Towards development of fuzzy spatial datacubes : fundamental concepts with example for multidimensional coastal erosion risk assessment and representation

Les systèmes actuels de base de données géodécisionnels (GeoBI) ne tiennent généralement pas compte de l'incertitude liée à l'imprécision et le flou des objets; ils supposent que les objets ont une sémantique, une géométrie et une temporalité bien définies et précises. Un exemple de cela est la représentation des zones à risque par des polygones avec des limites bien définies. Ces polygones sont créés en utilisant des agrégations d'un ensemble d'unités spatiales définies sur soit des intérêts des organismes responsables ou les divisions de recensement national. Malgré la variation spatio-temporelle des multiples critères impliqués dans l’analyse du risque, chaque polygone a une valeur unique de risque attribué de façon homogène sur l'étendue du territoire. En réalité, la valeur du risque change progressivement d'un polygone à l'autre. Le passage d'une zone à l'autre n'est donc pas bien représenté avec les modèles d’objets bien définis (crisp). Cette thèse propose des concepts fondamentaux pour le développement d'une approche combinant le paradigme GeoBI et le concept flou de considérer la présence de l’incertitude spatiale dans la représentation des zones à risque. En fin de compte, nous supposons cela devrait améliorer l’analyse du risque. Pour ce faire, un cadre conceptuel est développé pour créer un model conceptuel d’une base de donnée multidimensionnelle avec une application pour l’analyse du risque d’érosion côtier. Ensuite, une approche de la représentation des risques fondée sur la logique floue est développée pour traiter l'incertitude spatiale inhérente liée à l'imprécision et le flou des objets. Pour cela, les fonctions d'appartenance floues sont définies en basant sur l’indice de vulnérabilité qui est un composant important du risque. Au lieu de déterminer les limites bien définies entre les zones à risque, l'approche proposée permet une transition en douceur d'une zone à une autre. Les valeurs d'appartenance de plusieurs indicateurs sont ensuite agrégées basées sur la formule des risques et les règles SI-ALORS de la logique floue pour représenter les zones à risque. Ensuite, les éléments clés d'un cube de données spatiales floues sont formalisés en combinant la théorie des ensembles flous et le paradigme de GeoBI. En plus, certains opérateurs d'agrégation spatiale floue sont présentés. En résumé, la principale contribution de cette thèse se réfère de la combinaison de la théorie des ensembles flous et le paradigme de GeoBI. Cela permet l’extraction de connaissances plus compréhensibles et appropriées avec le raisonnement humain à partir de données spatiales et non-spatiales. Pour ce faire, un cadre conceptuel a été proposé sur la base de paradigme GéoBI afin de développer un cube de données spatiale floue dans le system de Spatial Online Analytical Processing (SOLAP) pour évaluer le risque de l'érosion côtière. Cela nécessite d'abord d'élaborer un cadre pour concevoir le modèle conceptuel basé sur les paramètres de risque, d'autre part, de mettre en œuvre l’objet spatial flou dans une base de données spatiales multidimensionnelle, puis l'agrégation des objets spatiaux flous pour envisager à la représentation multi-échelle des zones à risque. Pour valider l'approche proposée, elle est appliquée à la région Perce (Est du Québec, Canada) comme une étude de cas.Current Geospatial Business Intelligence (GeoBI) systems typically do not take into account the uncertainty related to vagueness and fuzziness of objects; they assume that the objects have well-defined and exact semantics, geometry, and temporality. Representation of fuzzy zones by polygons with well-defined boundaries is an example of such approximation. This thesis uses an application in Coastal Erosion Risk Analysis (CERA) to illustrate the problems. CERA polygons are created using aggregations of a set of spatial units defined by either the stakeholders’ interests or national census divisions. Despite spatiotemporal variation of the multiple criteria involved in estimating the extent of coastal erosion risk, each polygon typically has a unique value of risk attributed homogeneously across its spatial extent. In reality, risk value changes gradually within polygons and when going from one polygon to another. Therefore, the transition from one zone to another is not properly represented with crisp object models. The main objective of the present thesis is to develop a new approach combining GeoBI paradigm and fuzzy concept to consider the presence of the spatial uncertainty in the representation of risk zones. Ultimately, we assume this should improve coastal erosion risk assessment. To do so, a comprehensive GeoBI-based conceptual framework is developed with an application for Coastal Erosion Risk Assessment (CERA). Then, a fuzzy-based risk representation approach is developed to handle the inherent spatial uncertainty related to vagueness and fuzziness of objects. Fuzzy membership functions are defined by an expert-based vulnerability index. Instead of determining well-defined boundaries between risk zones, the proposed approach permits a smooth transition from one zone to another. The membership values of multiple indicators (e.g. slop and elevation of region under study, infrastructures, houses, hydrology network and so on) are then aggregated based on risk formula and Fuzzy IF-THEN rules to represent risk zones. Also, the key elements of a fuzzy spatial datacube are formally defined by combining fuzzy set theory and GeoBI paradigm. In this regard, some operators of fuzzy spatial aggregation are also formally defined. The main contribution of this study is combining fuzzy set theory and GeoBI. This makes spatial knowledge discovery more understandable with human reasoning and perception. Hence, an analytical conceptual framework was proposed based on GeoBI paradigm to develop a fuzzy spatial datacube within Spatial Online Analytical Processing (SOLAP) to assess coastal erosion risk. This necessitates developing a framework to design a conceptual model based on risk parameters, implementing fuzzy spatial objects in a spatial multi-dimensional database, and aggregating fuzzy spatial objects to deal with multi-scale representation of risk zones. To validate the proposed approach, it is applied to Perce region (Eastern Quebec, Canada) as a case study

