The use of machine and deep learning techniques for dealing with spatial data is progressively increasing as the amount of such kind of information consistently grows. At the same time, the quality of the obtained results strictly depends on the quality of the training data. In regression and classification tasks, the balancing of the training set with respect to both the characteristics of the input data and the ground truth values is essential to correctly capture all the eventualities and cases in the right way. However, as already pointed out in the literature, producing balanced training sets is not simple, even when they are synthetically generated. This demonstration presents a tool for producing balanced training sets for spatial operation estimation, which starts from the synthetic generation of spatial datasets resembling real-world situations, with respect to distribution and other spatial characteristics, and then apply spatial queries for obtaining a first collection on which balancing analysis and spatial augmentation techniques are applied to obtain a final balanced collection with respect to specific metrics. This tool is a step towards the generation of good-quality training sets for different spatial query optimization and evaluation models.

Understanding tourist behavior patterns is crucial for developing effective recommendation and decision support systems. The behaviors are often captured through the trajectories followed by tourists during their journeys or the sequences of visited Points of Interest (PoIs). Identifying common patterns and tracking their evolution over time can enhance the ability to understand, predict, and influence tourist choices, ultimately supporting goals like promoting specific destinations and fostering sustainable visitation patterns. Clustering algorithms like k-Means are commonly used to extract frequent patterns, requiring a tailored distance metric suited to the task. Since tourist trajectories combine spatial, temporal, and semantic features, defining a distance function that accurately captures these multifaceted aspects is essential. This paper examines various methods for encoding trajectory data and explores their effects on the clustering process. Finally, we compare and validate their suitability by using a real-world dataset of visits performed by tourists in Verona (Italy) from 2014 to 2022.

Thanks to the availability of a huge amount of spatial data, many new machine and deep learning (ML/DL) applications have emerged that are able to deal with such kind of information. In particular, new cost models have been developed with the aim of predicting the cost of spatial operations carefully. For obtaining good ML/DL models, the training activity is usually performed with synthetically generated datasets that capture as many spatial distributions as possible and as many combinations of features as desired (e.g., cardinality, geometry complexity, etc), with the aim to improve the generalization capabilities of the trained models. However, when a model is used to estimate some properties of a spatial operation, like the range query selectivity, balancing the characteristics of the input datasets could be not enough to guarantee a balancing in the ground truth values of the target variable. Therefore, we need to develop a way to balance the final results without recomputing the operation from scratch. This paper formalizes the notion of dataset balancing in the context of spatial ML/DL, proposes a set of metrics for evaluating the degree of balancing of the input domains and the target values, and defines a set of augmentation techniques specifically tailored for spatial data. Finally, it tests the effects of such augmentations in the training of a generic ML cost model for estimating the selectivity of spatial range query.

Abstract The importance and complexity of spatial join operation resulted in the availability of many join algorithms, some of which are tailored for big-data platforms like Hadoop and Spark. The choice among them is not trivial and depends on different factors. This paper proposes the first machine-learning-based framework for spatial join query optimization which can accommodate both the characteristics of spatial datasets and the complexity of the different algorithms. The main challenge is how to develop portable cost models that once trained can be applied to any pair of input datasets, because they are able to extract the important input characteristics, such as data distribution and spatial partitioning, the logic of spatial join algorithms, and the relationship between the two input datasets. The proposed system defines a set of features that can be computed efficiently for the data to catch the intricate aspects of spatial join. Then, it uses these features to train five machine learning models that are used to identify the best spatial join algorithm. The first two are regression models that estimate two important measures of the spatial join performance and they act as the cost model. The third model chooses the best partitioning strategy to use with spatial join. The fourth and fifth models further tune two important parameters, number of partitions and plane-sweep direction, to get the best performance. Experiments on large-scale synthetic and real data show the efficiency of the proposed models over baseline methods.

In the era of massive sharing of information, the term social provenance is used to denote the ownership, source or origin of a piece of information which has been propagated through social media. Tracking the provenance of information is becoming increasingly important as social platforms acquire more relevance as source of news. In this scenario, Twitter is considered one of the most important social networks for information sharing and dissemination which can be accelerated through the use of retweets and quotes. However, the Twitter API does not provide a complete tracking of the retweet chains, since only the connection between a retweet and the original post is stored, while all the intermediate connections are lost. This can limit the ability to track the diffusion of information as well as the estimation of the importance of specific users, who can rapidly become influencers, in the news dissemination. This paper proposes an innovative approach for rebuilding the possible chains of retweets and also providing an estimation of the contributions given by each user in the information spread. For this purpose, we define the concept of Provenance Constraint Network and a modified version of the Path Consistency Algorithm. An application of the proposed technique to a real-world dataset is presented at the end of the paper.

