This document is a lecture by Jean-Antoine Moreau on predictive modeling and geographic information systems. It discusses modeling methodologies including inductive and deductive approaches. It also describes the components of a geographic information system including databases, mapping, analysis and modeling systems. Predictive techniques like neural networks and their applications to business and geographic information systems are also covered.

1. Conference - Study : Jean-Antoine Moreau (Engineer - Lecturer)
Predictive ModelingPredictive Modeling
Modelling MethodologyModelling Methodology
Geographic Information SystemGeographic Information System
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2. Conference - Study : Jean-Antoine Moreau (Engineer - Lecturer)
DATA SCIENCEDATA SCIENCE
Lecture 5Lecture 5
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« Each problem that I solved became a rule,
which served afterwards to solve other problems. »
Rene Descartes

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• Image processing;
• Spatial analysis;
• Cartography;
• Database management system;
• Statistical analysis;
• Business application;
Database (spatial)
Geographic Information System
Statistical Summary

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Database Structure of Spatial Character
• Object-based spatial model;
• Spatial objects;
• Thematic objects.

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Spatial Object
Physical Object Abstract Object

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Spatial Object Combinatorial Network Geometric Network
Topological relation within 3D Objects

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• The geographic data base is made:
a geographical base, which includes spatial
objects;
a thematic base, which includes thematic
descriptions (attributes) of these objects.

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Subsystems that make up the geographic
information system:

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The mapping system
 selects items from the basic geographic data,
 represents them cartographically on media
(monitors, printers, tablets, plotters) in compatible
formats.

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The digital recording system
• Converts analogic information into digital
information.

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The spatial analysis & modelling system
• Extending the capabilities of traditional databases;
• Consideration of the location of the observations;
• Allows the spatial overlap of entity.

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• The image processing system:
– Remote image processing;
– Includes statistical analysis procedures;
– Allows the transformation of original image
into a thematic content.

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• The Statistical Analysis System:
– Procedure of statistical analysis;
– Thematic dimension;
– Statistical procedures for analyzing the spatial
dimension.

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Predictive Techniques
• Digital representation techniques of spatial
data:
– approach in object mode,
• vector structure;
– approach raster (data)
• structure or mesh.

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Raster storage

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Acquisition
Creating layers
Verification
Integration
Grouping
Precision
Creating for vector files
Rasterization files
Pearson correlation test
Qualitative award
Meaningful categories
Predictive modeling
Boolean supperposition
Using the probability (location / time)
Definition of the area
Development of a predictive model

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Inductive approach
location parameter
model

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Deductive approach
location hypothesis
model

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Inductive modelisation
• Inductive modeling consists in a Boolean
superposition of all significant layers, with
the logical AND operator.

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Methods
• Neural networks;
• The Temporal series;
• Event models.

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Neural networks
Modeling

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Neural networks
Modeling

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Neural networks
Modeling

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• The neural network model predicts from
influences:
– Input received information are factors of
influence;
– Dendrites, which transform information
between neurons are chosen in mathematical
functions;
– The synthesis of information made is the
phenomenon, to predict.

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Neural networks
Function Modeling

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Neural networks
Function with Data Base Modeling

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Neural networks
Function with Data Base Modeling
Business Information systemGeographic Information System

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Temporal series’ module
is used for the prediction of fluctuating quantity.
• Decomposition of a set of data by:
– a trend;
– cyclical items;
– dependent components of past values of the series or
trends of influencing factors;
– random residues.

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spatial representation

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The fractal theory
takes into account the continuity and discontinuity
of developments.

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Chaos theory
• System with high sensitivity to the initial
conditions;
– The initial conditions can be very different
from forecasts.

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A break … you can ask your questions
« Change your opinions, keep to your principles; change your leaves, keep intact your roots »
Victor Hugo

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Behavioral expectations
• Decision to purchase of a customer,
– according to its own characteristics;
• Industrial component failure;
• ....

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Behavioral expectations
• Behavioral prediction;
• Statistical theory;
• Analytical models:
– Analysis of variance;
– Mathematical regressions;
– Duration of models;
• Artificial intelligence oriented real-time.

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Machine Learning
• Optimization criteria;
• Prediction indicator;
• Search the data in relational form;
• Automatic optimization;
• Model “black box” depiction of the system’s
model and illustrates the relationships between the
inputs, states, and output.

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systemic view

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Input Output
Environment
Black Box Model

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Black Box Model

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Predictive modeling - uncertainties and variations

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• Concept of virtual measurement:
– Measure calculated as opposed to added value,
the real mesure;
– Focus on the associated measurement
uncertainty.

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• Errors - Uncertainties:
– Measurement error: the difference between the
measured value of a quantity and a reference
value;
– Systematic error components of the
measurement error, the variation is predictable.
– Measurement uncertainty: Non-negative
parameter characterizing the dispersion of the
assigned values.

