Geometric Algebra Model for Geometry‐oriented Topological Relation Computation

Classical topological relation expressions and computations are primarily based on abstract algebra. In this article, the representation and computation of geometry‐oriented topological relations (GOTR) are developed. GOTR is the integration of geometry and topology. The geometries are represented by blades, which contain both algebraic expressions and construction structures of the geometries in the conformal geometric algebra space. With the meet, inner, and outer products, two topology operators, the MeetOp and BoundOp operators, are developed to reveal the disjoint/intersection and inside/on‐surface/outside relations, respectively. A theoretical framework is then formulated to compute the topological relations between any pair of elementary geometries using the two operators. A multidimensional, unified and geometry‐oriented algorithm is developed to compute topological relations between geometries. With this framework, the internal results of the topological relations computation are geometries. The topological relations can be illustrated with clear geometric meanings; at the same time, it can also be modified and updated parametrically. Case studies evaluating the topological relations between 3D objects are performed. The result suggests that our model can express and compute the topological relations between objects in a symbolic and geometry‐oriented way. The method can also support topological relation series computation between objects with location or shape changes.     

A spatially explicit reinforcement learning model for geographic knowledge graph summarization

Web‐scale knowledge graphs such as the global Linked Data cloud consist of billions of individual statements about millions of entities. In recent years, this has fueled the interest in knowledge graph summarization techniques that compute representative subgraphs for a given collection of nodes. In addition, many of the most densely connected entities in knowledge graphs are places and regions, often characterized by thousands of incoming and outgoing relationships to other places, actors, events, and objects. In this article, we propose a novel summarization method that incorporates spatially explicit components into a reinforcement learning framework in order to help summarize geographic knowledge graphs, a topic that has not been considered in previous work. Our model considers the intrinsic graph structure as well as the extrinsic information to gain a more comprehensive and holistic view of the summarization task. By collecting a standard data set and evaluating our proposed models, we demonstrate that the spatially explicit model yields better results than non‐spatial models, thereby demonstrating that spatial is indeed special as far as summarization is concerned.     

Deeply integrating Linked Data with Geographic Information Systems

The realization that knowledge often forms a densely interconnected graph has fueled the development of graph databases, Web‐scale knowledge graphs and query languages for them, novel visualization and query paradigms, as well as new machine learning methods tailored to graphs as data structures. One such example is the densely connected and global Linked Data cloud that contains billions of statements about numerous domains, including life science and geography. While Linked Data has found its way into everyday applications such as search engines and question answering systems, there is a growing disconnect between the classical ways in which Geographic Information Systems (GIS) are still used today and the open‐ended, exploratory approaches used to retrieve and consume data from knowledge graphs such as Linked Data. In this work, we conceptualize and prototypically implement a Linked Data connector framework as a set of toolboxes for Esri's ArcGIS to close this gap and enable the retrieval, integration, and analysis of Linked Data from within GIS. We discuss how to connect to Linked Data endpoints, how to use ontologies to probe data and derive appropriate GIS representations on the fly, how to make use of reasoning, how to derive data that are ready for spatial analysis out of RDF triples, and, most importantly, how to utilize the link structure of Linked Data to enable analysis. The proposed Linked Data connector framework can also be regarded as the first step toward a guided geographic question answering system over geographic knowledge graphs.     

基于粗集的多尺度空间拓扑关系不确定性定量评价模型

空间拓扑关系不确定性的定量评价可为多尺度拓扑关系一致性的自动评价、空间推理与空间查询等应用的可靠性提供依据。定义了基于几何度量的拓扑距离,构建了拓扑关系不确定性的粗集表达模型;提出了不确定性粗集表达中拓扑距离的量化方法;进而提出了基于粗集的多尺度空间拓扑关系不确定性度量指标。实例研究证明了本文提出模型的科学性与合理性,该方法可用于多尺度表达过程中引起的拓扑关系不确定性的定量评价。     

Classification of topological relations between spatial objects in two‐dimensional space within the dimensionally extended 9‐intersection model

As an important topological relation model, the dimensionally extended 9‐intersection model (DE‐9IM) has been widely used as a basis for standards of queries in spatial databases. However, the negative conditions for the specification of the topological relations within the DE‐9IM have not been studied. The specification of the topological relations is closely related to the definition of the spatial objects and the topological relation models. The interior, boundary, and exterior of the spatial objects, including the point, line, and region, are defined. Within the framework of the DE‐9IM, 43 negative conditions are proposed to eliminate impossible topological relations. Configurations of region/region, region/line, line/line, region/point, line/point, and point/point relations are drawn. The mutual exclusion of the negative conditions is discussed, and the topological relations within the framework of 9IM and DE‐9IM are compared. The results show that: (1) impossible topological relations between spatial objects can be eliminated by the application of 43 negative conditions; and (2) 12 relations between two regions, 31 relations between a region and a line, 47 relations between two lines, three relations between a region and a point, three relations between a line and a point, and two relations between two points can be distinguished by the DE‐9IM.     

