Presented at METALITHICUM COLLOQUY #5 CODING AS LITERACY: SELF ORGANIZING MAPS

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
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2. Landscape of Scientific Modeling
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First Section

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

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Idealization toward perfection or simplification?!!

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

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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
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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?
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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)
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Rational Numbers
Natural Numbers

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

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

22. Relational Modeling
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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…
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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
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25. Classical Simulation
SpaceSyntax, London
“The social logic of space,(1984)”
33,000+ taxicabs
GPS Trajectory of Taxicabs,
Beijing, 2012
Inversion in
Modeling
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26. Link
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Multi-Model Idealization
(Agent Based Transportation Modeling)

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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
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30. How to explain SOM or What is a good story for SOM?
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31. SOM from the Context of (Nonlinear) Transformation:
Dimensionality Reduction
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32. • Finding an ideal (global) transformation: e.g. PCA
• Observations are instances of an abstract representation
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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.
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Second General Approach: Indirect Transformation

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

38. Data Driven Urban Pollution Modeling beyond Idealization
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SOM: Approximating joint probability distribution

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

41. 41Original Distribution SOM Based Distribution

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SOM: Computing with contextual numbers (signs!?)

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

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This is the classical time series analysis.

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contextual numbers

49. 49
contextual numbers

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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)

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But it is more than visualization…

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It improves the overall prediction accuracy

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

55. SOM: A Generic Computing Machine Beyond Ideal Forms
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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!!
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57. Thanks!
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