet decomposition and deep NNs was introduced vector by adding new features, such as characteristics for predicting vessel trafic flow with time frame interval derived from neighbor-surrounding grid cells and the equal to three hours. The method was applied to trafic time characteristics of trafic flow. lfow data derived during July 2017 from the Caofeidian
More importantly, UA-VTFF unifies the direct and in- Port bounded by parallels 38.76°N and 39.21°N, and by direct VTFF cases by utilizing the results of the proposed meridians 118.16°W and 118.79°W; i.e. the tested area VRF method within the abovementioned feature vector was about 50km x 55km. analysis, i.e. this feature vector analysis is applied to Wang et al. [25] presented the DWT-Prophet, a hybrid the available historical vessel flows and at the same time prediction model for vessel trafic flow that combines the to the future vessel locations produced by the proposed discrete wavelet decomposition and the Prophet frameVRF method. The trafic flows resulting by the proposed work; data were decomposed into an approximate compofeature vector analysis are being fed to an ML method, nent and several high-frequency components by wavelet which is being trained appropriately in order to predict decomposition, and then the Prophet framework was the future vessel trafic flow up to 30 min. We experiment trained to predict every component. This method was with diferent ML methods, such as XgBoost [ 14][15], Au- tested on vessel trafic flow data during January 2018 of toregressive Integrated Moving Average (ARIMA) models the whole area of Wuhan Port Yangtze River Bridge. [16][17], Facebook Prophet [18], and Neural Networks In [26] a multimodal learning method named Prophet(NNs) [19] (static [20] and dynamic [13]). and-GRU was proposed for vessel trafic prediction,
In summary, this work builds upon our previous work which focuses on predictions with time interval within an presented in [11] and substantially improves it in terms hour. This method is based on a Prophet model to decomof accuracy on smaller sea areas and prediction horizon pose trafic flow sequence into components of diferent (from 15 min. to 30 min.). periods and on Gated Recurrent Units (GRU) to make ac
The rest of this paper is organized as follows: Section 2 curate forecasts. For evaluation purposes, a dataset was discusses related work; Section 3 provides background employed that includes vessel trafic every 30 min in Xiand preliminary terms; Section 4 presents the proposed azhimen channel, Ningbo-Zhoushan Port during March unified VTFF methodology; Section 5 describes the avail- 2020. Also, the observation rectangle is of length and able AIS data, presents the experimental setup, and dis- width equal to 3.19 and 1.04 nautical miles, respectively. cusses the results of our experimental study; Section 6 Rong et al. [27] presented an approach for forecastconcludes the paper and discusses future extensions. ing long-term maritime trafic that takes into account vessel destination prediction (by using a Multinomial Logistic Regression model) and trajectory prediction (by 2. Related Work using Gaussian Process) within a certain route. The aggregation of all ships’ positions predictions results in a Research on ML models has created impressive achieve- probabilistic picture of the future maritime trafic characments in the past few years [21]. A number of studies teristics and hotspot areas. The method was tested on an covering VTFF problem have been published in the rel- area near the coast of Portugal (bounded by parallels 36°N evant literature. We briefly present the relevant works and 42°N, and by meridians 7°W and 11°W), which was during the last two years, while an overview of less recent divided into four trafic-groups. According to the authors related works can be found in [11]. their model cannot be used for collision avoidance.
Li and Ren [22] introduced a multi-step vessel traf- In [28], Xu and Zhang proposed a method for forecastifc flow prediction method based on a Long Short-Term ing trafic volume in wind farm locations based on PearMemory Encoder-Decoder architecture. Also, they pro- son’s Correlation Coeficient (PCC) and on GRU model. posed a statistical approach of vessel trafic flow based on The GRU model takes as input the spatial impacts of AIS data. This method was tested on trafic flow during vessel trafic flow on diferent routes. To verify model’s April 2019 of the Liuhe Waterway in the Jiangsu section efectiveness and feasibility, the wind farm water area of the Yangtze River; this area is about 9km x 11km. in Jiangsu Province was selected, where 11 observation
Gargari et.al. [23] presented an approach for long-term sections were chosen; if a ship passes through the obsertrafic forecasting on a container port based on learn- vation section, the trafic volume increases by 1.