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Errors and Uncertainties in modeling
• Formalization (mathematical) model:
– Approximation, structural uncertainties.
• Numerical implementation of the models:
– Details of algorithms ;
– Convergence thresholds;
– Stochastic models.
• Parametric uncertainties:
– Accuracy of the parameters;
– Model definition.

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Numerical uncertainties
• Precision of calculations related to the finite;
• Representation of numbers on computers;
• Unit convertion;
• Threshold effects;
• Sensitivity to initial conditions;
• Non-breeding calculations;
• Stochastic method.

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Numerical uncertainties
• Threshold effects;
• Stop criterion of an algorithm;
• Convergence threshold effect.

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Digital uncertainty
• Non-repeatability;
• The response order of CPU (Central Processing Unit) :
– the outcome;
– on the order of operations.

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• Bayesian error estimation in density functional theory
Error estimates for Density Functional Theory
calculations.
 The approach which is based on ideas from Bayesian statistics
involves creating an ensemble of exchange-correlation functionals by
comparing with an experimental database.

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The major uncertainty is the failure of a
model to represent the experimental data.

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Predictive modeling
Simplified process

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• Spatial structure of the data
– Geographical database,
– The predictive models;
– Referenced data.

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Information Modeling

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Define the Database
Use of a database management system
Creating a validated and secure repository

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Define the method of consultation
Consultation tools

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example: Method of decision trees.
• Statistical method applicable to area discrimination and
regression.
• Statistical discrimination consists from a sample of data
representation of considered phenomena, to build a model
to predict the class of a new observation.
• The class of an observation (a qualitative variable) is this
the binary variable indicating the presence or absence (true
or false proposition, boolean 1 or 0).

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example: Method of decision trees.

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example: Method of decision trees.

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The generalization ability of the model is
the quality of the model on new data.

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Construction of the decision tree
• The first phase:
– Récurssif binary partitioning algorithm;
– The recursion stops when the subset is homogeneous.
• The second phase:
– Removal of the least significant statistically branches of
the decision tree;
– Breiman method;
– Ranking according to the resistance to the reduction of
the error criterion.

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• The performance of decision trees should be assessed in
their ability to predict:
– presence;
– no;
– true;
– false;
– yes;
– no;
– ...
geolocated

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a break, to ask your questions.
« There is nothing either good or bad but thinking makes it so. »
William Shakespeare

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• Correlation and regression:
– The correlation is a statistical characteristic of the
existence or absence of a connection in two samples X
and Y, values taken on a group of subject.
– The coefficient coeficient quantifies this relationship by
a sign of the correlation (positive and negative), and by
the strength of this correlation.
– The degree of correlation is measured from 0 to 1.
• 0: no correlation;
• 1: perfect correlation.

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• Calculating the variance
between samples:
• Calculation of the
covariance:
• The correlation index:
Coefficient calculation

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The correlation
• The linear correlation was studied by:
– a scattergram;
– the linear correlation coefficient, which is a
measure of the direction and intensity of the
linear association.

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Strong linear relationship
Positive or negative correlation almost perfect.

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Pearson test
This is to test whether the data are consistent with a
probability law defined a priori. We begin with the
case of the multinomial distribution, for which the
probability distribution is a finite number of values.
In the general case, it is reduced to the multinomial
distribution by splitting the data into classes.

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Spearman Test
• Spearman's coefficient, like any correlation calculation, is appropriate
for both continuous and discrete variables, including ordinal variables.
• The Spearman correlation coefficient is defined as the Pearson
correlation coefficient between the ranked variables.For a sample of
size n, the n raw scores are converted to ranks , and ρ is computed
from:

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Raster and Vector Structure
• Raster :
– Conceptual model = continuous surface;
• Pixel;
• Vector :
– Conceptual model = discrete objects;
• Points, ligne, polygone, bodies.

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• Vector structure;
• Raster structure;
• Storage in the computer.
• Vector data;
• Storage of vector data;
• Topology;
• Generalization methods.

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• Longitude;
• Latitude;
• Elevation;
• Roads;
• Building;
• Plants;
• Lakes;
• …
Spatial Vector in a Geographical Information system
They have position in X, Y , Z

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NON Spatial data in a
GGeographical IInformation SSystem (GIEGIE)
Data that describe the properties of the object.
Examples:
Tree layer > hight, perimeter, age;
River layer > depth;
House layer > owner, no, individual.

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Non-Spatial data in a
GGeographical IInformation SSystem (GIEGIE)
• Attribute forms :
• Tables;
• Text;
• Documents;
• Pictures;
• Video;
• Sound;
• …

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• Attribute data
– Each object is represented as a row in the table;
– The row in the table are linked to the
geographical objects throughthe ID-number.

