1) The document discusses different approaches to modeling complex systems, noting that current approaches are often limited and idealized. It proposes that a new formalism is needed that avoids ideals and encapsulates all potential modeling perspectives. 2) As an example, it compares rational modeling, based on ideals, to relational modeling using large datasets. Relational modeling inverts the concept of empirical research by using "data deluge". 3) Self-organizing maps are presented as a method that creates abstractions from data while preserving topological relationships, providing both a transformation and primal-dual representation. This allows SOM to be used for various tasks from simulation to computing with contextual numbers.

1. svm@arch.ethz.ch
SEC
Data Driven Modeling Beyond Idealization
Vahid Moosavi
PhD Student at Chair for Computer Aided Architectural Design (CAAD),
Professor Ludger Hovestadt, ETH Zurich
Researcher at ETH-Singapore Centre, Future Cities Laboratory (FCL)
24 May 2014
1

2. Landscape of Scientific Modeling
2
First Section

3. Models as the way we conceive of the real phenomena are one of
the fundamental elements of any investigation…
3

5. 5
On the other hand, what we encounter…
…A Landscape of Modeling Approaches in
Competition, Challenging Complex Systems

7. First Try: Formal Definitions
• No specific definition so far (Stanford Plato) but some classifications:
• Models and Representation
– Scale models. (Black 1962)
– Idealized models (Michael Weisberg)
• Aristotelian (Minimal)
• Galilean (McMullin 1985)
• Caricatures
– Analogical models (Hesse 1963)
– Approximations
– Phenomenological models: (McMullin 1968)
– …

8. Idealization toward perfection or simplification?!!

9. 9
Idealization toward perfection or simplification?!!

10. A Model of the Modeling Process
“Rational Models: Models, based on Ideals”
10
Second Section

11. 11
Natural
System
Formal
System
Decoding
Encoding
Inference
Causality
A Model of Modeling Process (Let’s call it Rational Modeling.)
By: Robert Rosen

12. 12
A Normal Distribution with
outlier or a “unique case”?
Fourier Transformation: any
form is a linear combination
of some ideal forms
Each Code Follows On An Ideal Form

13. Each code consists of certain aspects (features) of the natural system
(Models as Pairs of Glasses): Minimalist Idealizations and multi-models
Networks: Structural thinking
Agents (actors): Interactions
between different agencies
System Dynamics: Process
Oriented View
13

15. Challenge: What to do in dealing with Complex Adaptive
Systems? Which glasses (i.e. modeling approach) is
sufficient, when in principle each view is arbitrary?
15
Hypothesis: Majority of current modeling approaches
are fundamentally limited in dealing with complex
systems and what we need is an abstraction from the
concept of “rational modeling”.
Idea: Is it conceptually possible to have all the views at
once?

16. Complex Numbers
Real Numbers
What do we mean by “Abstraction”? (A Metaphore)
16
Rational Numbers
Natural Numbers

17. Current Trend: Parametricism (multi-model Idealization) and the
Curse of Dimensionality…
17
…Complicated, but not complex models
Properties of the system for modeling
PossibleRelations
(typesandnumbers)
Complex Systems
Simple Systems
Minimal
idealization
Multi-model
idealization

18. 18
A new realm of modeling?!
Properties of the system for modeling
PossibleRelations
(typesandnumbers)
Multi-Agent
Systems
Urban Cellular
automata
Urban Dynamics
Basic Statistics
(Hypothesis Testing)
Urban Metabolism
Urban Scaling
Social Physics
Fractal Models

19. Toward a new formalism for the concept of modeling
“Models without Ideals or All the Potential Ideals”
19
Third Section

20. How to avoid the curse of dimensionality? (Or How to
Encapsulate all the potentialities?)
Selected Features to Represent the Objects
Objects
Encapsulation RelationalityRationality
Examples:
• Cities
• Streets
• Buildings
• People
• Companies
• Food
• Energy
• Medicine
• Internet
• Words in a text
Abstract Universals (ideal forms)
Concrete Universals
20