Geographical Linked Data: The Administrative Geography of Great Britain on the Semantic Web

Ordnance Survey, the national mapping agency of Great Britain, is investigating how semantic web technologies assist its role as a geographical information provider. A major part of this work involves the development of prototype products and datasets in RDF. This article discusses the production of an example dataset for the administrative geography of Great Britain, demonstrating the advantages of explicitly encoding topological relations between geographic entities over traditional spatial queries. We also outline how these data can be linked to other datasets on the web of linked data and some of the challenges that this raises.     

Reference data enhancement for geographic information retrieval using linked data

Gazetteers are instrumental in recognizing place names in documents such as Web pages, news, and social media messages. However, creating and maintaining gazetteers is still a complex task. Even though some online gazetteers provide rich sets of geographic names in planetary scale (e.g. GeoNames), other sources must be used to recognize references to urban locations, such as street names, neighborhood names or landmarks. We propose integrating Linked Data sources to create a gazetteer that combines a broad coverage of places with urban detail, including content on geographic and semantic relationships involving places, their multiple names and related non‐geographic entities. Our final goal is to expand the possibilities for recognizing, disambiguating and filtering references to places in texts for geographic information retrieval (GIR) and related applications. The resulting ontological gazetteer, named LoG (Linked OntoGazetteer), is accessible through Web services by applications and research initiatives on GIR, text processing, named entity recognition and others. The gazetteer currently contains over 13 million places, 140 million attributes and relationships, and 4.5 million non‐geographic entities. Data sources include GeoNames, Freebase, DBPedia and LinkedGeoData, which is based on OpenStreetMap data. An analysis on how these datasets overlap and complement one another is also presented.     

A parallel approach for improving Geo-SPARQL query performance

Geospatial Semantic Web promises better retrieval geospatial information for Digital Earth systems by explicitly representing the semantics of data through ontologies. It also promotes sharing and reuse of geospatial data by encoding it in Semantic Web languages, such as RDF, to form geospatial knowledge base. For many applications, rapid retrieval of spatial data from the knowledge base is critical. However, spatial data retrieval using the standard Semantic Web query language – Geo-SPARQL – can be very inefficient because the data in the knowledge base are no longer indexed to support efficient spatial queries. While recent research has been devoted to improving query performance on general knowledge base, it is still challenging to support efficient query of the spatial data with complex topological relationships. This research introduces a query strategy to improve the query performance of geospatial knowledge base by creating spatial indexing on-the-fly to prune the search space for spatial queries and by parallelizing the spatial join computations within the queries. We focus on improving the performance of Geo-SPARQL queries on knowledge bases encoded in RDF. Our initial experiments show that the proposed strategy can greatly reduce the runtime costs of Geo-SPARQL query through on-the-fly spatial indexing and parallel execution.     

The Basic Formal Ontology as a Reference Framework for Modeling the Evolution of Administrative Units

In information systems, ontologies promise advantages such as enhanced interoperability, knowledge sharing, and integration of data sources. In this article, we show that the upper ontology Basic Formal Ontology can facilitate the modeling of an evolution of administrative units. This is demonstrated by creating a spatiotemporal ontology for the administrative units of Switzerland. The ontology tackles the problem that the geometric data is typically captured by taking snapshots at regular intervals while the thematic data is continually updated. The ontology presented merges time‐stamped geometries with a formally described history of administrative units, allowing for complex spatiotemporal queries neither standard approach would support. The resulting populated knowledge base was evaluated against a set of spatiotemporal test queries. The evaluation showed that this knowledge base supports a wide range of queries on the evolution of the administrative units of Switzerland between 1960 and 2010.     

Spatial‐Scene Similarity Queries

Assessing spatial scenes for similarity is difficult from a cognitive and computational perspective. Solutions to spatial‐scene similarity assessments are sensible only if corresponding elements in the compared scenes are identified correctly. This matching process becomes increasingly complex and error‐prone for large spatial scenes as it is questionable how to choose one set of associations over another or how to account quantitatively for unmatched elements. We develop a comprehensive methodology for similarity queries over spatial scenes that incorporates cognitively motivated approaches about scene comparisons, together with explicit domain knowledge about spatial objects and their relations for the relaxation of spatial query constraints. Along with a sound graph‐theoretical methodology, this approach provides the foundation for plausible reasoning about spatial‐scene similarity queries.     

