GeoComputation

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GeoComputation

• Gordon Green
• Hunter College
• Department of Geography
• 11/2006

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What is GeoComputation?

• the eclectic application of computational
  methods and techniques to portray spatial
  properties, to explain geographic phenomena, and
  to solve geographical problems -Couclelis, 1998
• The application of a computational science
  paradigm to study a wide range of problems in
  geographical and earth systems. Openshaw, 2000
• "The universe of computational techniques
  applicable to spatial problems" -Reed and Tuton,
  1998

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What is GeoComputation?

• Its champions consider it a new discipline.
• Others consider it just a toolbox of
  computationally intensive techniques.

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What is GeoComputation?

• Geo - emphasizes geographical and spatial
  aspects. Some other approaches entail spatial
  additions to methods that arose in non-spatial
  fields. GeoComputational methods tend to be
  inherently spatial.
• Computation - equally important as the spatial
  aspect. The approaches tend to come out of
  computer science, rather than geography.
• Traditional statistics tends to reduce and
  summarize information GeoComputation tends to
  retain or generate more complexity in its
  operations.

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What is GeoComputation?

• Fotheringham differentiates between Weak GC,
  where the computer is used to augment existing
  quantitative methods and Strong GC, where the
  computer "drives" the form of analysis.
• Confirmatory versus exploratory techniques -- GC
  tends to fall in the latter category.
• The challenge of GC is to develop the ideas, the
  methods, the models, and the paradigms able to
  use the increasing computer speeds to do useful,
  worthwhile, innovative ad new science in a
  variety of geo-contexts. (Openshaw)

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What is GeoComputation?

• Aspects of GeoComputation
• Multi-Agent Modeling
• Cellular Automata
• Fuzzy Modeling
• Genetic Programming
• Neural Networks

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Agent-Based Models

• An agent-based model is one in which the basic
  unit of activity is a software agent.
• Usually a model will contain many agents (at
  least tens, occasionally many thousands).
• Its outcomes are determined by the interactions
  of the agents.
• A agent is an identifiable unit of computer
  program code which is autonomous and
  goal-directed.
• (from Schelhorn, OSullivan, Haklay,
  Thurstain-Goodwin, 1999)

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Agent-Based Models

• An early example of agent-based modeling is Boids
  (Reynolds, 1987), a model that describes flocking
  behavior.
• Explaining flocking using functional models is
  complex.
• By approaching it by modeling autonomous agents
  with simple rules, it was easier to create an
  explanatory model.
• Agent models typically work by maintaining a
  collection of agents, and a timer that advances
  the state of each agent with each tick, each
  agent updating its state based on characteristics
  and location of the other agents and other
  entities in the landscape.
• Agent models are best implemented in an
  object-oriented fashion

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Agent-Based Models

• Each agent has a simple set of rules defining its
  behavior. Creating multiple instances of the
  model and adjusting the rules made it possible to
  model flocking behavior concisely.
• Boids animation
• More elaborate example

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Agent-Based Models

• These animations exhibit the phenomenon of
  emergence, whereby complex behavior emerges from
  the behavior of simple components.
• Another example of agent-based modeling is
  pedestrian modeling
• Pedestrian model note formation of lanes.
• Other sample pedestrian models

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Agent-Based Models

• Pedestrian model implementation (Batty, 1999)

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Agent-Based Models

• Pedestrian model implementation (Batty, 1999)

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Agent-Based Models

• Pedestrian model implementation (Batty, 1999)

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Agent-Based Models

• Pedestrian model implementation (Batty, 1999)

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• Pedestrian model design (Schelhorn, OSullivan,
  Haklay, Thurstain-Goodwin, 1999)

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(No Transcript)
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Software for agent-based modeling (from Najlis,
Janssen, and Parker, 2001)
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Agent-Based Models

• When to use agents? Axtell (1999) describes three
  basic cases when agent-based models might be
  used
• 1. Agent models as simulation of mathematical
  models agent models can be used to implement
  monte-carlo simulations that can also be solved
  using other numerical methods. Even though the
  simulation can be solved in a functional manner,
  an agent-based implementation can act as an
  alternative implementation that can validate the
  results.
• Similarly, an agent-based model can be useful as
  an illustration of a complex numerical model.
  Even though the agent-based model may not be
  necessary to come up with a solution, it may be
  very helpful in illustrating the results to a
  general audience.