Uncertainty representation in software models: a survey

This paper provides a comprehensive overview and analysis of research work on how uncertainty is currently represented in software models. The survey presents the definitions and current research status of different proposals for addressing uncertainty modeling and introduces a classification framework that allows to compare and classify existing proposals, analyze their current status and identify new trends. In addition, we discuss possible future research directions, opportunities and challenges.This work is partially supported by the European Commission (FEDER) and the Spanish Government under projects APOLO (US1264651), HORATIO (RTI2018-101204-B-C21), EKIPMENT-PLUS (P18-FR-2895) and COSCA (PGC2018-094905-B-I00)

TRAJECTORY DATA FUZZY MODELING : AMBULANCES MANAGEMENT USE CASE

ABSTRAC

Periodic pattern mining from spatio-temporal trajectory data

Rapid development in GPS tracking techniques produces a large number of spatio-temporal trajectory data. The analysis of these data provides us with a new opportunity to discover useful behavioural patterns. Spatio-temporal periodic pattern mining is employed to find temporal regularities for interesting places. Mining periodic patterns from spatio-temporal trajectories can reveal useful, important and valuable information about people's regular and recurrent movements and behaviours. Previous studies have been proposed to extract people's regular and repeating movement behavior from spatio-temporal trajectories. These previous approaches can target three following issues, (1) long individual trajectory; (2) spatial fuzziness; and (3) temporal fuzziness. First, periodic pattern mining is different to other pattern mining, such as association rule ming and sequential pattern mining, periodic pattern mining requires a very long trajectory from an individual so that the regular period can be extracted from this long single trajectory, for example, one month or one year period. Second, spatial fuzziness shows although a moving object can regularly move along the similar route, it is impossible for it to appear at the exactly same location. For instance, Bob goes to work everyday, and although he can follow a similar path from home to his workplace, the same location cannot be repeated across different days. Third, temporal fuzziness shows that periodicity is complicated including partial time span and multiple interleaving periods. In reality, the period is partial, it is highly impossible to occur through the whole movement of the object. Alternatively, the moving object has only a few periods, such as a daily period for work, or yearly period for holidays. However, it is insufficient to find effective periodic patterns considering these three issues only. This thesis aims to develop a new framework to extract more effective, understandable and meaningful periodic patterns by taking more features of spatio-temporal trajectories into account. The first feature is trajectory sequence, GPS trajectory data is temporally ordered sequences of geolocation which can be represented as consecutive trajectory segments, where each entry in each trajectory segment is closely related to the previous sampled point (trajectory node) and the latter one, rather than being isolated. Existing approaches disregard the important sequential nature of trajectory. Furthermore, they introduce both unwanted false positive reference spots and false negative reference spots. The second feature is spatial and temporal aspects. GPS trajectory data can be presented as triple data (x; y; t), x and y represent longitude and latitude respectively whilst t shows corresponding time in this location. Obviously, spatial and temporal aspects are two key factors. Existing methods do not consider these two aspects together in periodic pattern mining. Irregular time interval is the third feature of spatio-temporal trajectory. In reality, due to weather conditions, device malfunctions, or battery issues, the trajectory data are not always regularly sampled. Existing algorithms cannot deal with this issue but instead require a computationally expensive trajectory interpolation process, or it is assumed that trajectory is with regular time interval. The fourth feature is hierarchy of space. Hierarchy is an inherent property