Geospatial data comprise around 60% of all the publicly available data. One of the essential and most complex operations that brings together multiple geospatial datasets is the spatial join operation. Due to its complexity, there is a lot of partitioning techniques and parallel algorithms for the spatial join problem. This leads to a complex query optimization problem: which algorithm to use for a given pair of input datasets that we want to join? With the rise of machine learning, there is a promise in addressing this problem with the use of various learned models. However, one of the concerns is the lack of a standard and publicly available data to train and test on, as well as the lack of accessible baseline models. This resource paper helps the research community to solve this problem by providing synthetic and real datasets for spatial join, source code for constructing more datasets, and several baseline solutions that researchers can further extend and compare to.

Machine learning and deep learning techniques are increasingly applied to produce efficient query optimizers, in particular in regards to big data systems. The optimization of spatial operations is even more challenging due to the inherent complexity of such kind of operations, like spatial join, range queries, and the peculiarities of spatial data. Even though a few ML-based spatial query optimizers have been proposed in literature, their design limits their use, since each one is tailored for a specific collection of datasets, a specific operation, or specific a hardware. Changes to any of these will require building and training a completely new model which entails collecting a new very large training data to obtain a good model

The importance and complexity of spatial join resulted in many join algorithms, some of which run on big-data platforms such as Hadoop and Spark. This paper proposes the first machine-learning-based query optimizer for spatial join operation which can accommodate the skewness of the spatial datasets and the complexity of the different algorithms. The main challenge is how to develop portable cost models that take into account the important input characteristics such as data distribution, spatial partitioning, logic of spatial join algorithms, and the relationship between the two datasets. The proposed system defines a set of features that can all be computed efficiently for the data to catch the intricate aspects of spatial join. Then, it uses these features to train three machine learning models that capture several metrics to estimate the cost of four spatial join algorithms according to user requirements. The first model can estimate the cardinality of spatial join algorithm. The second model can predict the number of rough comparisons for a specific join algorithm. Finally, the third model is a classification model that can choose the best join algorithm to run. Experiments on large scale synthetic and real data show the efficiency of the proposed models over baseline methods.

This demonstration presents a web-based generator for spatial data. This generator allows users to choose from a wide range of spatial data distributions and configure the cardinality of the data and the distribution parameters. It then provides three functionalities. First, it provides a visualization of how the data will look like. Second, it allows users to download this data in several standard formats including CSV and GeoJSON. Third, it provides a permalink that users can bookmark or share with their team members to reproduce the same dataset later. This service is a step towards standardized benchmarking for spatial data systems.

In recent years several extensions of Hadoop system have been proposed for dealing with spatial data and SpatialHadoop belongs to this group. In the MapReduce paradigm a task can be parallelized by partitioning data into chunks and performing the same operation on them, eventually combining the partial results at the end. Thus, the applied partitioning technique can tremendously affect the performance of a parallel execution, since it is the key point for obtaining balanced map tasks. However, when skewed distributed datasets are considered, using a regular grid might not be the right choice and other techniques have to be applied, which in turn are more expensive to build. This paper illustrates an approach for detecting the degree of skewness of a spatial dataset, based on the box counting function. Moreover, given the degree of skewness and some experimental observations, a heuristic is sketched in order to decide which partitioning technique to apply in order to improve as much as possible the performance of subsequent operations.

In the last few years the amount of available spatial data has increased both in volume and in heterogeneity, so that dealing with this huge amount of information has become an interesting new research challenge. In particular, spatial data are usually represented through a vector model upon which several spatial relations have been defined. Such relations represent the basic tools for querying and manipulating spatial data and their robust evaluation in a distributed heterogeneous environment is an important issue to consider for allowing the effective usage of these data. Among all possible spatial relations, this paper considers the topological ones, since they are generally provided by all existing systems and represent the building blocks for the implementation of other spatial relations. The conditions and the operations needed to make a dataset robust w.r.t. topological interpretations strictly depends on the adopted evaluation model. This paper considers an environment where two different evaluation models for topological relations exist, one in which equality is based on the identity of geometric primitives, and the other one where a tolerance in equality evaluation is introduced. Given such premises, the paper proposes a set of rules for guaranteeing the robustness in both models, and discusses the applicability of available algorithms of the Snap Rounding family, in order to preserve robustness in case of perturbations.