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Agent-Based Models

• An example of this first use can be found in the
  classic problem of modeling a bank-teller line
• The queuing process is commonly simulated using a
  the Monte Carlo method to arrive at a
  distribution of waiting times.
• This is can be equivalently modeled using agents
  that each have different arrival times and other
  parameters, and running the model with many
  agents to similarly build up the resulting
  distribution function.
• (Axtell, 1999)

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Agent-Based Models

• 2. Agent models as complementary to mathematical
  models a mathematical model may adequately
  model some aspects of a problem but not others,
  or may be awkward or incapable of a comprehensive
  solution. Or a mathematical model may be known,
  but so complex as to be practically insoluble.
• An artificial stock market is an example of such
  a model. Trading agents have the choice of
  investments with varying stochastic levels of
  risk, adapt their behavior based on the results
  of prior trading.
• Even though the basic features of such a model
  may be functionally describable, an agent-based
  model can evolve over time into a system that
  actually replicates some of the complexity of a
  real stock market. These complexities are
  impractical to model using a mathematical model.
  (Axtell, 1999)

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Agent-Based Models

• 3. Agent models as substitutes for mathematical
  models some problems are not amenable to
  mathematical modeling.
• Examples include the behavior of individuals in
  animal population, or groups of pedestrians as
  described earlier.

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Agent-Based Models

• Pros
• An argument from economics, which could also be
  applied to geography
• The reason why large scale computable general
  equilibrium problems are difficult for economists
  to solve is that they are using the wrong
  hardware and software. Economists should design
  their computations to mimic the real economy,
  using massively parallel computers and
  decentralized algorithms that allow competitive
  equilibria to arise as emergent
  computations...The most promising way for
  economists to avoid the computational burdens
  associated with solving realistic large scale
  general equilibrium models is to adopt an
  agent-based modeling strategy where equilibrium
  prices and quantities emerge endogenously from
  the decentralized interactions of agents. (Rust,
  1996, in Axtell)
• The quality of emergent behavior doesnt
  correspond to any part of a traditional
  statistical analysis. Agent-based models
  uniquely provide the opportunity to model a
  process, and see what happens when it runs
  (Axtell).

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Agent-Based Models

• Cons
• When dealing with agent models, we are quickly
  involved in a world where everything - both the
  agents and their environment - are designed, and
  the reliable scientific analysis of the real
  world may be compromised by the complexity of the
  models (paraphrased from Couclelis, Why I No
  Longer Work with Agents, discussing
  human/environment agent models).
• Agent models dont have a convenient way of
  measuring their accuracy, unlike statistical
  models. This can only be overcome by running the
  agent model many times, varying the parameters to
  discover the robustness of the results. There is
  a limit as to how many such variations can be
  executed (although this is increasing with
  increases in computer power) (Axtell).

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Cellular Automata

• Cellular automata are closely related to
  agent-based models.
• Instead of an autonomous agents being given
  simple behavioral rules, the states of cells in a
  surface are dictated by similarly simple rules.
• Those rules use the state of surrounding cells in
  a grid to determine the state of any given cell
  in the next iteration of the model.

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Cellular Automata

• CAs develop in space and time.
• Space and time are defined in discrete steps.
• Cells are lined up in a string for
  one-dimensional automata, or arranged in a two or
  higher dimensional lattice for two- or higher-
  dimensional automata.
• The number of states of each cell is finite.
• The states of each cell are discrete.
• All cells are identical.
• The future state of each cell depends only of the
  current state of the cell and the states of the
  cells in the neighborhood, determined by rules
  (from Alexander Schatten).

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Cellular Automata

• The simplest CAs are one-dimensional. For
  example, here are a set of rules and the results
  of a few iterations (from David R. Green)

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Cellular Automata

• For geographical applications, CAs are usually
  2-dimensional, often using one of these cell
  neighborhoods

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Cellular Automata

• Conways Game of life rules
• Mathematician John Conway invented CAs in his
  Game of Life, first described in a 1970
  Scientific American article.
• A cell that is dead at the time step t, becomes
  alive at time t1 if exactly three of the eight
  neighboring cells at time t were alive.
• A cell that is alive at time t dies at time t1
  if at time t less than two (loneliness) or more
  than three cells (overcrowding) are alive.
  (Alexander Schatten)
• From these very simple rules, very complex
  behaviors can be modeled.

