Models and spatial information

Models and ontology

particular classification vs general taxonomies

• ontology: the study of general classification of, and relationships between, those things that exist in the world.
  • aims to develop general taxonomies of what exists
• modeling: the process of representing the source domain in the target domain
  • aims to develop classifications within a particular application domain
  • purpose is to simplify and abstract away from source domain
  • the distinction between substance and property is not a data modeling issue
  • the decision to represent a road in a navigation system as a polyline or as an area is a data modeling question
  • insight, results and computations in the target domain may then be interpreted in the source domain
  • usefulness is determined by how closely the model can simulate the source domain, and how easy it is to move between the two domains.

The modeling process

Type of models

• Field-based model: treats geographic information as collections of spatial distributions

  • distribution may be formalized as a mathematical function from a spatial framework to an attribute domain
  • patterns of topographic altitudes, rainfall, and temperature fit neatly into this view.
  • field-based: treats information as a collection of fields
    • each field defines the spatial variation of an attribute as a function from the set of locations to an attribute domain

• Object-based model: treats the space as populated by discrete, identifiable entities each with a geospatial reference

  • buildings or roads
  • geospatial relationships
  • clumps a relation as single or groups of tuples

• Field-based models

  • Spatial framework: a partition of a region of space, forming a finite tessellation of spatial objects.

    • polygons
    • must be a finite structure
    • however, the application domain will not be finite and sampling is necessary
    • imprecision is introduced by the sampling process

  • Layers: the combination of the spatial framework and the field that assigns values for each location

  • Spatial fields: z-coordinates, or heights

  • regular tessellation, square grid->raster-based data structures

  • irregular tessellation, triangulations->vector-based data structures

  • Properties of the attribute domain -> four levels of measurement(Stevens 1946)

    • qualitative
      • nominal attribute: simple labels, cannot be ordered
      • ordinal attribute: ordered labels,
    • quantitative
      • interval attributes: quantities on a scale without any fixed point, the ratio of two interval attributes values is not meaningful
      • ratio attributes: quantities on a scale with respect to a fixed point

  • continuous field: small changes in location leads to small changes in the corresponding attribute value

  • differential field: rate of change is defined everywhere

  • spatial framework and attribute domain must be continuous for both these types of fields

  • Isotropic fields: properties are independent of direction

  • anisotropic fields: properties are dependent on direction

  • Spatial autocorrelation is a quantitative expression of first law of geography

    • everything is related to everything else, but near things are more related than distant thing
    • measures the degree of clustering of values in a spatial field
    • positive
    • zero
    • negative

  • Operations on fields

    • map Algebra
    • local: one ore more spatial fields-> one new field

Object-based models

• decompose an information space into objects or entities
• an entity must be
  • identifiable
  • relevant
  • describable
• spatial objects
  • inside space, embedding space
  • a set of primitive objects
  • point, line, polygon
• topological spatial operations-> spatial relationships
  • connected
  • is within
  • some affects the object
  • some don't alter

Questions

• What it is we are trying to model in GIS?

In GIS, models are needed to define the relationship between our geographic environment (the source domain) and the representation of that environment within in a computer(the target domain). geographic environment<->model<->computer

• What is a model?

A model defines a representation of parts of one domain in another. e.g., a flight simulator

• What is the purpose of the model?

To simplify and abstract away from the source domain.

• What is the constituents of the domain?

Entities, relationships, processes, or any other phenomena of interest.

• What is the modeling process?

initial study->system analysis->system design->system implementation->physical computational model->logical computational model->conceptual model->application domain model->application domain

• How to evaluate a model's usefulness?

By how closely it can simulate the source domain, and how easy it is to move between the two domains.

• What is the field-based model?

Treat space is made of a set of locations with properties (absolute space). location->attributes

• When to use the field-based model?

Analysis continuously varying geographic phenomena, like temperature or rainfall. regional climate variations, or regional health variations Conceptualize urbanization as a field based on the density of house (objects)

• What is the object-based model?

Treat space is made of a set of objects with spatial properties (relative space). attributes->location

• When to use the object-based model?

Analysis discrete geographic phenomena, like buildings or roads. Conceptualize a zone of very low rainfall (field) as an object (a desert)

• What is the difference between field- and object-based models?

The way to conceptualize the relationships between location and attributes. Field-based model uses a fixes spatial framework as a reference (such as regular grid) and then measures the variation in attribute values with respect to this reference. Object-based model populates the information space with spatially referenced entities with attributes

• Why we need to learn basic ontological distinctions?

Because it can help us avoid some basic modeling mistakes. Typical modeling errors arising from a lack of ontological awareness. e.g., failing to distinguish substances from their properties.

• What is the spatial framework?

It's a partition of a region of space, forming a finite tessellation of spatial objects.

• What is the layer?

The combination of the spatial framework and the field that assigns values for each location in the framework.