of spatial data that can be expressed in different levels, such as a country includes many states, a shopping mall is comprised of many shops. Hierarchy of space can find more hidden and valuable periodic patterns. Existing studies do not consider this inherent property of trajectory. Hidden background semantic information is the final feature. Aspatial semantic information is one of important features in spatio-temporal data, and it is embedded into the trajectory data. If the background semantic information is considered, more meaningful, understandable and useful periodic patterns can be extracted. However, existing methods do not consider the geographical information underlying trajectories. In addition, at times we are interested in finding periodic patterns among trajectory paths rather than trajectory nodes for different applications. This means periodic patterns should be identified and detected against trajectory paths rather than trajectory nodes for some applications. Existing approaches for periodic pattern mining focus on trajectories nodes rather than paths. To sum up, the aim of this thesis is to investigate solutions to these problems in periodic pattern mining in order to extract more meaningful, understandable periodic patterns. Each of three chapters addresses a different problem and then proposes adequate solutions to problems currently not addressed in existing studies. Finally, this thesis proposes a new framework to address all problems. First, we investigated a path-based solution which can target trajectory sequence and spatio-temporal aspects. We proposed an algorithm called Traclus (spatio-temporal) which can take spatial and temporal aspects into account at the same time instead of only considering spatial aspect. The result indicated our method produced more effective periodic patterns based on trajectory paths than existing node-based methods using two real-world trajectories. In order to consider hierarchy of space, we investigated existing hierarchical clustering approaches to obtain hierarchical reference spots (trajectory paths) for periodic pattern mining. HDBSCAN is an incremental version of DBSCAN which is able to handle clusters with different densities to generate a hierarchical clustering result using the single-linkage method, and then it automatically extracts clusters from a hierarchical tree. Thus, we modified traditional clustering method DBSCAN in Traclus (spatio-temporal) to HDBSCAN for extraction of hierarchical reference spots. The result is convincing, and reveals more periodic patterns than those of existing methods. Second, we introduced a stop/move method to annotate each spatio-temporal entry with a semantic label, such as restaurant, university and hospital. This method can enrich a trajectory with background semantic information so that we can easily infer people's repeating behaviors. In addition, existing methods use interpolation to make trajectory regular and then apply Fourier transform and autocorrelation to automatically detect period for each reference spot. An increasing number of trajectory nodes leads to an exponential increase of running time. Thus, we employed Lomb-Scargle periodogram to detect period for each reference spot based on raw trajectory without requiring any interpolation method. The results showed our method outperformed existing approaches on effectiveness and efficiency based on two real datasets. For hierarchical aspect, we extended previous work to find hierarchical semantic periodic patterns by applying HDBSCAN. The results were promising. Third, we apply our methodology to a case study, which reveals many interesting medical periodic patterns. These patterns can effectively explore human movement behaviors for positive medical outcomes. To sum up, this research proposed a new framework to gradually target the problems that existing methods cannot handle. These include: how to consider trajectory sequence, how to consider spatial temporal aspects together, how to deal with trajectory with irregular time interval, how to consider hierarchy of space and how to extract semantic information behind trajectory. After addressing all these problems, the experimental results demonstrate that our method can find more understandable, meaningful and effective periodic patterns than existing approaches