Based on the literature review in [11] and the abovementioned research works, we can conclude that valuable knowledge from vessels’ behaviour can be extracted through the analysis of historical data. However, these works focused on specific places of maritime interest and/or quite big areas that cannot assist efective collision avoidance. Also, most of these works are based on specific VTFF strategies (direct or indirect). On the other hand, in our work we propose the UA-VTFF method, which takes advantage both the indirect and direct paradigms and is capable of predicting trafic flow in open sea and at the same time in smaller sea areas.
In this section, background and preliminary terms are provided. The main definitions employed in this paper are as follows: Consider a maritime dataset composed of vessels, where the -th vessel consists of trajectories and the -th trajectory is comprised of timestamped positions (sampled at asynchronous time intervals) and can be represented as follows:
P = [︀ p(1), ..., p()]︀ = ︀[ [(1), o(1)], ..., [ (), o ()]]︀ , (1) = 1, ..., , = 1, ..., where p is a timestamped position, which consists of timestamp and location o(, ) in the Universal Transverse Mercator (UTM) system.
• Given: – a set of vessel trajectories D, – a vessel’s trajectory [p(1), . . . , p(′)] consisting of ′ consecutive points, ︀[ o(′ + 1), ..., o(′ + )]︀ (2)
• Given: – a time duration (prediction horizon) ∆ , – a number of temporal transitions , – a set of vessel trajectories D spanning in Ds (minimum bounding box of locations) in space and in time, – a set of future vessel trajectories spanning in Ds and ∪ ∆ , – a spatiotemporal (i.e., 3D) grid that splits a) Ds into grid cells of resolution × , and b) ∪ ∆ into time frames • Predict: the volume of vessels in each cell of the spatiotemporal grid.
enhanced VRF model and the UA-VTFF methodology. An overview of the proposed methodology is illustrated in Fig. 2. More specifically, first, historical AIS data pass through processing operations. Then the VRF method is applied. The processed historical data along with the produced points of the VRF are arranged into a spatiotemporal grid. Subsequently, the resulting trafic flows pass through a feature vector analysis, which are then fed to an ML method for VTFF prediction purposes. 4.1. The enhanced VRF model In this work, we consider the VRF problem as a direct trajectory forecasting problem. More specifically, in order to train the model, the output data are interpolated on the trajectory’s transitions. Also, the NN consists of * 2 outputs, where for one predicted point, there are necessary two neurons for the two coordinates for space and, as a result, each pair of output neurons gives one forecast for each trajectory’s transition. Thus, after the (described in the previous section) in order to predict the training procedure, we need to execute the NN model future trajectories. Subsequently, the vessels’ historical only one time in order to produce the desired predictions. and future trajectories are assigned into the spatiotem
As far as the input information is concerned, three poral grid (presented in Section 3) and the calculation of features are given including information regarding the the amount of vessels that are placed in every grid cell is time and the two space coordinates, actually the dif- performed. The resulting amounts indicate the volume ferences in time and space between consecutive times- of the historical vessels and the predicted vessels tamped positions. More specifically, for each timestep (produced by the proposed VRF model), which represent = 1, . . . , − 1, where is the length of the -th the trafic sequence in a specific cell-region and time trajectory, the NN is fed with the input vector: frame. Then, these trafic sequences for every grid cell are enhanced with additional features, including infor∆ u() = [︀ ∆ (), ∆ (), ∆ ()]︀ . (3) mation regarding timestamp and the volume of vessels in surrounding cells. Finally, the produced sequences are
Regarding the NN architecture it consists of an in- fed to an ML algorithm for predicting the future trafic put layer of three neurons, a Long Short-Term Memory lfow in the grids, i.e. the vessels’ amount in a particular (LSTM) [29] hidden layer, a fully-connected hidden layer cell in future time frame ∆ . Fig. 2 presents the above and an output layer of * 2 neurons. Also, the model pipeline. parameters can be updated through the Backward Prop- It should be noted that for training purposes the data agation Through Time (BPTT) algorithm [30] and the in the output are also processed as the data in the input. synaptic weights can be optimized according to the Adam More specifically, in order to predict the vessels’ amount approach [31] in the training set. Overall the NN training in the -th grid cell in the future time frame + 1, i.e., phase is followed by a validation phase and, eventually, model selection; the use of a validation set results in to produce the model output ˆ+1, the corresponding measuring the model’s generalization ability. model input +1 for the -th cell within the grid that
