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Data Driven Modeling Beyond Idealization
Vahid MoosaviPhD Student at Chair for Computer Aided Architectural Design (CAAD), Professor Ludger Hovestadt, ETH ZurichResearcher at ETH-Singapore Centre, Future Cities Laboratory (FCL)
24 May 2014
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Landscape of Scientific Modeling
First Section
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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
How to find a unify
ing
(abstract)
perspecti
ve for
assessm
ent, while keeping
the diversities?
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)– …
Idealization toward perfection or simplification?!!
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Idealization toward perfection or simplification?!!
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A Model of the Modeling Process“Rational Models: Models, based on Ideals”
Second Section
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Natural System
Formal System
Decoding
Encoding
Infe
renc
eCausality
A Model of Modeling Process (Let’s call it Rational Modeling.)
By: Robert Rosen
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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
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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
But which
glasses?
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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?
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?
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Complex Numbers
Real Numbers
What do we mean by “Abstraction”? (A Metaphore)
Rational Numbers
Natural Numbers
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Current Trend: Parametricism (multi-model Idealization) and the Curse of Dimensionality…
…Complicated, but not complex models
Properties of the system for modeling
Possible Relations (types and num
bers)
Complex Systems
Simple Systems
Minimal idealization
Multi-model idealization
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A new realm of modeling?!
Properties of the system for modeling
Possible Relations (types and num
bers)
Multi-Agent Systems
Urban Cellular automata
Urban Dynamics
Basic Statistics(Hypothesis Testing)
Urban Metabolism
Urban ScalingSocial Physics
Fractal Models
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Toward a new formalism for the concept of modeling“Models without Ideals or All the Potential Ideals”
Third Section
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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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It is a self-referential Setup
Page Rank
..Can be local or global
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Relational ModelingAn 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
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However, it took a century…
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
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…this Data Deluge has inverted the concept of empirical research
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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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Link
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Complicated-N
ess!!! Multi-Model Idealization
(Agent Based Transportation Modeling)
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Symboliza
tion of Complexit
y
(Encapsulating a
ll the potential id
eals)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 dynamicsCan be developed for :
• Simulation• community detection• Network Engineering• Sensitivity Analysis
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Fourth Section
Self Organizing MapsAnd
Data Deluge
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How to explain SOM or What is a good story for SOM?
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SOM from the Context of (Nonlinear) Transformation: Dimensionality Reduction
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• Finding an ideal (global) transformation: e.g. PCA• Observations are instances of an abstract representation
Selected Features to Represent the Objects
ObjectsFirst General Approach: Direct Transformation
X TW
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• Each observation is a dimension itself: e.g. MDS, LLE, ISOMAP,… • There is always a mechanism to preserve neighborhood topology.
Second General Approach: Indirect Transformation
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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.A Primal-Dual Representation
X TSOM
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Pre-Specific City Modeling
Footprint of buildings in Orchard area, Singapore
Similar buildings are in the same area of SOM
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Data Driven Urban Pollution Modeling beyond Idealization
Idealization in traditional simulation models
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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)
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
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contextual numbers
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1-Median list Price2-Median sale price3-Median list price -sq. ft.4-Median sale price-sq. ft.5-Sold for loss6-Sold for gain7-Increasing values8-Decreasing values9-Listings with price cut10-Median price cut11-Sold in past year12-Homes for Rent13-Homes foreclosed14-Foreclosure re-sales15-Sale-to-list price ratio16-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.
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SOM: A Generic Computing Machine Beyond Ideal Forms
Democratic Computing Social computing(Computing with any function)
Observed Data
Resamples of Data by SOM
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AdditionSubtractionMultiplication…SOMification as any operation in coexistence with data!!
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Thanks!