A process-oriented data model for fuzzy spatial objects

The complexity of the natural environment, its polythetic and dynamic character, requires appropriate new methods to represent it in GISs, if only because in the past there has been a tendency to force reality into sharp and static objects. A more generalized spatio-temporal data model is required to deal with fuzziness and dynamics of objects. This need is the motivation behind the research reported in this thesis. In particular, the objective of this research was to develop a spatio-temporal data model for objects with fuzzy spatial extent.This thesis discusses three aspects related to achieving this objective:identification of fuzzy objects,detection of dynamic changes in fuzzy objects, andrepresentation of objects and their dynamics in a spatio-temporal data model.For the identification of fuzzy objects, a six-step procedure was proposed to extract objects from field observation data: sampling, interpolation, classification, segmentation, merging and identification. The uncertainties involved in these six steps were investigated and their effect on the mapped objects was analyzed. Three fuzzy object models were proposed to represent fuzzy objects of different application contexts. The concepts of conditional spatial extent, conditional boundary and transition zones of fuzzy objects were put forward and formalized based upon the formal data structure (FDS). In this procedure, uncertainty was transferred from thematic aspects to geometric aspects of objects, i.e. the existential uncertainty was converted to extensional uncertainty. The spatial effect of uncertainty in thematic aspect was expressed by the relationship between uncertainty of a cell belonging to the spatial extent of an object and the uncertainty of the cell belonging to classes.To detect dynamic changes in fuzzy objects, a method was proposed to identify objects and their state transitions from fuzzy spatial extents (regions) at different epochs. Similarity indicators of fuzzy regions were calculated based upon overlap between regions at consecutive epochs. Different combinations of indicator values imply different relationships between regions. Regions that were very similar represent the consecutive states of one object. By linking the regions, the historic lifelines of objects are built automatically. Then the relationship between regions became the relationship or interactions between objects, which were expressed in terms of processes, such as shift, merge or split. By comparing the spatial extents of objects at consecutive epochs, the change of objects was detected. The uncertainty of the change was analyzed by a series of change maps at different certainty levels. These can provide decision makers with more accurate information about change.For the third, and last, a process-oriented spatio-temporal data model was proposed to represent change and interaction of objects. The model was conceptually designed based upon the formalized representation of state and process of objects and was represented by a star-styled extended entity relationship, which I have called the Star Model. The conceptual design of the Star Model was translated into a relational logical design since many commercial relational database management systems are available. A prototype of the process-oriented spatio-temporal data model was implemented in ArcView based upon the case of Ameland. The user interface and queries of the prototype were developed using Avenue, the programming language of ArcView.The procedure of identification of fuzzy objects, which extracts fuzzy object data from field observations, unifies the existing field-oriented and object-oriented approaches. Therefore a generalized object concept - object with fuzzy spatial extent - has been developed. This concept links the object-oriented and the field-oriented characteristics of natural phenomena. The objects have conditional boundaries, representing their object characteristics; the interiors of the objects have field properties, representing their gradual and continuous distribution. Furthermore, the concept can handle both fuzzy and crisp objects. In the fuzzy object case, the objects have fuzzy transition or boundary zones, in which conditional boundaries may be defined; whereas crisp objects can be considered as a special case, i.e. there are sharp boundaries for crisp objects. Beyond that, both the boundary-oriented approach and the pixel-oriented approach of object extraction can use this generalized object concept, since the uncertainties of objects are expressed in the formal data structures (FDSs), which is applicable for either approach.The proposed process-oriented spatio-temporal data model is a general one, from which other models can be derived. It can support analysis and queries of time series data from varying perspectives through location-oriented, time-oriented, feature-oriented and process-oriented queries, in order to understand the behavior of dynamic spatial complexes of natural phenomena. Multi-strands of time can also be generated in this Star Model, each representing the (spatio-temporal) lifeline of an object. The model can represent dynamic processes affecting the spatial and thematic aspects of individual objects and object complexes. Because the model explicitly stores change (process) relative to time, procedures for answering queries relating to temporal relationships, as well as analytical tasks for comparing different sequences of change, are facilitated.The research findings in this thesis contribute theoretically and practically to the development of spatio-temporal data models for objects with fuzzy spatial extent.</p