It should be noted that the VRF problem in [11] was comprises total cells is composed of the following feaconsidered as a multipoint location forecasting task and tures: the model presented in [13] was employed for predicting • − , ..., − 1, : the vessels’ amount in time the vessel’s future locations. This model (after following frame in the -th cell grid the training procedure) needs to be executed times in • −′ , ..., −′ 1, ′ : the vessels’ amount in time order to provide predictions for the transitions forming frame in the neighbor-surrounding cell grids ′ the future trajectory. On the other hand, our proposed of -th cell grid method needs to be executed only one time to produce the desired trajectory and thus the time prediction duration significantly decreases, as it will be shown in the experimental study (in Section 5). 4.2. The Unified Approach for VTFF
(UA-VTFF) UA-VTFF method starts by giving the available vessels’ historical trajectories into the proposed VRF algorithm • −′′ , ..., −′′ 1, ′′ : the vessels’ amount in time frame in the neighbor-surrounding cell grids with high trafic ′′ of -th cell grid • +1: the vessels’ amount produced by the enhanced VRF in the future time frame + 1 in the -th cell grid • +′1: the vessels’ amount produced by the enhanced VRF in the future time frame + 1 in the neighbor-surrounding cell grids ′ of -th cell grid
• +′′1: the vessels’ amount produced by the enhanced VRF in the future time frame + 1 in the neighbor-surrounding cell grids with high trafic ′′ of -th cell grid • − , ..., − 1, : the day of the month
in each time frame in the -th cell grid • − , ..., − 1, : the day of week in
each time frame in the -th cell grid • − , ..., − 1, : the time of day in each time frame in the -th cell grid before the final evaluation. In particular, the XgBoost models were optimized regarding the learning rate, the minimum leaf size for pruning, the number of features on a node, and the number of regression trees. Also, the ARIMA model was optimised regarding the lag order, the degree of diferencing, and the order of the moving average by evaluating the Partial Autocorrelation plot, the Augmented Dickey Fuller test and the Autocorrelation plots, respectively. Furthermore, the MLP and LSTM NNs were optimised regarding the hidden layers’ size, while an early stopping procedure [33] is employed to prevent the networks from overfitting by using a validation set. As far as the Facebook Prophet parameterization is concerned, two parameters were tuned that express Seasonality variance and Trend variance: Seasonality Prior Scale influences the seasonality component of the time series and the values tested ranged from 0.01 (small influence) to 10 (very high influence); Changepoint Prior Scale influences the variance of the trend component and the values tested ranged from 0.05 (underfitting variance) to 0.5 (overfitting variance).
Regarding the calculation of the neighbor-surrounding grid cells and those with high trafic, the neighbor 5. Experimental Study cells correspond to those cells that surround the centertargeted. The surrounding grid cells with the highest This section presents the experimental setup, along with trafic are those with the highest correlation with the the results of the tested ML methods. center-targeted and are defined based on statistical analysis and taking into account that these cells should correspond to regions areas associated with a high risk of 5.1. Experimental setup accidents [32]. To clarify the above discussion, Fig. 3 illus- All the methods were implemented using Python and the trates a grid with nearby cells only in space of 7 × 7. The experiments were conducted in a workstation composed green cell illustrates the central-targeted cell for which a of 64 GB RAM, Intel Core i9-9900KX CPU and GeForce prediction will take place. The yellow cells correspond to RTX2080Ti GPU. the neighborhood cells, while the pink cells present the The proposed method was evaluated on real-world AIS neighborhood cells with high trafic and high correlation data provided by MarineTrafic.com. More specifically, with the center-targeted. 1,757,440 AIS records received from 2344 diferent vessels
Several ML techniques were used in this study to tackle of various types sailing during November, 2018, in the the VTFF problem. Particularly, we employ XgBoost Aegean Sea rectangle bounded by longitude [23...26] and and ARIMA models, which were trained according to latitude in [36...38]. [11]. Also, we employ Facebook Prophet [18], which is a As far as the parameters of the VTFF problem formurecently presented forecasting technique inspired by the lation are concerned, we used a spatial grid of = 2km, nature of time series predicting at Facebook. a prediction horizon of ∆ = 30min and a number of
Furthermore, we use static and dynamic NNs. Partic- temporal transitions of = 6. The produced trafic flow ularly, for the static NNs, the Multi-Layer Perceptron is as follows: A number of 14,340 cells was created, with (MLP) architecture was employed composed of two hid- the trafic flow of min, max, median and mean values den neurons and trained with the Backpropagation algo- equal to 0, 103617, 25, and 120 vessels, respectively. Of rithm [19]. Regarding the dynamic NNs, LSTM networks the whole grid cells, only 768 cells presented trafic flow were used composed of an input layer, an LSTM hid- of more than 300 vessels across the entire period, while den layer, a fully-connected hidden layer and an output 4,000 cells included less than 10 vessels in the whole pelayer of two neurons. The LSTM-based architecture was riod. The top 10 grid cells have more than 5 vessels on trained following the same procedure as it was described average every 5 minutes and include more than 300,000 in Section 4.1. vessels in the entire period.