Observation‐Driven Geo‐Ontology Engineering

Big Data, Linked Data, Smart Dust, Digital Earth, and e‐Science are just some of the names for research trends that surfaced over the last years. While all of them address different visions and needs, they share a common theme: How do we manage massive amounts of heterogeneous data, derive knowledge out of them instead of drowning in information, and how do we make our findings reproducible and reusable by others? In a network of knowledge, topics span across scientific disciplines and the idea of domain ontologies as common agreements seems like an illusion. In this work, we argue that these trends require a radical paradigm shift in ontology engineering away from a small number of authoritative, global ontologies developed top‐down, to a high number of local ontologies that are driven by application needs and developed bottom‐up out of observation data. Similarly as the early Web was replaced by a social Web in which volunteers produce data instead of purely consuming it, the next generation of knowledge infrastructures has to enable users to become knowledge engineers themselves. Surprisingly, existing ontology engineering frameworks are not well suited for this new perspective. Hence, we propose an observation‐driven ontology engineering framework, show how its layers can be realized using specific methodologies, and relate the framework to existing work on geo‐ontologies.     

SE‐KGE: A location‐aware Knowledge Graph Embedding model for Geographic Question Answering and Spatial Semantic Lifting

Learning knowledge graph (KG) embeddings is an emerging technique for a variety of downstream tasks such as summarization, link prediction, information retrieval, and question answering. However, most existing KG embedding models neglect space and, therefore, do not perform well when applied to (geo)spatial data and tasks. Most models that do consider space primarily rely on some notions of distance. These models suffer from higher computational complexity during training while still losing information beyond the relative distance between entities. In this work, we propose a location‐aware KG embedding model called SE‐KGE. It directly encodes spatial information such as point coordinates or bounding boxes of geographic entities into the KG embedding space. The resulting model is capable of handling different types of spatial reasoning. We also construct a geographic knowledge graph as well as a set of geographic query–answer pairs called DBGeo to evaluate the performance of SE‐KGE in comparison to multiple baselines. Evaluation results show that SE‐KGE outperforms these baselines on the DBGeo data set for the geographic logic query answering task. This demonstrates the effectiveness of our spatially‐explicit model and the importance of considering the scale of different geographic entities. Finally, we introduce a novel downstream task called spatial semantic lifting which links an arbitrary location in the study area to entities in the KG via some relations. Evaluation on DBGeo shows that our model outperforms the baseline by a substantial margin.     

Spatial signatures for geographic feature types: examining gazetteer ontologies using spatial statistics

Digital gazetteers play a key role in modern information systems and infrastructures. They facilitate (spatial) search, deliver contextual information to recommended systems, enrich textual information with geographical references, and provide stable identifiers to interlink actors, events, and objects by the places they interact with. Hence, it is unsurprising that gazetteers, such as GeoNames, are among the most densely interlinked hubs on the Web of Linked Data. A wide variety of digital gazetteers have been developed over the years to serve different communities and needs. These gazetteers differ in their overall coverage, underlying data sources, provided functionality, and geographic feature type ontologies. Consequently, place types that share a common name may differ substantially between gazetteers, whereas types labeled differently may, in fact, specify the same or similar places. This makes data integration and federated queries challenging, if not impossible. To further complicate the situation, most popular and widely adopted geo‐ontologies are lightweight and thus under‐specific to a degree where their alignment and matching become nothing more than educated guesses. The most promising approach to addressing this problem, and thereby enabling the meaningful integration of gazetteer data across feature types, seems to be a combination of top‐down knowledge representation with bottom‐up data‐driven techniques such as feature engineering and machine learning. In this work, we propose to derive indicative spatial signatures for geographic feature types by using spatial statistics. We discuss how to create such signatures by feature engineering and demonstrate how the signatures can be applied to better understand the differences and commonalities of three major gazetteers, namely DBpedia Places, GeoNames, and TGN.     

简单面目标与带孔洞面目标间拓扑关系的层次表达方法

带孔洞的面目标是现实中较为常见的一类复杂目标,它们之间的拓扑关系要比简单面目标复杂得多.本文基于空间划分和目标分解的思想,利用点集(拓扑学)理论中的邻域概念详细分析和描述带孔洞面目标的点集拓扑分量,这种描述方法实质上是简单面目标点集拓扑分量描述的一种自然延展.进而,对简单面目标间拓扑关系的描述和区分方法进行了扩展,层次地分析和区分简单面目标与带孔洞面目标间的拓扑关系.相比于Egenhofer等人提出的代数描述和间接表达方法,本文提出的方法是一种直接描述和层次表达的方法,并且与简单面目标间拓扑关系的表达方法是相统一的.     