21. It is a self-referential Setup
21
Page Rank
..Can be local or global

22. Relational Modeling
22
An Example in Natural Language Modeling
Rational Modeling Relational Modeling
External Reference
We have the Ideal model of the
language
No External Reference
We have A Huge Corpus of
language
Main Assumption
Relational Representation of symbols in a language
Noam Chomsky MarkovHeroes
Based on
Approach

23. However, it took a century…
23
Markov (1907) Shannon(1948) Google 2000-
“For Linguists it is hard to
believe it as a practical
approach”
“Interesting idea, but
Computationally
Expensive”
“Getting Feasible! With Billions
of text documents”
Relational Representation of symbols in a language
Data
Deluge

24. …this Data Deluge has inverted the concept of empirical
research
24

25. Classical Simulation
SpaceSyntax, London
“The social logic of space,(1984)”
33,000+ taxicabs
GPS Trajectory of Taxicabs,
Beijing, 2012
Inversion in
Modeling
25

26. Link
26

27. 27
Multi-Model Idealization
(Agent Based Transportation Modeling)

28. 28
Using GPS tracks of cars within a city:
Taking urban cells as a word in a language,
each individual driver is a unique story teller,
while driving within urban grid cells…
...A Markov Chain Model of traffic dynamics
Can be developed for :
• Simulation
• community detection
• Network Engineering
• Sensitivity Analysis

29. Fourth Section
Self Organizing Maps
And
Data Deluge
29

30. How to explain SOM or What is a good story for SOM?
30

31. SOM from the Context of (Nonlinear) Transformation:
Dimensionality Reduction
31

32. • Finding an ideal (global) transformation: e.g. PCA
• Observations are instances of an abstract representation
32
Selected Features to Represent the Objects
Objects
First General Approach: Direct Transformation
X TW

33. • Each observation is a dimension itself: e.g. MDS, LLE, ISOMAP,…
• There is always a mechanism to preserve neighborhood topology.
33
Second General Approach: Indirect Transformation

34. 34

35. Self Organizing Map (SOM) : A generic setup, based on
symbolic indexes
• SOM as a transformation
based on topology
preserving mechanism,
but at the same time
creating an abstraction
from observations.
35
A Primal-Dual Representation
X TSOM

36. Pre-Specific City Modeling
Footprint of buildings in
Orchard area,
Singapore
Similar
buildings are
in the same
area of SOM
36

37. Data Driven Urban Pollution Modeling beyond Idealization
37Idealization in traditional simulation models

38. Data Driven Urban Pollution Modeling beyond Idealization
38

39. 39
SOM: Approximating joint probability distribution

40. 40
Frequencies of occurrence
P.E. Bieringer et al. / Atmospheric Environment 80 (2013)

41. 41Original Distribution SOM Based Distribution

42. 42
SOM: Computing with contextual numbers (signs!?)

43. 43
The classic notion of (natural) number is based on a one directional
arrow.

44. 44
This is the classical time series analysis.

45. 45

46. 46

47. 47

48. 48
contextual numbers

49. 49
contextual numbers

50. 50
1-Median list Price
2-Median sale price
3-Median list price -sq. ft.
4-Median sale price-sq. ft.
5-Sold for loss
6-Sold for gain
7-Increasing values
8-Decreasing values
9-Listings with price cut
10-Median price cut
11-Sold in past year
12-Homes for Rent
13-Homes foreclosed
14-Foreclosure re-sales
15-Sale-to-list price ratio
16-Price to rent ratio
Multi-Dimensional Time Series
Modeling (Real Estate Dynamics)

51. 51

52. 52
But it is more than visualization…

53. 53
It improves the overall prediction accuracy

54. 54
In general, it can be a part of larger computing machine.

55. SOM: A Generic Computing Machine Beyond Ideal Forms
55
Democratic Computing Social computing
(Computing with any function)
Observed Data
Resamples of Data by SOM

56. Addition
Subtraction
Multiplication
…
SOMification as any operation in coexistence with
data!!
56

57. Thanks!
57