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example
Masts for Mobile telecommunication
• Position for possible locations :
Vector model points give a best precision;
• Topography expressed as elevation in meters above sea level :
– Raster model (continuous surface);
• Building including their heights in meter:
– Vector model, point or polygons;
– The height presented in the attribute table.

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• Simple exercice :
About a molecule
Using a real-time combinatorial model

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• File extensions (examples):
– The geometrical objects: • . shp
– The link between the geometrical objects and
the attribute data: : • . shx
– The attribute data : • . dbf
– The spatial reference (projected coordinate
system) : • . prj

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The file
The contents of files
• . shp - coordinate file ;
• . shx - index list ;
• . prj - Text string in a specified order ;
• . dbf - rows and columns.

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Point
• No dimension ;
• No extension in space ;
• Each point has a unique ID-value ;
• One coordinate pair (3 coordinates, in 3D).

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Lines
• 1 dimension ;
• Each line segment = a start node + an end node;
• Node in between = vertices (breakpoints);
• Each line segment has an ID-number.

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Polygons – simple
– 2 dimensional;
– Lines that enclose themselves > surface is
homogeneous;
– Each polygon > an ID-number.

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Polygons – simple model
Simple model = spaghetti model
• Storage problem
– Boundaries are stored twice;
• Searches of the neighbor
– Entire list of coordinates is searched until an
identical pair is found.

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Polygone - simple model + a coordinate liste
– List of coordinates;
– List of the points;
– Attribute table.

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• How could objects be related to each
other ?

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Topological line structure
• Analysis of flows / transport;
• Connectivity and direction.

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Topological Line Network
Example
• Required information about attributes
(time, speed, …);
• How they are connected;
• Node:
– start, end, intersections in separate table.

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Topological Line Wetwork
The Graph

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Examples
Models

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« Start by doing what's necessary; then do what's
possible; and suddenly you are doing the impossible. »
Francis of Assisi

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Topological polygon structure
• Shares lines stored once;
• Different tables for describing different
aspects of the topology.

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File structure for a geometric object
Two dimensions

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File Structure for a geometric object
three-dimensional

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Generalization
• Set of data volume;
• To synchronize data based on different
scales (level of detail);
• Define a good requirements;
• To cut down on processing.

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Types of generalization
• Simplification – reduce the number of coordinate pairs;
• Smoothing – apply an equation to describe the shape;
• Aggregation – aggregate several objects;
• Merge – merge smaller objects to larger;
• Collapse –change data type.

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Line generalization : polynominal equation
Polynomial equation
P(x) = B + B X + B X + …. + B X K0 1
n
2
2
n
0B , B , B … , B coefficients that decide the shape of the curve
21 k
K = the degree of the polynomial

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Splines
Cubic - polynominal
P(x) = B + B X + B X + …. + B X K0 1
n3
2
2
n
• 2 points, then a new cubic polynomial must be added;
• Rules are added to keep a « smooth » passage between the polynomial.

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Vectors advantages
• Small amount of data
– storage efficiency;
• Easy to update;
• Easy to combine with attributed data;
• Geometric precision;
• Management of topological relation.

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Vectors disadvantages
• Data continuity is not represented effectively;
• Spatial analysis and filtering within polygon is
impossible.

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Repetition raster / vector
• Raster
– Continuous varying surface.

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Examples of raster images
• Photos;
• Photogrammetry and Remote Sensing;
• Scanned Images of Maps;
• Modeling - terrain;
• Land cover analysis for continuous surfaces.

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0,0
Raster in co-ordinate space
Position (i,j)
Column: i
Row: j
n
X axis
Y axis

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Spatial Resolution
• Spatial Resolution = minimum distance
over which change is recorded;
• Smallest units are the cells or pixels;
• High resolution = small cell dimensions;
• High resolution = lots of detail.

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• Every cell has a positional coordinates;
• These may be referenced in terms of cell
positions (i,j) or in coordinate space (x,y);
• Therefore we have (x,y,z) or (i,j,z).

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Representation of the reality
Example
• No cell can be empty, all cells must have a
value;
• Numbers represent an object;
• The numbers present an ID-number in one
complex attribute data (table).

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Raster representation
example

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Raster representation
example

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Raster representation
example
Vector data
representation
Raster data
representation

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Raster representation
example

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Raster
Advantages / Disadvantages

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Raster advantages
• Simple data structure;
• Easy to generate;
• Easy workflow;
• Easy analysis.

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Raster disadvantages
• Tends to generate huge files, depending on
resolution;
• Cell arrangement does not respect natural
borders;
• Low in precision.

