Author: George Mimoglou
Supervisor: Yannis Theodoridis, Professor
Location: University of Piraeus - 2021

• Create a conda enviroment using the environment.yml
• Execute all cells in notebooks test_ais.ipynb and test_dummy.ipynb

In the scope of the dissertation, two methods were implemented and tested on simulated and real data. Both detect spatial clusters (anchorages), but each one characterizes them either as long/short-term based on their temporal persistence Spatio-Temporal Clustering (STC), or as hot/cold spot based on their spatio-temporal autocorrelation Spatio-Temporal Hot Spots (STHS). These can answer questions like "how do anchorages influence each other in the spatio-temporal dimensions?". Both methods got inspired by the grid-based method Trajectory Hot Spots¹, where cells in a spatio-temporal partition are clustered and statistically characterized based on the total duration of vessel existence.

Most statistical spatial analysis methods of modern tools use Complete Spatial Randomness (CSR) as the Null Hypothesis, i.e., spatial data does not present any underline structure. Although they excel when applied to dense data, e.g., states in a country, they produce misleading results on sparse grids of maritime data. Furthermore, the results of grid-based methods depend significantly on size parameters and are subject to the Modifiable Areal Unit Problem².

The proposed methods overcome these issues by using a series of clustering in a rolling window manner and partitioning only the time dimension with domain-interpretable parameters.

The methods were tested using simulated and real AIS data; see Run tests.

Even though both methods apply to various domains, anchorage cases require specific data preprocessing. Vessel data are Automated Identification System (AIS) signals, providing position, speed, rate of turn, heading, and vessel identity, among others, so it is needed to transform them into an appropriate form to extract anchorages.

In this implementation, the points indicating that the vessel enters and exits a possible anchorage are extracted using simple heuristics, for example, very low speed and rapid change of bearing. Then, their midpoint is calculated, indicating a stationary point in a possible anchorage. Lastly, we partition time and assign each midpoint to the timeslices it exists. The models are fitted to a list of midpoints.

AIS data collected from the Argosaronic Gulf were used for testing. The noise was cleansed using mask operations in QGIS and spatial queries in PostgreSQL.

This model breaks down the meaning of spatio-temporal autocorrelation using logical reasoning and tries to approximate it without using statistics. Intuitively, the sparsity of the data and the stationarity of anchorages allow us to focus on temporal characteristics. In other words, we expect that anchorages do not influence each other in the spatial domain. However, each instance can influence itself in the future, thus existing for either long or short durations.

In the first phase, STC applies a clustering algorithm, g_clustering, on the midpoints (see Preprocessing) for each timeslice to detect the anchorages for a particular period (timeslice). The noise should be ignored. In the second phase, the centroid for each cluster is calculated. Then, a second clustering-with-noise algorithm, v_clustering, is applied to the centroids of $w$ timeslices projected onto a common plane in a rolling window manner. The detected clusters are the long-term anchorages, and the noise is the short-term anchorages.

The first clustering approximates the spatial autocorrelation notion by detecting structure, i.e., anchorages, while the second clustering integrates time and encapsulates the association of an anchorage with itself through time.

The choice of the clustering algorithms is free; however, they are associated with interpreting the results. g_clustering is used to detect anchorages, so KMeans, which requires prior knowledge of clusters, is not an appropriate choice. In contrast, with DBSCAN, one can determine the minimum number of vessels n_samples to exist in a proximity eps to detect an anchorage. At v_clustering, DBSCAN parameters can be used to determine the minimum duration or instances of an anchorage n_samples, out of $w$ timeslices to characterize it as long-term or short-term otherwise.

STHS follows the same rationale, but the second clustering, v_clustering is replaced with hot spot analysis using Getis-Ord $G^*_i$³. It differentiates itself from STC since it considers the cardinality of the clusters. STC aggregates this information into a single centroid without paying attention to the evolution of cardinality. For example, a long-term anchorage can be a hot spot if there is high cardinality for a couple of consecutive timeslices. There is spatial autocorrelation due to the stationarity of the cluster, and temporal autocorrelation due to the consistently high cardinality. Also, after some timeslices, the same anchorage can be a cold spot when the number of vessels declines.

Once g_clustering finishes, each cluster midpoint and its cardinality are calculated. Then, using the same rolling window method, the Getis-Ord $G^*_i$ is calculated considering cardinality as the characteristic attribute. Getis-Ord $G^*_i$ requires the spatial weight between two clusters. For the spatio-temporal dimensions, we have defined the Inverse Distance Weighting (IDW) as:

$$w_{K_{xa}, K_{yb}} = {m \over e^{\lparen z+1 \rparenφ\lparen K_{xa}, K_{yb}\rparen}}$$

where $K_{xa}, K_{yb}$ anchorages from timeslices $x$ and $y$, $z=\lvert x-y \rvert$ the distance of the timeslices and $φ$ a spatial distane function. $m$ is related to scale.

The clusters are characterized as Hot, Cold spots, or None based on the Getis-Ord $G^*_i$ value and the sign of the z-scores.

Maritime Surveillance, Clustering, Statistically Significant Regions, Anchorages, AIS, Spatio-temporal Dimensions