GEOG 475 Final Exam

negative feedback

a mechanism of response in which a stimulus initiates reactions that reduce the stimulus

Partitioning in Classifications results

specific biophysical variations inside a broad generalized class. ex: forest, dense forest, grasslands, dense agriculture are all within vegetation

4 Components that are included in Disaster risk;

- hazard - exposure - vulnerability - capacity and measures

Residual Analysis Objectiives within Multiple linear regression

Analysis to evaluate the residual error term Amount of variance not explained by regression model Permits testing of the assumptions of the MLR model Identification of specific violations Refinement of the MLR model Linear and nonlinear variance components Identification of new independent variables

Logistic Regression Methodological steps (Multiple linear): 6 (last step)

Apply model to geographic area

Fundamentals of Multiple Linear Regression:

Can be used to describe data and explain relationships Can be used for predicting continuous conditions Explain relationship between dependent & independent variables Based on cause and effect relationships Dependent variable must be continuous Independent variables must be continuous Empirical modeling technique (requires training)

Logistic Regression Methodological steps (Multiple linear): 1

Develop your model (Surface Irradiance Example)( solar panels) Cause and effect; variables (account for atmosphere) As altitude increases surface irradiance increase Slope azimuth (shadows) Slope angle Need good conceptual model

Multiple Linear Regression Model Assumptions:

Linear relationship (correlation based) between independent and dependant Hard since most earth systems are nonlinear Normal distribution (Y, all independent variables)for independent and dependant Homogeneity of variance (Homoscedasticity) Variance of $Y$ is the same as $X$. No outliers in the data; use standard scores; -3.29-3.29 (exceeding more than 3 standard dev) Independent variables; no multicollinearity Random sampling- no sampling error (should account for spatial auto correlation)

Logistic Regression Methodological steps (Multiple linear): 5

Test model on non-training data set Conduct a statistical accuracy assessment Go back to step one and re-evaluate Improve your MLR model

Modeling Process: 4. - Implementation and uncertainty/sensitivity analysis:

o 1. Validate parameter output with other parameterization schemes o 2. Compare spatial output results (other models) o 3. Compare temporal output results (other models) o 4. Determine most important parameters o 5. Vary parameter magnitude & examine variability of output results o This sensitivity model allows us to compare the parameters of the model on the overall results. Facilitates our model results.

Characterize methodology sequencing (workflow)

- very important to build an understanding that will enable us to continue our efforts.

Main question of Conceptual modeling:

- what concepts do we need to represent to have some sort of grasp on reality

Characterization of coupled systems

- (topographic evolution) - we want to see how the topography changes over time - geological system. Tectonic forcing - increases the topography. Erosional processes can bring down the topology. Mass erosion vs mass uplift determines the left relief which influences climate and that influences surface process - huge feedback mechanism: o Climate o Surface processes o Geological

Types of Models:

- 1. Inductive models (logic) - general models based upon data and empirical tests. Ex: empirical regression modeling - 2. Deductive models (logic) - algorithmic in nature - much more detail based on known knowledge of variables and interactions. Ex: Bedrock river incision. These models can be physics based or approximate formulations of a process - 3. Descriptive models - passive (purpose). Provides a description of parts. Ex: conceptual modeling - the parameters or features that play a role in a model. - 4. Prescriptive (purpose) - models are active. Impose an optimized solution to a problem (suitability-site model). Better for prediction than descriptive. - 5. Stochastic (methodology) - models incorporate random components. Probability theory based used of statistics. Ex: precipitation falling. - where it would fall? Physics based approach they fall randomly over the landscape. Account for how it falls and flows. For a given set of inputs - randomized - you don't always get the same results every time. - 6. Deterministic (methodology) - knowledge based with regard to parameters, process and interactions. Based upon cause-effect relationships. It will always produce the same results based on the parameters put in. - 7. Mixed types - inductive-deductive-stochastic-deterministic à use a regression model for these mixed types.