As far as the model parameterization is concerned, var- It should be noted that we resulted in the abovemenious characteristics of every model type were taken into tioned parameters ( = 2km, ∆ = 30min and = 6) account and adjusted with intermediate observation tests after experimenting with diferent values of spatial grid’s resolution (of equal to 2km, 5 km and 10 km), number of temporal transitions (of equal to 3 and 6) and prediction horizon (of ∆ equal to 15 min. and 30 min.; based on the tested values of the overall corresponding time frames were of 5 min. and 10 min.). We observed that the UA-VTFF method is aefcted by these parameters. More specifically, the model predicts better when the spatial resolution (based on ) is higher and the time frames (based on in combination with ∆ ) are bigger, while the impact of the prediction horizon is limited.
Regarding the evaluation of the implemented algorithms, it was performed in the busy grid cells [34], which correspond to regions with regular navigation and heavy trafic, with a high risk of accidents [ 32]. Areas with low vessel density denote a low level of trafic flow complexity, which implies regular and predictable vessel travel time sequences [35]. This is also confirmed by the experimental study in [11], where the ML model predicts better when there are also non-busy regions; the same ML model was tested on the whole available cells (there were cells with zero trafic) and only on the busy ones.
For all the algorithms, except the indirect VTFF [11], the corresponding trafic flow sequences of the busy grid cells are arranged into input and output data, where for each grid cell, the initial 75% of the trafic flow sequence is used for the training purpose, whereas the remaining 25% of the trafic flow sequence, except for the last six observations (corresponding to 30 min.), is organized in the testing set. Regarding the indirect VTFF, following [11] the trajectories derived from the busy grid cells are then arranged into training, validation, and testing sets of a 50%–25%–25% percent ratio, respectively. Experimental results are evaluated using the Symmetric Mean Absolute Percentage Error (SMAPE) [11]. Table 1 presents results for the UA-VTFF approach using diferent ML techniques. More specifically, LSTM, MLP, XgBoost, ARIMA and Prophet are employed. Also, Table 2 presents results for the UA-VTFF approach, the indirect and direct VTFF strategies presented in [11].
The results presented in Table 1 confirm that the
LSTMbased UA-VTFF method can accurately capture the
vessel trafic flow in short-term to assist in efective
collision avoidance. This is due to the fact that LSTM have
emerged as an efective technique for several dificult
learning problems [
Also, our proposed UA-VTFF approach (using LSTM or XgBoost) outperforms the indirect and direct VTFF strategies as summarized in Table 2.