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Cellular Automata

• Sample game of life pattern (glider)

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Cellular Automata

• There are many other examples available on the
  web, such as
• http//www.ibiblio.org/lifepatterns/
• These simple rules can be expanded to generate
  many, many patterns of change
• http//www.collidoscope.com/modernca/

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Cellular Automata

• There are many enhancements involved in
  generating more complex evolutionary patterns
• Probabilistic CAs, where, instead of having
  binary rules (and binary states), the changes are
  described by probabilities, give an increased
  level of control over how a CA develops. The
  rules can express the chance of a cell changing
  state, and each step of the CA involves selecting
  the state of each cell based on a random number
  falling within its probability range.
• CAs can also be self-modifying, that is, they can
  respond to changes in the states of the grid as
  it develops.
• Irregular grid cell sizes
• Action a distance, instead of just immediately
  adjacent cells.
• Incorporating agents within CA landscapes

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Cellular Automata

• These more sophisticated CAs have been used to
  model diverse geographic phenomena, such as
• Wildfire
• Formation of a Megalopolis
• West Nile Virus Infection Risk
• 2 from Paul Torrens, http//geosimulation.org/sim
  ulating-sprawl/, 3 from Sean Ahearn.

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Cellular Automata

• Cons (Batty and Xie, 2005)
• Most CA rules have little relationship to the
  actual causes of the phenomenon being studied.
  Even if the model happens to model the process
  successfully, it doesnt really prove anything,
  and is difficult to use as the basis of any kind
  of policy decision.
• They tend not to model spatial interaction well.
• In practice, CA cells tend not to match units of
  the phenomenon under study.

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Fuzzy Modeling

• A frequent problem in geography is how to
  identify an geographic entity.
• Geographic phenomena tend to be described by
  vague terms.
• For example a study concerns the major cities in
  Europe. Each of the terms major, city, in,
  and Europe are somewhat vague.
• Fuzzy set theory is an attempt to deal with the
  problems posed to traditional set and logic
  theory by vagueness.
• (section paraphrased from Fisher, 2000)

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Fuzzy Modeling

• Sorites paradox
• If a grain of sand is placed on a surface, is
  there a heap?
• If a second grain of sand is placed next to it,
  is there a heap?
• If a third grain of sand is placed next to the
  second, is there a heap?
• If a ten-millionth grain of sand is placed next
  to the 9,999,999th, is there a heap?
• Heap is a vague concept. Other examples are
  tall, near, far, etc.
• Many geographic values such as vegetation
  coverage, soil types, etc, are similarly
  Sorites-susceptible.

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Fuzzy Modeling

• Classical sets follow the logic described in
  familiar Venn diagram (examples drawn from
  behavior of boolean search terms)

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Fuzzy Modeling

• These can also be expressed using linear graphs

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Fuzzy Modeling

• Membership in a set is determined by some
  threshold value. This value can be subject to
  error, and can be assigned a probability, Those
  probabilities can then be used in set-based
  calculations

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Fuzzy Modeling

• Boolean set theory is used throughout most
  conventional set and statistical analysis, For
  example does the result of a test disprove the
  null hypothesis? We set a threshold value to the
  t test statistics and respond based on whether or
  not the results of the hypothesis are above or
  below that test. In many cases, there is
  actually a continuous probability of the null
  hypothesis being correct.
• Zadeh 1965 put forward concept of fuzzy sets in
  response to shortcomings of boolean sets.

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Fuzzy Modeling

• Fuzzy set membership is at the core of fuzzy set
  theory. Boolean sets are encoded with 0 or 1,
  wherein an entity is or is not part of a set.
  Fuzzy set membership is defined by any value
  between (and including) 0 and 1.

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Fuzzy Modeling

• Fuzzy set membership can take varied forms

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Fuzzy Modeling

• These then result in boolean calculations that
  take into account partial set membership

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Fuzzy Modeling

• Boolean operations become functions rather than
  boolean values

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Fuzzy Modeling
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Fuzzy Modeling
Example of fuzzy versus crisp classifications
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Fuzzy Modeling
The concept of fuzziness can also be applied to
polygon boundaries
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Fuzzy Modeling

• Key question How do you choose the membership
  function (MF)? Is it linear or curved?
• The semantic import (SI) approach estimates
  based on domain expertise and iterative
  evaluation of the results.
• Fuzzy K-means approach uses iterative
  mathematical estimates of the best function.

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Fuzzy Modeling

• Fuzzy K-Means
• Usually starts with random allocation of objects
  into k clusters.
• The center of each cluster is calculated
• Objects are re-allocated based on similarity of
  attributes using a similarity index, usually a
  distance measurement.
• This process is repeated until a stable solution
  is reached.
• Membership in each cluster is calculated as a
  range of from 0 to 1, instead of 1 as in crisp
  k-means (Burrough and McDonnell)

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Fuzzy Modeling

• Fuzzy K-Means

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Fuzzy Modeling

• Fuzzy modeling is often used in conjunction with
  genetic algorithms, which provide a way of
  iteratively refining the results of automated
  models.
• The following few slides will review this before
  concluding the section on fuzzy modeling.