ANN Learning Parameters:

- 1. Select a learning rate - size of weight and bias change in learning. They use the back-propagation algorithm - popular. If its too small algorithm takes a long time to converge. A learning rate of 0.35 is very popular and a good choice. - 2. Select a momentum rate - determines the fraction of change and speeds up the convergence of the system. Typical value is 0.9 - 3. Choose an epoch value - when the training stops and the amount of iterations that exceeds the value of 5000000. It counts the iterations in order to recognize the pattern. You can use in conjunction with minimum error. But training will stop when you hit that value. - 4. Choose a minimum error - Typical value is 0.01. Even less specific error - use 0.001 or 0.0001. These parameters will have to be played around with.

Basic description of Artificial Neural Networks (ANN)

- Artificial neural networks are trying to model the same human neural visualization system has. o Unsupervised and supervised approaches can be utilized during the ANN algorithms o Soft classification - ANN fuzzy uncertainties - likelihood o Discrete classification o Nonlinear pattern recognition capabilities o Generalize form can be recognized very accurately under this ANN tec o Also builds the ANN structure/architecture

Steps to produce a simple index model:

- Compute a particular index value for each spatial unit (vector or raster) - Then establish inforation criteria (n GIS layers) - 2, 10, 20 etc. doesn't matter - Transform data into information via analysis (data can be substituted) - Transform information into ordinal ranking of suitability or potential - taking interval ratio scale data and transforming to ordinal data where the ranking as a meaning - Compute composite index by summing up the ranked GIS layers

Types of models:

- Data model - characterizing data within your database - Entity model - points, lines polygons - vector data structure - Conceptual model - identifies parts of a system, object of a system, interrelationships, processes - Semantic model - attempts to define terms or individual concepts through qualitative or quantitative information

Fundamental objectives of multi-faceted concepts:

- Demonstrates conceptual understanding - Must have that to implement numerical models - Conceptual modeling is seriously important for numerical modeling - Components of a system or problem - check for subcomponents - Characterizing the structure of the environment - Need to identify attribute parameters - Identify forcing factors - Identify processes - Characterize relationships

Regression model Methodological steps: 1.

- Develop your model § Cause and effect; varibles § Dependent variable must be dichotomous or binary in nature (1s and 0s) § Attempt to identify variables that can represent the dependent varibles - cause and effect § Independent variables will represnet your x variables - in the matrix

Density slicing steps

- Establish a reasonable feature space to submit to the algorithm - Data should be based on classifying a particular theme - Select a 1-D FS based upon the objective - We must decide what threshold value we'll use for a classification. We choose the value on the x axis between the two distributions. Conditional test. - Requires diagnostic 1-D separability between the distributions of the featured space - Earth's surface - 1-D thresholding is not appropriate because the earth produces greater complex patterns - Classify Vegetation - use NDVI - Classify Water - classify based on the near infrared spectrum of the data

What does GIS modeling predict?

- Modeling can try and formalize the concepts and interactions - involves identification of parameters to identify the nature of the relationships to recognize the dynamic of the predictions. - Parameter/attribute - check for the spatial and temporal domain à how altitude can be manipulated and what does that manipulate. - Process rates - deposition, that would increase the altitude of the topography. Predict the change in temperature in the atmosphere - global warming effect. à geological processes deep within the earth. o Climate change - Climate forcing - temp and precipitation, Tectonic forcing Anthropogenic forcing

what is a model?

- Models can be spatially explicit - the model has the ability to predict spatial parameters or process rates spatially or system characteristics. - Models can be temporally explicit - temporal variability of a parameter or a process rate or how the system responds to forcing factors - Models can be spatio-temporally explicit - space and time - in respect to parameters, processes and system behavior

Role of GIS Modeling: Intro

- Numerical modeling of any type allows us to characterize process pattern relationships. -> on the landscape. - Difference of sand dunes patterns on mars and earth - not confined - mars is different. Numerical modeling can help define these differences. - DEM - difference in topological patterns. - Urban pattern environments - they all differ across the world. Many factors that can alter the urban landscape from an aerial standpoint. Humans can dictate different characterization based on confinement.