A Historical Account of Types of Fuzzy Sets and Their Relationships

In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used

Multi-Temporal Remote-Sensing-based Mapping and Characterization of Landscape Evolution of a Meandering River Floodplain

Large meandering river floodplains are critical components of the Earth ecosystems for their high biodiversity and productivity. However, it is challenging to study these regions because of their complex land-covers and dynamic surface processes. This study applies soft classification and change-detection analysis to five Landsat 5 Thematic Mapper (TM) satellite images to examine long-term surface-cover composition and configuration change of the Rio Beni floodplain in Bolivia from 1987 to 2006. One hard/crisp classification algorithm (i.e., ISODATA) and two soft classification algorithms (i.e., Bayes classification and fuzzy classification) were applied to the study-area satellite images to examine the performances of classifying and mapping meandering river-floodplain environments between hard and soft classification approaches. In all five scenes, three algorithms achieved ~90% classification accuracy via hard classification outputs. However, the two soft algorithms were of more utility in this study because their results were less affected by “salt-and-pepper” noise and provided extra land-cover probability/membership layers. A novel change-detection algorithm was proposed in this study, namely Modified Change Vector Analysis (MCVA). The MCVA operated in fuzzy-membership space, considered change uncertainty during the thresholding stage, and utilized change-vector directions to modify the determination of change/no-change status for each pixel. A fuzzy Markov Random Field (FMRF) model was applied to further refine the change maps by incorporating spatial change uncertainty. A second thresholding stage was also applied to separate a type of change referred to as “transitional change,” which preserved fuzzy membership information and provided a concise map output. Compared with three traditional change-detection algorithms, the MCVA achieved higher change-detection accuracy and provided more detailed change dynamics regarding the land-surface change. Dynamics of major floodplain cover types (i.e., oxbow lakes, river, sand, forest, non-forest vegetation, and dry and wet soil) were investigated via multi-temporal analysis. Over the observing period of 1987 to 2006, 74.4% of pixels remained the same land-cover, 20% experienced clear land-cover change and 5.6% experienced transitional land-cover change. The riparian area experienced more dramatic change than other parts of the Rio Beni floodplain during this period. Additional analysis of landscape metrics provided information regarding the spatial patterns of the land-cover, but future work would be needed to further examine its utility in understanding floodplain dynamics. This study provides information on remote-sensing-based mapping and quantitative characterization methods for meandering river floodplains. The spatiotemporal patterns of landscape on Rio Beni floodplain can be used in sustainable management and protection of floodplain ecosystems

Huppauf, Bernd and Christoph Wulf, eds. Dynamics and Performativity of Imagination: The Image between the Visible and the Invisible.

A truly dense and elaborate collection, the Dynamics and Performativity of Imagination: The Image between the Visible and the Invisible is an anthology of interdisciplinary essays covering themes of imagination, creativity and the image, both material and mental, under perspectives and spectrums that are as diverse as the fields intersecting in the analyses. Indeed, the multifarious philosophical commitments and domains of the authors contributing to this anthology results in a compilation of..