In order to investigate further the performance of the proposed UA-VTFF, we also present results in the two highest trafic grid cells. Particularly, figs 4a and 4b depict the prediction performance of the direct VTFF strategy [11] and the XgBoost-based UA-VTFF algorithm, respectively in the grid cell with id #19837. Also, figs 5a and 5b depict the prediction performance of the direct VTFF strategy [11] and the XgBoost-based UA-VTFF algorithm, respectively in the grid cell with id #19653. More specifically, the figures illustrate the original and predicted trafic flow in the training and testing sets. The figure for the training graphic corresponds to the number of vessels for the first 75% of the 5 min time frames(first 7000 time frames), while the testing graphic corresponds to the number of vessels for the last 25% of the 5 minutes time frames(last 1600 time frames). Finally, we have included the performance of each method on the last six observations of the dataset corresponding to the last 30 minutes. Based on figs 4b, 4a, 5b and 5a we can observe that UA-VTFF has less overfitting in the training data compared to the direct VTFF [11], since in the latter method the training graphic seems to have a much better performance than the testing one. Finally, the XgBoost-based UA-VTFF method performs better in the scoring dataset than the direct VTFF [11], which also uses XgBoost models.
Finally, we should mention that the proposed VRF method manages to predict a vessel trajectory composed of 6 transitions with a latency of about 0.5secs on average.
On the other hand, the VRF method used in the indirect VTFF [11] predicts 6 transitions with a latency of about 2.5 secs on average.
diction, in terms of accuracy and execution times, can provide the fundamental basis for managing safety and (a) (a)
(b) Figure 5: Prediction performance in training and testing sets for grid cell id 19653 of the: (a) XgBoost-based direct VTFF [11], and (b) XgBoost-based UA-VTFF. assisting efective collision avoidance at sea. In order to tackle the VTFF problem, in this paper we build upon previous work, which investigated two diferent VTFF strategies. Particularly, we take advantage of both the strategies by combining them, we enhance the feature vector analysis, we propose a VRF method that is able to predict the desired vessel trajectory in one execution, and we employ a longer prediction time horizon (up to 30 min.) in finer granularity (of resolution 2km x 2km). Through our experimental study of a real AIS dataset it is obvious that the proposed UA-VTFF method can eficiently forecast the trafic flow in terms of high accuracy. Future work includes the investigation of: a) weather impact on vessel trafic flow, b) tensor factorization analysis, and c) extreme trafic events to fine-tune the model.
132–154. time prediction using gtfs data, Int. J. Inf. Manage. [7] A. Nowy, K. Łazuga, L. Gucma, A. Androjna, Data Ins. 2 (2022) 100086.
M. Perkovič, J. Srše, Modeling of vessel trafic flow [21] N. Korovesis, D. Kandris, G. Koulouras, A. Alexanfor waterway design–port of świnoujście case study, dridis, Robot motion control via an eeg-based brainApplied Sciences 11 (2021) 8126. computer interface by using neural networks and [8] P. Petrou, P. Nikitopoulos, P. Tampakis, A. Gle- alpha brainwaves, Electronics 8 (2019) 1387. nis, N. Koutroumanis, G. M. Santipantakis, K. Pa- [22] Y. Li, H. Ren, Vessel trafic flow prediction using troumpas, A. Vlachou, H. Georgiou, E. Chon- lstm encoder-decoder, in: 5th Int. Conf. SPML, drodima, et al., Argo: a big data framework for Association for Computing Machinery, New York, online trajectory prediction, in: 16th Int. Symp. NY, USA, 2022, p. 1–7.
SSTD, 2019, pp. 194–197. [23] N. S. Gargari, R. Panahi, H. Akbari, A. K. Ng, Long[9] Z. Xiao, X. Fu, L. Zhang, R. S. M. Goh, Trafic pat- term trafic forecast using neural network and seatern mining and forecasting technologies in mar- sonal autoregressive integrated moving average: itime trafic service networks: A comprehensive Case of a container port, Transp. Res. Rec. 2676 survey, IEEE Trans. Intell. Transp. Syst. 21 (2020) (2022) 236–252.
1796–1825. [24] Z. Dong, Prediction of ship trafic flow based on [10] D. Nguyen, C. L. Van, M. I. Ali, Vessel trajectory wavelet decomposition and lstm, in: 7th Int. Conf. prediction using sequence-to-sequence models over ICCCBDA, IEEE, 2022, pp. 88–93. spatial grid, in: 12th ACM Int. Conf. DEBS, 2018, [25] D. Wang, Y. Meng, S. Chen, C. Xie, Z. Liu, A hybrid pp. 258–261. model for vessel trafic flow prediction based on [11] P. Mandalis, E. Chondrodima, Y. Kontoulis, wavelet and prophet, J. Mar. Sci. Eng. 9 (2021).