Basics of Conceptual Modeling

- Represents the formalization of concepts and the understanding of what it represents - Abstraction of an idea - Mental understanding - Mental awareness - may or may not be aware of the processes going on in a phenomena - Based: Cognition - understanding levels of abstraction associated with ideas. Processes, systems, algorithms, parameters, etc. - Represented in terminology/communicated - must account for representation

Logistic Regression Modeling applications:

- Spatial entity characterization instead of vector structures - we can expand to humans, matter. Landform - predict the nature of human characteristics or matter usign independent variables - Spatial suitability site location - identify the independent variables that give the suitability for a specific site -so we get a binary response of yes or no - Spatial mapping of a theme (e.g., class theme: yes, no) - attempt to think about an ecosystem or ecoregion that's dependent on climate and species - Spatial mapping of the variation of a theme (e.g., concept-multiple concepts) - the probability of that theme - look at the variation instead of yes or no answer

Modeling Fundamental Objectives:

- Spatial prediction - important to recognize different kinds of predictions - spatial patterns - predicting urban growth based on population. - Temporal prediction - temporally predict what will happen in the prediction - Spatio - temporal prediction - how things happened in the past

Geohazard risk components:

- Threat - can act on weakness - Vulnerability - weakness of components - political, social, resource, etc - Risk - potential loss/damage - Flooding, tornadoes, hurricanes We want to predict the potential threat and vulnerabilities to predict over space in time the loss and damage from a point of view of disaster.

Regression model Methodological Steps: 2

- Variable Representation § Measurement scale (binary, nominal, ordinal, interval/ratio) § Information characterization (dummy variable, index, property, data) - tow or three index values or a property variable like a slope angle. Or it's possible to submit raw continuous data - altitude.

Different concept system examples:

- geochemical, pedological, hydrological, human

5th step in supervised analysis maximum likelihood algorithm: Accuracy Assessment

- if you have locations of known types of classes -> you can compute a statistical accuracy assessment based on pixels that are classified correctly. Class by class basis then an overall assessment. Difficult to produce these assessments cause sometimes there is no reference data. At lest 2% of the FS must be evaluated to even be considered. The probability to have high accuracy first time through is very low.

Models (problem)

- simplified representation of an optimal solution

Model (science)

- simplified representation of parameter, process or system

Examples of conceptual modeling:

- spatial properties - temporal properties - functional properties - spatial entities or objects that exists in the real world

Dynamic GIS Models

- the model does account for temporal variation in processes, system responses and parameters

ANN Deep Learning

-dealing with hidden layers. You can have any number of neurons or nodes to represent your ANN. This helps us recognize more patterns and increases the level of specificity.

Geographically Weighted Regression (GWR):

A variation of multiple linear regression - accounts for distance and direction more explicitly

Bivariate correlation (r pearson product moment correlation)

Always a correlation between dependent variable and independent variable

Multiple correlation coefficient (_R_):

Coefficient of determination and the total amount of explained variation want at least .9 (or 90 of the variation explained 0 = no explained variation

Which data suitability transformation shows greater complexity?

Continuous Fuzzy Ranking

Logistic Regression Model Assumptions

Dependent variable must be binary Linear relationship with odds (log (p/1-p) = model) No outliers in the data; use standard scores; -3.29-3.29 If less than -3.29 or greater than 3.29 - remove those outliers before you continue your thresholding Independent variables; no multicollinearity Model accurately predicts the probability of an event (estimated) - those probabilities of an event are estimated. The magnitude is dependent on the assumptions being conformed to Model fit and overfitting; adding more independent variables always increases the amount of variance explained; overfitting reduces the generalization capability of the model; this governs universal applicability. Model fit accurately explains the variation in the dependent variable; assume R2 is an accurate characterization; use R@ or goodness of fit approach

Application issues for MLR include:

Explicit accounting for spatial dimension (lat; long; z) gravity Explicit accounting for time (diurnal, seasonal, longer-term perturbations) Explicit accounting for processes - process mechanics that govern a certain variable Conceptual modelling Explicit accounting for non-linear feedback mechanisms Degree of cause and effect Generally does not have universal applicability Modelling processes

positive feedback mechanism

Feedback that tends to cause the level of a variable to change in the same direction as an initial change

MLR: Relation between correlation and error:

Low error = high degree of correlation High error = low degree of correlation R is low then std error of estimate = high

Equation to Compute index by using a weighted average of the ranked GIS layers

R = ranked GIS layers W = weights

Logistic Regression Methodological steps (Multiple linear): 4

Regression analysis Preform regression analysis compute beta values Multiple correlation coefficient Residual analysis