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Genetic Algorithms

• First developed in the 70s.
• The basic idea is to model a problem with many
  parameters by treating those parameters like
  genes.
• These are selected over time by iteratively
  applying a measure of fitness, selecting the
  fittest elements, and applying the process again.

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Genetic Algorithms

• Steps in an evolutionary algorithm
• Create a new population of alternatives using
  random values.
• Select individuals from the population weighting
  towards the individual that represents the best
  solution so far.
• Use them as the basis of a new set of
  alternatives, by combining them (crossover) or
  randomly changing them (mutation).
• Continue this process until some terminating
  condition is met.

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Genetic Algorithms

• Sample chromosome
• A contrived simple problem
• Given the digits 0 through 9 and the operators
  , -, and /,  find a sequence that will
  represent a given target number. The operators
  will be applied sequentially from left to right
  as you read.
• Encoding

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Genetic Algorithms

• Encoded solution
• Crossover
• Mutation Randomly changing bits

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Genetic Algorithms

• While not necessarily spatial per-se, a genetic
  approach to model evaluation and selection can be
  applied to many problems that require selecting
  among many possible models.

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Fuzzy Modeling

• Using fuzzy modeling to classify coverage in
  remotely sensed data involves fuzzy logic in
  combination with a genetic classification process
  (from TNTMips user guide)

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Fuzzy Modeling
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Fuzzy Modeling

• The right-hand image shows the first-cut results
  of an unsupervised image classification. The
  right-hand image shows the extent to which each
  cell differs from the center of its assigned
  spectral class, so darker areas are more likely
  to be in the assigned class

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Fuzzy Modeling

• The Fuzzy classification method uses rules of
  fuzzy logic, which recognize that class
  boundaries may be imprecise or gradational.
• It creates an initial set of prototype classes,
  then determines a membership grade for each
  class for every cell.
• The grades are used to adjust the class
  assignments and calculate new class centers, and
  the process repeats until the iteration limit is
  reached. (TNTMips user guide).

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Fuzzy Modeling

• Champions of fuzzy modeling consider probability
  theory to be a special case of fuzzy modeling.
• Others consider fuzzy modeling to be unnecessary,
  and replaceable by Bayesian probability.

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Neural Networks

• The last geocomputational technique we will cover
  is neural networks, or neurocomputing.
• Definition A computational neural network (NCC),
  is a parallel distributed information structure
  consisting of a set of adaptive processing
  (computational) elements and a set of
  unidirectional data connections (Fischer and
  Abrahard).
• These models have been inspired by neuroscience,
  but in no way actually model biological or
  neurological phenomena.

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Neural Networks

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Neural Networks

• Typical neural network diagram

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Neural Networks

• A Neural Network consists of various layers.
• Each layer can any number of neurons in it.
• The first layer of the network is called an input
  layer, and it is here we apply the input.
• The last layer is called the output layer, and it
  is from here we take the output.
• A neural network can have any number of hidden
  layers, between the input and output layer.
• In most neural network models, a neuron in one
  layer is connected to all neurons in the next
  layer (from a description by Anoop Madhusudanan).

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Neural Networks

• Here is a diagram of the simplest possible neural
  network. N1 and N2 are inputs, N3 and N4 are in
  a hidden layer, and N5 is the output

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Neural Networks

• Within each node, or neuron, there is a
  function that determines the output of the node
  based on the inputs
• Input data are typically specified to take values
  in any range, whereas output is given in limited
  ranges.

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Neural Networks

• Each input has a weight. The totals of the input
  constitute an activity level. When the
  activity level reaches a certain threshold, the
  output changes.
• The output may also change continuously with
  changes in input, for example following a curve.
  This curve represents the transfer function, by
  which inputs are converted to outputs

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Neural Networks

• Neural networks must be trained. Training
  consists of adjusting the weighting of inputs
  depending on the value of outputs.
• The can be accomplished with a feedback function,
  which for example, may take the output and feed
  it back to the hidden or input layers. The
  hidden layer may in turn then feedback to the
  input layer.
• The feedback function adjusts the weighting so
  that correct results are increased with further
  iterations of the network. Note that weights can
  be negative, so neurons may be either inhibitory
  or excitatory.