N. Pelekis, Y. Theodoridis, Machine learning models [26] H. Xiao, Y. Zhao, H. Zhang, Predict vessel trafic for vessel trafic flow forecasting: An experimental with weather conditions based on multimodal deep comparison, in: 23rd IEEE Int. Conf. MDM, 2022, learning, J. Mar. Sci. Eng. 11 (2023) 39. pp. 431–436. [27] H. Rong, A. Teixeira, C. G. Soares, Maritime traf[12] M. Papadimitrakis, M. Stogiannos, H. Sarimveis, ifc probabilistic prediction based on ship motion A. Alexandridis, Multi-ship control and collision pattern extraction, Reliab. Eng. Syst. Saf. 217 (2022). avoidance using mpc and rbf-based trajectory pre- [28] T. Xu, Q. Zhang, Ship trafic flow prediction in dictions, Sensors 21 (2021) 6959. wind farms water area based on spatiotemporal [13] E. Chondrodima, P. Mandalis, N. Pelekis, dependence, J. Mar. Sci. Eng. 10 (2022) 295.
Y. Theodoridis, Machine learning models for vessel [29] S. Hochreiter, J. Schmidhuber, Long short-term route forecasting: An experimental comparison, in: memory, Neural Computation 9 (1997) 1735–1780. 23rd IEEE Int. Conf. MDM, 2022, pp. 262–269. [30] P. J. Werbos, Backpropagation through time: what [14] T. Chen, C. Guestrin, Xgboost: A scalable tree it does and how to do it, Proc. IEEE 78 (1990).
boosting system, in: 22nd ACM SIGKDD, 2016. [31] P. D. Kingma, J. Ba, Adam: A method for stochastic [15] S. Mittal, S. Mahendra, V. Sanap, P. Churi, How can optimization, in: Int. Conf. ICLR, 2015. machine learning be used in stress management: [32] X. Wang, J. Li, T. Zhang, A machine-learning model A systematic literature review of applications in for zonal ship flow prediction using ais data: A case workplaces and education, Int. J. Inf. Manage. Data study in the south atlantic states region, J. Mar. Sci.
Ins. 2 (2022) 100110. Eng. 7 (2019) 463. [16] A. C. Harvey, ARIMA Models, Palgrave Macmillan [33] L. Prechelt, Early stopping - but when?, in: G. B.
UK, London, 1990, pp. 22–24. Orr, K.-R. Müller (Eds.), Neural Networks: Tricks [17] C. Tandon, S. Revankar, S. S. Parihar, How can we of the Trade, Springer Berlin Heidelberg, Berlin, predict the impact of the social media messages on Heidelberg, 1998, pp. 55–69. the value of cryptocurrency? insights from big data [34] M. Stogiannos, M. Papadimitrakis, H. Sarimveis, analytics, Int. J. Inf. Manage. Data Ins. 1 (2021). A. Alexandridis, Vessel trajectory prediction using [18] Y. Ensafi, S. H. Amin, G. Zhang, B. Shah, Time- radial basis function neural networks, in: IEEE series forecasting of seasonal items sales using ma- EUROCON 19th Int. Conf. Smart Tech., 2021. chine learning–a comparative analysis, Int. J. Inf. [35] M. Zhang, D. Zhang, S. Fu, P. Kujala, S. Hirdaris, Manage. Data Ins. 2 (2022) 100058. A predictive analytics method for maritime trafic [19] S. Haykin, Neural Networks: A Comprehensive lfow complexity estimation in inland waterways,
Foundation, 2nd ed., Prentice Hall PTR, USA, 1998. Reliab. Eng. Syst. Saf. 220 (2022) 108317. [20] E. Chondrodima, H. Georgiou, N. Pelekis, [36] S. Dai, Y. Yu, H. Fan, J. Dong, Spatio-temporal repY. Theodoridis, Particle swarm optimization and resentation learning with social tie for personalized rbf neural networks for public transport arrival poi recommendation, Data Sci. Eng. 7 (2022) 44–56.