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Data Driven Modeling Beyond Idealization

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

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Data Driven Modeling Beyond Idealization

  1. 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. 2. Landscape of Scientific Modeling 2 First Section
  3. 3. Models as the way we conceive of the real phenomena are one of the fundamental elements of any investigation… 3
  4. 4. 5 On the other hand, what we encounter… …A Landscape of Modeling Approaches in Competition, Challenging Complex Systems
  5. 5. 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) – …
  6. 6. Idealization toward perfection or simplification?!!
  7. 7. 9 Idealization toward perfection or simplification?!!
  8. 8. A Model of the Modeling Process “Rational Models: Models, based on Ideals” 10 Second Section
  9. 9. 11 Natural System Formal System Decoding Encoding Inference Causality A Model of Modeling Process (Let’s call it Rational Modeling.) By: Robert Rosen
  10. 10. 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
  11. 11. 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
  12. 12. 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?
  13. 13. Complex Numbers Real Numbers What do we mean by “Abstraction”? (A Metaphore) 16 Rational Numbers Natural Numbers
  14. 14. 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
  15. 15. 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
  16. 16. Toward a new formalism for the concept of modeling “Models without Ideals or All the Potential Ideals” 19 Third Section
  17. 17. 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
  18. 18. It is a self-referential Setup 21 Page Rank ..Can be local or global
  19. 19. 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
  20. 20. 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
  21. 21. …this Data Deluge has inverted the concept of empirical research 24
  22. 22. Classical Simulation SpaceSyntax, London “The social logic of space,(1984)” 33,000+ taxicabs GPS Trajectory of Taxicabs, Beijing, 2012 Inversion in Modeling 25
  23. 23. Link 26
  24. 24. 27 Multi-Model Idealization (Agent Based Transportation Modeling)
  25. 25. 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
  26. 26. Fourth Section Self Organizing Maps And Data Deluge 29
  27. 27. How to explain SOM or What is a good story for SOM? 30
  28. 28. SOM from the Context of (Nonlinear) Transformation: Dimensionality Reduction 31
  29. 29. • 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
  30. 30. • 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
  31. 31. 34
  32. 32. 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
  33. 33. Pre-Specific City Modeling Footprint of buildings in Orchard area, Singapore Similar buildings are in the same area of SOM 36
  34. 34. Data Driven Urban Pollution Modeling beyond Idealization 37Idealization in traditional simulation models
  35. 35. Data Driven Urban Pollution Modeling beyond Idealization 38
  36. 36. 39 SOM: Approximating joint probability distribution
  37. 37. 40 Frequencies of occurrence P.E. Bieringer et al. / Atmospheric Environment 80 (2013)
  38. 38. 41Original Distribution SOM Based Distribution
  39. 39. 42 SOM: Computing with contextual numbers (signs!?)
  40. 40. 43 The classic notion of (natural) number is based on a one directional arrow.
  41. 41. 44 This is the classical time series analysis.
  42. 42. 45
  43. 43. 46
  44. 44. 47
  45. 45. 48 contextual numbers
  46. 46. 49 contextual numbers
  47. 47. 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)
  48. 48. 51
  49. 49. 52 But it is more than visualization…
  50. 50. 53 It improves the overall prediction accuracy
  51. 51. 54 In general, it can be a part of larger computing machine.
  52. 52. SOM: A Generic Computing Machine Beyond Ideal Forms 55 Democratic Computing Social computing (Computing with any function) Observed Data Resamples of Data by SOM
  53. 53. Addition Subtraction Multiplication … SOMification as any operation in coexistence with data!! 56
  54. 54. Thanks! 57

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