Multiple Linear Regression Model: Least Squares

Residuals for error Optimized best fit line Positive or negative linear trend But can not do nonlinear

Logistic Regression Methodological steps (Multiple linear): 3

Sampling and training set Number of observations (sample size) - add data that contributes to variance structure Representative geographic sampling Random, systematic, stratified Non-training data sets (accuracy assessment)

Multiple Linear Regression - potential Applications

Spatial entity characterization (e.g., matter properties, rates, parameter) Spatial site analysis (e.g., magnitude of risk, vulnerability) Spatial mapping of a theme (e.g., vegetation density, erosion, migration) Spatial prediction (population, migration, erosion, deposition,....) Exploration of relationships for identifying causative factors Be careful of spurious factors - Correlation between atmospheric pressure and altitude but altitude does not cause atmospheric pressure

Overfitting

The process of fitting a model too closely to the training data for the model to be effective on other data.

MLR: Examine the Statistical Significance of R

Use F ratio to determine if R != 0.0; (g = N of independent variables) Examine F value given df1 and df2 in table for a level of significance D1 = number of independent variables d2 = number of observations - independent variables - 1 Level of significance (0.05, 0.01)

How to map the residuals for MLR:

Use standardized residuals Where did the model over-predict? Where did the model under-predict? Is there a unique spatial pattern of error? Unique pattern of under- versus over-prediction?

Logistic Regression Methodological steps (Multiple linear): 2

Variable representation (must be interval/ratio for independent) Measurement scale (interval/ratio; continuous) Information characterization (data, coefficient, index, property) Coefficient (0-1 value) Normalize independent variables

Binary Model

can be used for spatial prediction and is based on the selection of basic criteria

Goal dealing with an Artificial Neural Network:

convergence - - Depends on our feature space, no multi-collinearity, reasonable Euclidean distance, ANN structure is important, also depends on learning parameters. Optimize those aspects and the patterns should come alive.

Static GIS Models:

does no account for temporal dynamics or processes, systems, etc

Uncertainty

much error is associated with a system. Multifaceted - characterized in terms of temporal error, geographic error and sampling error

Flood hazard potential: slope angle

o (0-90) - low, medium, high - logical expressions - found between 0 and 90 degrees but we can normalize the slope angle to find values between 0-1. High = 0-0.3, medium = 0.31-0.6, low = 0.61-1 for potential of flooding.

2nd step in supervised analysis maximum likelihood algorithm: Selection of training samples

o . Selection of training samples - manually digitize training samples § 1. Representative samples - clarification à all variation of the FS that represents that class. EX: Water - clear water, water that exhibits chlorophyll or other water that puts off turbidity. All environmental variation associate with a feature. Forest vegetation - changes in the amount of biomass and density § 2. Number of samples - greater samples - more representative training - if you have complex varying environmental coverage. Bad to assume that. § 3. Geographic distribution - sample evenly across the entire study area § 4. Size of samples - smaller sample sizes may not catch all environmental variation

Modeling Process: 7. Model Refinement - numerical modeling

o 1. Accounting for nth order parameters to characterize a parameter - examination of parameterization schemes is fundamental to account for the earth's variability o 2. New parameters to characterize a parameter and/or process - fluvial bedrock river incision - lithology, stress, fracture patterns - include parameters that have a causal influence on the process. o 3. New characterization of linear/non-linear forms of relationships - reciprocal, logarithmic, etc. 4. Better characterization of scale dependencies - when computing a parameter - must realize that there are spatio-temporal scale dependencies 5. Establish new criteria - must be think about how they can refine their models and the scientific community must agree with the nature of your model and its predictability to gain credibility

Modeling process: 1. Develop model objectives

o 1. Concepts - characterizing your parameter, process or system o 2. Parameters/process rates - how they are interrelated to produce process rates o 3. Dynamics - then we can understand our dynamic o 4. Locations/routes - account for this to determine criteria for actually having solutions

Modeling Process: 6. Implementation and validation

o 1. Evaluate simulations given different initial conditions/forcing factors o 2. Validate simulations given different geographic area o 3. Validate simulations given different time periods

