1 / 51

Algorithmic Facets of Human Centricity in Computing with Fuzzy Sets

Algorithmic Facets of Human Centricity in Computing with Fuzzy Sets. Witold Pedrycz Department of Electrical & Computer Engineering University of Alberta, Edmonton, Canada and Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland. pedrycz@ee.ualberta.ca.

brooks
Download Presentation

Algorithmic Facets of Human Centricity in Computing with Fuzzy Sets

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Algorithmic Facets of Human Centricity in Computing with Fuzzy Sets Witold Pedrycz Department of Electrical & Computer Engineering University of Alberta, Edmonton, Canada and Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland pedrycz@ee.ualberta.ca ISDA-2009, Pisa, Italy, November 30-December 2, 2009

  2. Agenda Human centricity and information granules Design of information granules – approaches of knowledge-based clustering Granular representation of computing with fuzzy sets

  3. Human Centricity and information granules Information granules as conceptual entities inherently associated with human pursuits (decision-making, perception control, prediction) Interaction with and processing in intelligent systems realized at the level of information granules (fuzzy sets, rough sets, intervals…) Emergence of Human-Centric computing (HC2) Knowledge sharing and collaboration in distributed systems

  4. Human Centricity and fuzzy sets Two fundamental quests: Construction of information granules (fuzzy sets); use of existing experimental evidence and its interpretation Cast in the framework of users/designer Qualitative, user-centric interpretation of results of computing with fuzzy sets

  5. Clustering as a conceptual and algorithmic framework of information granulation Data information granules (clusters) abstraction of data Formalism of: set theory (K-Means) fuzzy sets (FCM) rough sets shadowed sets

  6. Main categories of clustering Graph-oriented and hierarchical (single linkage, complete linkage, average linkage..) Objective function-based clustering Diversity of formalisms and optimization tools (e.g., methods of Evolutionary Computing)

  7. Key challenges of clustering Data-driven methods Selection of distance function (geometry of clusters) Number of clusters Quality of clustering results

  8. The dichotomy and the shift of paradigm supervised learning unsupervised learning Human-centricity Guidance mechanisms

  9. Fuzzy C-Means (FCM)

  10. Fuzzy Clustering: Fuzzy C-Means (FCM) Given data x1, x2, …, xN, determine its structure by forming a collection of information granules – fuzzy sets Objective function Minimize Q; structure in data (partition matrix and prototypes)

  11. Fuzzy Clustering: Fuzzy C-Means (FCM) Vi– prototypes U- partition matrix

  12. FCM – optimization Minimize subject to (a) prototypes (b) partition matrix

  13. Domain Knowledge: Category of knowledge-oriented guidance Context-based guidance: clustering realized in a certain context specified with regard to some attribute Viewpoints: some structural information is provided Partially labeled data: some data are provided with labels (classes) Proximity knowledge: some pairs of data are quantified in terms of their proximity (resemblance, closeness)

  14. Clustering with domain knowledge(Knowledge-based clustering)

  15. Context-based fuzzy clustering

  16. Context-based clustering Clustering : construct clusters in input space X Active role of the designer [customization of processing] Context-based Clustering : construct clusters in input space X given some contextexpressed in output space Y

  17. Context-based clustering: Conmputational considerations structure structure context Data Data • computationally more efficient, • well-focused, • designer-guided clustering process

  18. Context-based clustering: focus mechanism Determine structure in input space given the output is high Determine structure in input space given the output is medium Determine structure in input space given the output is low Input space (data)

  19. Context-based clustering: examples Find a structure of customer data [clustering] Find a structure of customer data considering customers making weekly purchases in the range [$1,000 $3,000] Find a structure of customer data considering customers making weekly purchases at the level of around $ 2,500 Find a structure of customer data considering customers making significant weekly purchases who are young no context context context context (compound)

  20. Context-oriented FCM Data (xk, targetk), k=1,2,…,N Contexts: fuzzy sets W1, W2, …, Wp wjk = Wi(targetk) membership of j-th context for k-th data Context-driven partition matrix