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« Continuous effort - not strength or intelligence –
is the key to unlocking our potential. »
Winston Churchill

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Storage

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Data in the computer
• Binary system used for storing and computation;
• Computer store data as arrays of switches;, that are
either ‘on’ (1) or ‘off’ (0) called bits;
• 8 bits yields one byte;
• Several bytes strung together is call a word.

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Binary system = base 2
• base 10 = the decimal system;
• base 2 = the binary system.

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Value of an array of 3 switches on the binary system

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In the computer
• Binary system
• Array of 8 switches (0,1) = 1 byte;
• 8 bits – 1 bits ;

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Larger number in the computer
• 2 bytes =16 bits

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Larger and negative numbers
• One bit has to be set aside to represent the sign
• The range of numbers represented in decimal form : -32 768 to +32 768

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Decimal number

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Decimal number
• Lowest decimal number that can be stored = 1.2 x 10^38 ;
• Highest decimal number that can be stored => 3.4 x 10^38 ;
• Precision is limited to 7 significant digits ;
• Single precision real = 4 bytes
<the decimal point can ‘float’
• Double precision real = 8 bytes.

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INTEGER VALUE
• Byte 1 byte;
• Integer 2 bytes;
• Double integer 4 bytes.

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DECIMAL NUMBER – FLOAT
• Single precision (7 significant number(s) 4 bytes) ;
• Double precision (15 significant number(s) 8 bytes) .

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• ASCII 1 byte / character ;
• ANSI 1 byte / character.

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• Grids can also store continuous values like elevation

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Grids
Example
• Shuttle radar topography mission (SRTM)
• Digital Elevation Models (DEM)

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Grids
Example

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Grids
Example

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• Mathematical operations can be applied to
two raster and the result is in the output
raster.
• Functions include + , - , / , * , Log , Exp ,
Sin , Cos , Sqrt .

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Triangulated Irregular Network
a 3 Data structure for representing surface
rd

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Types of Data Representation
Vector data representation Raster data representation Triangulated data representation

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Topology
• Feature of the need to be connected using specific rules.

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Planar topology
• Planar topology specifies the topological
rules for features;
• Topological properties include adjacency,
connectivity, inside / outside, and direction.

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Planar topology

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Topology

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Topology

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Topological Relationships
• Vector ans TIN (Triangulated Irregular
Network) data can have topological
structure;
• Raster and image can not have a topology
structure.

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Questions for each project
• What data layers ?
• Vector, raster, TIN, image ?
• Topological structure :
– Network connectivity ?
– Planar topology ?
• Attributes ?
• Minimum required accuracy?

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« A leader is best when people barely know he exists, when his work is done,
his aim fulfilled, they will say: we did it ourselves. »
Lao Tzu

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SPATIAL OBJECTSSPATIAL OBJECTS
ANDAND
DATABASE MODELSDATABASE MODELS

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• The objects in a spatial database are
represented by real world entities with
associated attributes;
• The power of à GIS (geographical
Information System) comes from its ability
to look at data in their geographical context,
and examine them between entities.

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Point data
• The simplest type of spatial object;
• Choice of entities which will be represented a point
depends on the scale of the map study;
• The coordinates of each point can be stored as two
additional attributes;
• Information on a set of points can be viewed as an
extended attribute table;
• Each point is independent of every other point, represented
as a separate row in the database model.

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LINE DATA

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LINE DATA
Network Entities
• Infrastructures networks,
• Transportation network,
• Utility network.

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LINE DATA
Network characteristic
• Network is a composed of :
– Nodes – junction,
– Links – chains in the data base model;
– Diagramm;
– Valency of a node is the number of links at the node.

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• Example of link attributes
• Direction of traffic;
• Volume of traffic;
• Length;
• Number of lanes;
• Time to travel along link;
• Diameter of pipe;
• Direction of pipe;
• Direction of flow;
• Voltage of electrical transmission line;
• …

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AREA DATA
– Boundaries may be defined by natural phenomena;
Boundary are defined by the phenomenon itself.

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AREA Coverage
• Entities are isolated areas;
• Any place is within exactly one entity;
• The database must be able to deal them
correctly.

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Data structures for representative surface
Digital model
Result is a matrix of point

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Data structures for representative surface
• Digital Elevation Model;
• Based on sampling the elevation surface with a
regular intervals;
 Result is a matrix of points.

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Using the technique of a spatial interpolation

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Topological Data Model
Example 3D Urban Entity
Node-Relation Structure

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Node – Relation Structure (NRS)
• It represents :
– Topological relationships;
– Adjacency and connectivity relationship.

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Node – Relation Structure (NRS)

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Node – Relation Structure (NRS)

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Node – Relation Structure (NRS)

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Node – Relation Structure (NRS)

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Node – Relation Structure (NRS)

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