1st Step in supervised analysis maximum likelihood algorithm:

o 1. Geographic orientation: § 1. Fieldwork § 2. Maps § 3. Imagery - satellite, models, NDVI 4. Photography - aerial and ground

Modeling Process: 5. Implementation and calibration (sensitive parameters)

o 1. Identify preset parameters o 2. Identify empirical coefficients/weights o 3. Compare simulation to output o 4. Modify parameters/coefficients to obtain correct results o 5. Calibration maintains inherent model relationships/dynamics o The inherent model dynamics are constant

Modeling Process: Develop model (conceptual modeling/implantation)

o 1. Identify system and subsystem components - radiation transfer system, hydrological, etc o 2. Identify subcomponent parameters - what variables characterize the system and those processes - especially for the feedback mechanisms o 3. Characterize process mechanics (processes) o 4. Establish subsystem and system linkages

Modeling Process: 3. Establish initial conditions (human-environment example):

o 1. Parameters, land cover and topography - humans migrate and use land. o 2. Urban infrastructure - must be established and human interaction is confined to this piece of land coverage o 3. Agent properties, networks and locations - agent (weight, height, etc), o 4. Time Constraints - week, day or year or decade - establishing the initial conditions establishes how the model will react.

Steps for Parametric ISODATA Clustering Algorithm

o 1. Select number of classes o 2. Select convergence threshold - number of iterations o 3. Then computes the mean and variance for each FS dimension o 4. Compyte arbitrary cluster class centers o 5. Creates a new classification map and assign all pixels to 0 o 6. Each pixel is assigned the euclidiean distance to each lcuster mean o 7. Find the cluster class that is assigned the minimum Euclidean istance o 8. Assign cluster value to the classification map o 9. Keep track of how many times of classification number changes o 10. When finished with the iteration, recompute the cluster class means based upon classification results o 11. If the % of change is greater than the convergence threshold, go to step 6 again o If algorithm does not converge and does not stop you don't have enough variability within the dataset based upon the number of classes you chose

Training ANN - back propagation steps:

o 1. Select training data for learning points, areas and statistical samples. Must be based on training data. (points, areas, statistical sample) - error gets read to update the weights o 2. Learning - adjusting weights - error propagated back through previous layers to update the weights o 3. Weights initially assigned random value o 4. Feed-forward mode computes results o 5. Error is computed using training data and error is back-propagated. It's called backward pass mode. Adaptive learning weights modified. o 6. If epoch or minimum error is greater set values go back to step 4 to modify the weights in order to recognize the patterns

Steps in the Weighted Linear Combination Method: 5. Establish the importance of the criteria (set weights):

o 1.5 or 2.6 times more important than some other criteria o 5.0 times more important ....... o n times more important ........ o How can you justify the weighting scheme? o Minimally, qualitative scientific assessments (control) o Computation based upon statistical analysis o Statistical analysis to determine variability - based upon different associations of parameters. Find the relative difference in magnitude

Regression model Methodological Steps: 6

o Apply Model to geographic area: § Make predictions and examine the spatial variability in the probabilty estimates produced. § In many instances - one has interpret, however, if they are scientifically reasonable they can be used for results and distribution predictions

Steps in the Weighted Linear Combination Method: 3. Transform data into information via Analysis:

o Biophysical parameter estimation (Imagery, DEM) o Spatial metrics (spatial analysis; size, shape, topological properties) - perform a spatial analysis - we have basic geometry processes, spatial topological processes. Pattern recognition supplies very important tehmatic mapping o Thematic information (pattern recognition) - lithological zones, pattern recognition, hydrological zones o Biophysical parameters (modeling; parameterization schemes) - precipitation, erosion rate, deposition rate, evaporation rate o Process rates and system parameters (process models) - changing conditions, temporal,

Examples of a system in GIS Modeling

o Climate - Predict temperature, precipitation - CO2 loading, methane loading. Integrates surface systems as well o Geomorphological - mass movement, fluvial and glacial - climate influences this system by temp change, precip. o Geology - trying to assess stress, faulting deformation due to isostatic and uplift. Predicting when land forms come into existence and go out of existence. o Simulating the ecological - disease migration - plants, climate change o Human - social, politics and economical systems that display human interaction. Very complicated. Understanding human environment relationship. Agent based Modeling can be sued to characterize human systems.