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Neural Networks

• For example, a neural network designed to detect
  the pattern of the number four might have an
  input node for every pixel in a grid.
• It would be trained (weights adjusted) using
  multiple images of the number four

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Neural Networks

• Training may be supervised or unsupervised. Most
  implementations are supervised.
• In supervised training, the training data
  consists of inputs together with expected
  outputs.
• Neural networks work best with boolean or ordinal
  or real numeric data. Non-ordinal set-based data
  types tend not to work because they do not lend
  themselves to weighting.
• With enough training data where the inputs and
  outputs are known, the network implicitly begins
  to model a function which can be applied to
  unknown inputs.
• The training data selected depends on user
  knowledge and intuition about the problem domain.
  Neural networks take into account existing
  knowledge about a problem via the training
  process.
• (Paraphrased from StatSoft manual).

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Neural Networks

• Neural networks work best when there is a lot of
  training data. For most practical problems,
  hundreds or thousands of training cases are
  required. The exact number depends on the nature
  of the problem.
• Neural networks tend to be tolerant of noisy
  input, but there can be problems if the training
  data does not include outliers found in the
  subject data. In these cases the outliers may be
  ignored.
• They tend to work well with regression problems
  (where the output will be a specific number) and
  with classification problems (where the output
  may be a boolean value or a set of values).
  Pattern recognition is one common application.

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Neural Networks

• Applications in GIS
• Image classification neural networks can be
  used to optimally classify remotely sensed
  images.
• Feature detection the pattern-recognition
  strengths of neural networks could be used to
  identify features in remotely sensed data.
• Transportation route selection for example,
  route and congestion data can be used as inputs
  to neurons that optimize for shortest routes.
  Optimal routing could be the output.

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Neural Networks

• Transportation example (from Thurston, GIS
  Café.com)
• A is starting point and B is destination.
  Intersections are nodes in the network. The red
  square is the location of an accident.

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Neural Networks

• The weighting of node inputs can be calibrated to
  the traffic capacity of each. The accident
  causes the affected nodes to inhibit activation,
  resulting in the selection of non-affected nodes

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Related Topics

• Parallel processing and object-oriented software
  development are closely related to
  GeoComputation.
• The following slides give a quick overview of
  these related topics.

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Parallel Processing

• What is it?
• Parallel processing is using more than one CPU
  to perform computational tasks more quickly.
• Types of parallel processing
• SIMD Single instruction stream, multiple data
  stream.
• MIMD Multiple instruction streams, multiple
  data streams.
• SISD Single instruction stream, single data
  stream, is the model in place in most current
  PCs.
• MISD Multiple instruction stream, single data
  stream. This is really only a theoretical
  construct, because it is not practical to have
  multiple processors manage the same data.

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Parallel Processing

• SIMD each processor runs the same program on
  different data (from Johnston, introduction to
  HPC)

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Parallel Processing

• MIMD each processor runs different instructions
  on different data

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Parallel Processing

• MIMD has proven to be the most generally
  applicable parallel processing model.
• Splitting up tasks into chunks that can be
  executed in parallel is widely applicable to
  geographic problems, where similar tasks need to
  be applied to different data.
• This kind of processing model can be implemented
  on a SISD machine, and is a useful way of
  thinking about many geocomputational practices.

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Parallel Processing

• When does it make sense to use it?
• Some tasks are easier than others to make
  parallel old cliché nine women cant produce
  a baby in one month but 90 women can create 90
  babies in nine months.
• Whether or not a model can be implemented in a
  parallel fashion depends not only on the nature
  of the problem, but also on the number of
  iterations needed.
• Problems that are inherently serial, or that
  would be very difficult to make parallel
  (parallel code tends to take several times longer
  to write), are not suitable
• But most problems in geography are likely to be
  parallel (e.g., you can usually subdivide a map,
  and a problem, into sectors that can be processed
  independently).

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Parallel Processing

• One interesting sidebar Distributed computing
  or task farming across multiple machines

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Parallel Processing

• For example, large distributed networks of
  volunteer machines can be used to process large
  parallel processing tasks such as global climate
  modeling.
• BOINC software for distributed volunteer
  computing supports such processing

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Parallel Processing

• BOINC Applications
• Climate Prediction Model

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Object-Oriented Programming

• Traditional programming consists of functions
  that roughly approximate the notion of a
  mathematical function.
• Problems are modeled by breaking the down into
  layers of functions in a process called
  structured decomposition.
• Object oriented programming instead identifies
  units of behavior and data that can be grouped
  together to model some real-world entity.

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Object-Oriented Programming
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Object-Oriented Programming
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Object-Oriented Programming

• Parallel processing and object-oriented software
  development make it easy to approach
  computational problems in a bottom-up fashion,
  using simple components to model systems that
  would otherwise be extremely complex.
• An object encapsulates its state and behaviors,
  making it easy to create complex systems composed
  of autonomous software entities.
• An OOP and parallel-programming perspective
  applied to spatial modeling is a convenient
  approach for most GeoComputation techniques.