Topological relationships between geometric objects are important in several spatial applications, like spatial query evaluation, spatial integrity constraints checking, and spatial reasoning. Although the conceptual aspects of topological relationships between geometric objects embedded in the Euclidean space have been extensively studied, the problems arising when topological relationships are evaluated on real data have been much less explored. In particular, robustness problems arise in the evaluation of topological relationships between geometric objects implemented as vectors in a discrete space. A lack of robustness is characterized by the fact that different systems can produce different evaluations of topological relationships on the same data, and it is caused by the fact that coordinates are represented as finite numbers. The goal of this paper is to formally analyze some rules for increasing the robustness of a topological relationship evaluation and to give some examples w.r.t. a specific topological relationship.

The spatial data community recognizes the need for procedures that automatically validate spatial integrity constraints defined at conceptual level. This validation becomes particularly important in an open and distributed environment, like a Spatial Data Infrastructure (SDI), where the level of integration and interoperability is very high. However, the current gap between the conceptual design of a spatial database and its implementation into a GIS system makes the definition of spatial constraints useful only for documentation purposes and not for automatic validation. The GeoUML modeling language provides a set of predefined OCL templates for expressing the most common spatial constraints. In this paper, we deal with the validation problem by proposing a methodology for automatically translating the OCL constraints of GeoUML into SQL spatial queries, thus obtaining a platform independent general validation tool.

In the database research field the management of temporal and spatial information is crucial. Many information may be temporally and spatially qualified, i.e., data may be associated to temporal and spatial locations. In the management of qualified data, the notion of "granularity" plays an important role; it allows one to reason about temporal and spatial data expressed with different units of measure.

Geographical maps can be represented and manipulated using different data models, each dealing with different map properties: geometrical properties, describing the shape, extension and location of the objects composing the map, combinatorial properties, interpreting the map as a set of disjoint elements satisfying a certain set of combinatorial constraints, and topological properties, describing the topological relationships existing among map objects. These different representations (that we call layers) are typically supported in most geographical systems. However, all existing systems are downward closed, meaning that if some information A is contained in the combinatorial (topological) layer, the information required to compute A must be contained in the geometrical (combinatorial/geometrical) layer. Several applications do not require this closure. Rather, they can benefit from the incomplete representation of the map. The aim of this paper is the definition of a reference framework for integrating various and possibly incomplete representations of geographical maps.

Constraint relational databases use constraints to both model and query data. A constraint relation contains a finite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the specific conjunction of constraints, it may possibly represent an infinite set of relational tuples. For their characteristics, constraint databases are well suited to model multidimensional and structured data, like spatial and temporal data. The definition of an algebra for constraint relational databases is important in order to make constraint databases a practical technology. We extend the previously defined constraint algebra (called generalized relational algebra). First, we show that the relational model is not the only possible semantic reference model for constraint relational databases and we show how constraint relations can be interpreted under the nested relational model. Then, we introduce two distinct classes of constraint algebras, one based on the relational algebra, and one based on the nested relational algebra, and we present an algebra of the latter type. The algebra is proved equivalent to the generalized relational algebra when input relations are modified by introducing generalized tuple identifiers. However, from a user point of view, it is more suitable. Thus, the difference existing between such algebras is similar to the difference existing between the relational algebra and the nested relational algebra, dealing with only one level of nesting. We also show how external functions can be added to the proposed algebra.

The problem of selectivity estimation for queries of nontraditional databases is still an open issue. In this article, we examine the problem of selectivity estimation for some types of spatial queries in databases containing real data . We have shown earlier [Faloutsos and Kamel 1994] that real point sets typically have a nonuniform distribution, violating consistently the uniformity and independence assumptions. Moreover, we demonstrated that the theory of fractals can help to describe real point sets. In this article we show how the concept of fractal dimension, i.e., (noninteger) dimension, can lead to the solution for the selectivity estimation problem in spatial databases. Among the infinite family of fractal dimensions, we consider here the Hausdorff fractal dimension D 0 and the “Correlation” fractal dimension D 2 . Specifically, we show that (a) the average number of neighbors for a given point set follows a power law, with D 2 as exponent, and (b) the average number of nonempty range queries follows a power law with E − D 0 as exponent ( E is the dimension of the embedding space). We present the formulas to estimate the selectivity for “biased” range queries, for self-spatial joins, and for the average number of nonempty range queries. The result of some experiments on real and synthetic point sets are shown. Our formulas achieve very low relative errors, typically about 10%, versus 40%–100% of the formulas that are based on the uniformity and independence assumptions.