4th step in supervised analysis maximum likelihood algorithm: Compute probabilities and classify

o Compute probabilities and classify - probability contours in n-dimensional space. Probability will be high inward. Outward will be lower. WHY separability is so important and uniquely separable in n-dimensional space.

Steps in the Weighted Linear Combination Method: 4. Transform information into rankings of suitability or potential

o Discrete ordinal: Low-Medium-High (1-3) - potential for some phenomena - flood, slope failure, etc. through statistical analysis o Discrete ordinal: Poor-Fair-Good-Very Good-Excellent (0-10) - matter of establishing nth-number of intervals o Discrete ordinal levels (n): n = interval / distribution range beyond the previous examples. Then transform your information Continuous fuzzy ranking (0-1): Fuzzy membership functions (linear/nonlinear) - more sophisticated. Fuzzy suitability 1 = suitable, 0 = least suitable.

Multi-faceted concepts: Scale - very generalize term

o Distance - one to one location. 2-D distance vs 2.5-D vs true 3-D distance. Directionally dependent o Direction - anisotropy o Confinement (scale dependence) - what is the area confining the behavior of the humans on the landscape? Erosion or deposition o Space and time -

What complex components need to be addressed in an index model?

o Do you have a climate component? o Hydrological component? o Ecological component? o Human component? o Geological component? o Develop models for the subcomponents

Supervised ANN classification:

o First select an activation function for your nodes - use binary sigmoid o Select whether you want hard or soft output results. Hard - threshold value - to get nominal results o Generate an ANN architecture (objective based) - optimize your featured space - will be reflective on the number of input nodes. Only use 1 hidden layer network

ANN 3 layers:

o Input layer nodes - relates to the feature space (n dimensional normalized). Data that goes into an ANN should be normalized. 0-1 based on min and max values. o Hidden layer nodes - govern the degree of generalization as it relates to recognizing patterns in the data. Generalization/overfitting - based on those found patterns. Smaller number of nodes will be able to generalize more with less specificity. Sometimes there can be too much noise that's why this is important. o Output layer nodes - thematic classes - number of classes will equal the amount of output layer nodes. Uncertainties - 0-1 o Fuzzy uncertainties thematic likelihood - every pixel will have a value ranging from 01 to give a value of uncertainty for each.

ISODATA clustering algorithm

o Iterative self-organizing data analysis technique - identifies amount of clusters and partitions FS that the user requests o Brute force algorithm - could have no meaning whatsoever o Produces discrete classification results o It will perform better if it is submitted within an optimal Feature Space o Requires experimentation as well with numbers of classes

Multi-faceted concepts: Uncertainty:

o Magnitude - you need reference data to compare it to - but that is hard to come by. Uncertainty is always there. As normalization occurs - more uncertainty occurs o Location - GPS can help us determine error, but many phenomena there is not always just one point. We need to account for a spatial distribution pattern. o Sampling - random sampling will give us a representative sample, but a small sample may not give an accurate representation. Depends upon the distance and direction o Error propagation - through a GIS - data, manipulations, algorithms, present final product that contains error. Uncertainty is quite high here

Unsupervised clustering

o Minimal use of human input. o Widely utilized technique - many different approaches -statistical, graph theory, AI, etc o Most common approach is parametric statistical approach. Uses ISO method o Limited human machine interaction o Select algorithm to be discrete or fuzzy output o Submit optimized featured space to program to carefully think about objectives and what you need for your ideal FS o Select the number of cluster classes - 4,8 ,12, etc o Checking for accuracy and interpretation is absolutely required.

Steps in the Weighted Linear Combination Method: 2. Establish information criteria (n GIS layers, landslide example):

o Most people utilize opinions for information criteria (slope) o Opinions don't represent cause and effect - applying that criteria won't be good o Spatial associations/coincidence (occurences, lithology, vegetation) - it's not that simple. Other factors could be involved - cannot make a conclusive statement o Empirical relationships (precipitation and failure) - many studies find an empirical relationships with magnitude of precipitation and the landslide failure. But other factor could be involved. Need to find cause and effect to prove validity. o Cause and effect (topographic and tectonic stress, water pore pressure) - information criteria is much better here and you'll have better predictive capabilities.