Topological relations between a directed line and a directed region

Representing the topological relations between directed spatial objects has gained increasing attention in recent years. Although topological relations between directed lines and other types of spatial objects, such as regions and bodies, have been widely investigated, few studies have focused on the topological relations between directed lines and directed regions. This research focuses on the representation and application of directed line–directed region (DLDR) topological relations, and may contribute to spatial querying and spatial analyses related to directed spatial objects or time‐varying objects. Compared with other topological relation models, a DLDR model that considers the starting and ending points of the directed line and the front and back faces of directed regions is proposed in this research to describe the topological relations between directed lines and directed regions. DLDR topological relations are presented, the completeness of the 111 DLDR topological relations is proved, and the topological relations based on the 9‐intersection model (9IM), 9⁺‐intersection model (9⁺‐IM), and DLDR model are compared. The formalism of the DLDR model and the corresponding geometric interpretations of the 111 DLDR topological relations are presented, seven propositions are stated to prove the completeness of the 111 DLDR topological relations, and the case study shows that more detailed topological relation information can be obtained based on the DLDR model.     

Quantitative fuzzy topological relations of spatial objects by induced fuzzy topology

This paper presents a study on the modeling of fuzzy topological relations between uncertain objects in Geographic Information Systems (GIS). Based on the recently developed concept of computational fuzzy topological space, topological relations between simple fuzzy spatial objects are modeled. The fuzzy spatial objects here cover simple fuzzy region, simple fuzzy line segment and fuzzy point. To compute the topological relations between the simple spatial objects, intersection concepts and integration methods are applied and a computational 9-intersection model are proposed and developed. There are different types of intersection, and we have proposed different integration methods for computation in different cases. For example, surface integration method is applied to the case of the fuzzy region-to-fuzzy region relation, while the line integration method is used in the case of fuzzy line segment-to-fuzzy line segment relation. Moreover, this study has discovered that there are (a) sixteen topological relations between simple fuzzy region to line segment; (b) forty-six topological relations between simple fuzzy line segments; (c) three topological relations between simple fuzzy region to fuzzy point; and (d) three topological relations between simple fuzzy line segment to fuzzy point.     

复合面状对象拓扑关系的表达模型

为表达复合面状对象间的细节拓扑关系,对经典9-交集模型进行了改进,给出两种基于分解思想的9-交集模型,其中分解成简单区域的9-交集模型方法相对简单,但表现形式繁琐;分解成点集的9-交集模型的表现形式符合经典9-交集模型,但计算较为复杂。通过示例比较了两种扩展9-交集模型及经典9-交集模型的表达能力。结果表明,两种扩展交集模型均能准确地表达出复合面状对象各子部分之间的拓扑关系的细节,扩充了9-交集模型的表达能力。     

知识的综合发现:理论、概念及应用

提出了知识的综合发现思想，重点以空间对象关联中的相邻关系与空间特征属性为知识综合发现的研究对象，对相关问题进行了讨论，并提出了一个高效的知识综合发现算法。实例结果表明，本算法是高效的，发现的知识是有效、可理解的。     

线与面目标间拓扑关系的层次表达方法

拓扑关系已广泛应用于空间查询、相似性分析、制图综合、不一致性探测以及空间推理等实际应用中。本文研究IR2中一条线与一个简单面目标拓扑关系的描述和区分方法,采用的基本策略是分解与组合方法。首先,将线/面拓扑关系分为两类:基本关系和复合关系。其中复合关系描述为若干个基本关系的组合,即基本关系的一个集合。然后,提出了基本拓扑关系分类和区分方法,建立了相应的层次概念邻域图。针对复合拓扑关系,从空间集合的角度提出了具有三个层次的拓扑不变量,分别是(a)集合层次上的分离数和维数,(b)元素层次上的交分量类型和(c)综合层次上的交分量序列。分析发现,在IR2中一条线与一个简单面目标间具有16种潜在的基本关系。其中,它们的13种是描述复合线/面关系的基本构成单元。     

The cognition of change: scaling deformations in mind and spatial theories

The dynamics of the earth and its inhabitants have become a core topic and focus in research in the spatial sciences. The spatio-temporal data avalanche challenges researchers to provide efficient and effective means to process spatio-temporal data. It is of vital importance to develop mechanisms that allow for the transition of data not only into information but also into knowledge. Knowledge representation techniques from artificial intelligence play an important role in laying the foundations for theories dealing with spatio-temporal data. Specifically, the advances in the area of qualitative spatial representation and reasoning (QSTR) have led to promising results. Categorical distinctions of spatio-temporal information identified by QSTR calculi potentially correspond to those relevant to humans. This article presents the first behavioral evaluation of qualitative calculi modeling geographic events associated with scaling deformations of entities, that is, changes in size by either expansion or contraction. Examples of such dynamics include a lake flooding its surroundings or an expanding oil spill in the ocean. We compare four experiments using four different semantic domains. Each domain consists of two spatially extended entities: one entity is undergoing scaling deformations while the other is static. We kept the formal QSTR characterization, which are paths through a topologically defined conceptual neighborhood graph, identical across all semantic domains. Our results show that for geographic events associated with scaling deformations (a) topological relations are not equally salient cognitively; (b) domain semantics has an influence on the conceptual salience of topological relations.