  21. Context-oriented FCM: Optimization flow Objective function Subject to constraint U in U(Wj) Iterative adjustment of partition matrix and prototypes

  22. Fuzzy clustering with viewpoints

  23. Viewpoints: definition Description of entity (concept) which is deemed essential in describing phenomenon (system) and helpful in casting an overall analysis in a required setting “external” , “reinforced” clusters

  24. Viewpoints: definition viewpoint (a,b) viewpoint (a,?)

  25. Viewpoints: definition Description of entity (concept) which is deemed essential in describing phenomenon (system) and helpful in casting an overall analysis in a required setting “external” , “reinforced” clusters

  26. Viewpoints in fuzzy clustering B- Boolean matrix characterizing structure: viewpoints prototypes (induced by data)

  27. Viewpoints in localization of “extreme” information granules specification of viewpoints through evolutionary/population-based optimization

  28. Viewpoints in fuzzy clustering

  29. Fuzzy clustering with partial supervision

  30. Labelled data and their description Characterization in terms of membership degrees: F = [fik] i=12,…,c , k=1,2, …., N supervision indicator b = [bk], k=1,2,…, N

  31. Augmented objective function b > 0

  32. Fuzzy clustering with proximity hints

  33. Proximity hints Prox(k,l) Prox(s,t) Characterization in terms of proximity degrees: Prox(k, l), k, l=1,2, …., N and supervision indicator matrix B = [bkl], k, l=1,2,…, N

  34. Proximity measure • Properties of proximity: • Prox(k, k) =1 • Prox(k,l) = Prox(l,k) Proximity induced by partition matrix U: Linkages with kernel functions K(xk, xl)

  35. Augmented objective function b > 0

  36. Fuzzy clustering with collaboration mechanisms

  37. Two general development strategies SELECTION OF A “MEANINGFUL” SUBSET OF INFORMATION GRANULES

  38. Two general development strategies (1) HIERARCHICAL DEVELOPMENT OF INFORMATION GRANULES (INFORMMATION GRANULES OF HIGHER TYPE) Information granules Type -2 Information granules Type -1

  39. Two general development strategies (2) HIERARCHICAL DEVELOPMENT OF INFORMATION GRANULES AND THE USE OF VIEWPOINTS viewpoints Information granules Type -2 Information granules Type -1

  40. Two general development strategies (3) HIERARCHICAL DEVELOPMENT OF INFORMATION GRANULES – A MODE OF SUCCESSIVE CONSTRUCTION

  41. Fuzzy Computing: Interpretability Interpretation of fuzzy sets - departure from pure numeric quantification of membership grades A= [0.11 0.19 0.34 0.45 1.00 0.98 0.821 0.447…]

  42. Granulation of fuzzy sets Granulation of membership grades low, high, medium membership of alternative x Granulation of membership grades and universe of discourse low membership for a collection of alternatives….

  43. Granulation of membership grades A= [L L L M M L L M…] A= [0.11 0.19 0.34 0.45 1.00 0.98 0.821 0.447…]

  44. Granulation of membership grades: optimization A= [L L L M M L L M…] G= {G1, G2, …, Gc} Entropy minimization

  45. Granulation of fuzzy sets A= [L M L M…]

  46. Granulation of fuzzy sets: optimization Gc Gi Wi Wc G1 W1

  47. Interpretability of fuzzy set computing Granulation of fuzzy sets Interpretability layer Fuzzy set computing

  48. Interpretability of fuzzy set computing Granulation of fuzzy sets Interpretability layer Fuzzy set computing

  49. Interpretability of fuzzy set computing • Equivalence sought with respect with assumed level • interpretability: • stability • Equivalence of models Non-distinguishability distinguishability

  50. Fuzzy set computing: a retrospective interpretability ~1970 evolutionary after ~1990 Rule-based neurofuzzy accuracy

More Related