Modeling process: 8 Go to step 2:

o Must go back and implement better models. Can be implemented within a GIS or be external. Implement a new uncertainty analysis and continue to redefine parameters and make new ones.

Parallel piped algorithm

o Non-parametric algorithm - we decide the dimensions. Up to the user to decide the range for the dimensions. It does not require assumption of normality or homogeneity of variance. o This is a Discrete classification - producing nominal values o Requires unique ranges - no overlap between ranges or else misclassification will occur

Steps in the Weighted Linear Combination Method: 1. Compute an index value for each spatial unit (vector or raster):

o Points - lines polygons - tessellation - water wells, roads, pol units, area

Regression model Methodological Steps: 3

o Sampling training set: - biggest issues involves sampling § Number of observations (sample size) - small sample sizes does not repersent good sampling. Large sampler sizes are built to provide better representations. Minimum for a large sample size - 30 or more classes § Representative geographic sampling (random, systematic, stratified) Collect non-training data sets (accuracy assessment) - required for accuracy assessments for your logistical regression model.

Scientific method of knowledge generation:

o Set initial conditions (geospatial data) o Run simulations o Compare results to observations and geospatial data - from the field. Gives us a magnitude of the error and see if a pattern is occurring from the result. Evaluate parameterization of schemes and predictions - then formally and mathematically characterize and then predict based on forcing factor patterns given

ANN Mathematics:

o Transfer function - weights and bias set - sums of the multiplication of the weights plus the bias to determine the neural nodes o Activation function (-1-1 or 0-1) - input data is submitted here - popular function is binary sigmoid function o Output layer nodes - thematic classes Fuzzy uncertainties (0-1) - use post classification on the result from the activation function using the binary sigmoid. Propagate the data is the output classes and get the likelihood or uncertainty for the last step.

Maximum likelihood algorithm

o Use of this algorithm represents a supervised approach. This algorithm is a parametric algorithm- the assumption of a normality and homogeneity of variance associated with the data you are using o Brute Force algorithm o Discrete classification - output will be nominally encoded from 1 and 2 o Based upon probability estimates o Critical for producing accurate probability estimates o This is the most widely utilized supervised classification in the world o Regardless, the robustness of the mathematics, accuracy can be relatively low - used an optimized FS to boost the ability of the algorithm as well as the training classes.

Flood hazard potential: relative angle

o low (0-0.3), medium(0.31-0.6), high(0.61-1) - logical expressions - normalize à Each pixel would have 1 of three values.

6th step in supervised analysis maximum likelihood algorithm: Go to steps 1 and 2

o results first time is quite poor - go back to steps 1 and 2 and reorient themselves of the study area better and get new training samples or modify certain samples.

Post classification for ANN:

o thresholding - discrete results o Error analysis (spatial analysis) - use heterogeneity - higher variance would have that error o Unsupervised classification - ISOdata to see how it would produce a discrete classification

Regression modeling approach:

odds = (Probability of presence of characteristics) / (Probability of absence of characteristics)

What is the holy grail of numerical modeling?

that of producing new knowledge and mathematical formalization of knowledge

If you can get your ANN to converge:

your dataset will be superior to statistical classifiers

Regression model Methodological Steps: 5

§ 1. Conduct a statistical accuracy assessment - measurement scales, adequately sample your data § 2. Go back to step one and re-evaluate

3rd step in supervised analysis maximum likelihood algorithm: Analysis of training samples

§ 1. Normal distribution § 2. Homogeneity of variance § 3. Multi-model distribution - combine pink and red to get a multi-model. Not a homogeneity condition - can cause serious problems to the maximum algorithm

Main Components/structure for neural networks:

§ Neurons/nodes - certain amount of input, hidden and output nodes. Each neuron represents a processing unit. Fundamental processing unit § Layers - always be an input, output and hidden layers - defines the architecture of the ANN § Connectivity - connected to every other neuron in the network. Synapses (human brain), links (network) and weights (computer science).

Regression model Methodological Steps: 4

§ Submit to software and Perform regression analysis (compute beta values) § Many approaches for estimation (Maximum-likelihood) - an estimate § Iterative process to optimize or produce best fit to equation 4 - § Software (Matlab, R, SAS, SPSS, GIS)