Machine Learning meets Granular Computing: the emergence of granular models in the Big Data era ** Presentation Slides from Dr Rafael Falcon, from Larus Technologies, for the February 2018 Ottawa Machine Learning & Artificial Intelligence Meetup Abstract Traditional Machine Learning (ML) models are unable to effectively cope with the challenges posed by the many V’s (volume, velocity, variety, etc.) characterizing the Big Data phenomenon. This has triggered the need to revisit the underlying principles and assumptions ML stands upon. Dimensionality reduction, feature/instance selection, increased computational power and parallel/distributed algorithm implementations are well-known approaches to deal with these large volumes of data. In this talk we will introduce Granular Computing (GrC), a vibrant research discipline devoted to the design of high-level information granules and their inference frameworks. By adopting more symbolic constructs such as sets, intervals or similarity classes to describe numerical data, GrC has paved the way for a more human-centric manner of interacting with and reasoning about the real world. We will go over several granular models that address common ML tasks such as classification/clustering and will outline a methodology to appropriately design information granules for the problem at hand. Though not a mainstream concept yet, GrC is a promising direction for ML systems to harness Big Data.

1. 2/27/2018 1
Machine Learning meets Granular Computing:
the emergence of granular models in the Big Data era
Dr. Rafael Falcon, Larus Technologies & University of Ottawa
rfalcon@ieee.org
Machine Learning and Artificial Intelligence Ottawa
February 26, 2018 | Ottawa, Canada

2. Agenda
2/27/2018 2
‣Introduction to Larus Technologies
‣The Big Data Era
‣Limitations of Traditional Machine Learning Models
‣Taming the Big Data Monster: Popular Solutions
‣Granular Computing: an Introduction
‣The Emergence of Granular [Machine Learning] Models
‣Examples of Granular Models
‣Granular Classifiers
‣Granular Clustering Algorithms
‣Granular Cognitive Maps
‣Conclusions

3. 2/27/2018 3
Total::Insight ©
High Level Information Fusion and Predictive & Big Data Analytics
Total::Perception ©
Automated Data Collection using AI/ML and Nature-Inspired Optimization

4. What We Do
High Level Information Fusion and Predictive Analytics
Multi-source
Information Fusion
Behavioural
Learning and
Analysis
Technology
TECHNOLOGY
Research and
Engineering
Custom
Solutions
Development
ACTIVITIES
Defence and
Security
Maritime Logistics
Commercial Video
Surveillance
Analytics
EXPERIENCE
TOTAL::INSIGHT
Patented (USPTO) behavioral
learning and analysis technology
Leveraging analytical tools to make data-driven decisions
through the production of high quality and time-critical information

5. Larus’ Key Competencies
Big Data Analytics
Data Visualization
Data Infrastructure
Data Warehousing
Business Intelligence
Knowledge Discovery
Cloud and Large Scale Computing
Statistical and Quantitative Analysis
Software Engineering and Development
Resellers
White Papers
Trade Shows
Supply Channels
Product Branding
Thought Leadership
Marketing and Sales Strategy
Technical Presentations by SMEs
Machine Learning
Artificial Intelligence
Predictive Analytics
Data Mining and Fusion
Video and Text Analytics
Modeling and Simulation
Multi-Objective Optimization
Intelligent Processing Architectures
Wireless Sensor and Robot Networks

6. Total::Insight ©

7. Total::Perception ©
Total::Perception can automate and optimize data collection
Automatic cueing and tasking of sensors and assets
Provides a more efficient and timely generation of actionable intelligence
Significantly reduce the cost of surveillance mission management

8. NSERC Maritime IoT Research Project
Product will model and optimize the entire maritime supply chain!
Scenario 1 [Freight Ship Companies]
Scenario 2 [Port Authorities]
Scenario 3 [Trucking and Insurance Companies]

9. The Big Data Era
2/27/2018 9
“Data is big when data size
becomes part of the problem”
“Big Data is the result of collecting information at its most granular
level — it’s what you get when you instrument a system and keep
all of the data that your instrumentation is able to gather.”
Jon Bruner, O’Reilly Media

10. The Increasing V’s of Big Data
2/27/2018 10

11. The Increasing V’s of Big Data
2/27/2018 11

12. The Increasing V’s of Big Data
2/27/2018 12

13. The Increasing V’s of Big Data
2/27/2018 13

14. The Increasing V’s of Big Data
2/27/2018 14
Some interesting V’s:
‣ Vanilla: Even the simplest models, constructed with rigor, can provide value.
‣ Varmint: As big data gets bigger, so can software bugs!
‣ Vivify: Data science has the potential to animate all manner of decision
making and business processes, from marketing to fraud detection.
‣ Voodoo: Data science and big data aren't voodoo, but how can we convince
potential customers of data science's value to deliver results with real-world
impact?

15. Internet of Things (IoT)
2/27/2018 15
“The interconnection via the
Internet of computing devices
embedded in everyday objects,
enabling them to send and
receive data”

16. Limitations of Traditional Machine Learning Models
‣ Volume:
‣ Training time could be computationally intractable with large data sets
‣ Velocity:
‣ Offline ML models not suitable
‣ Variety:
‣ Curse of dimensionality: the amount of data needed to support a sound
inference often grows exponentially with the dimensionality.
‣ Veracity:
‣ Most ML models do not take into account the uncertainty of the data
 Outlier detection will not do
‣ Volatility:
‣ Stationarity assumption: data distribution will not change during analysis
2/27/2018 16

17. Taming the Big Data Monster: Popular Solutions
‣ Dimensionality reduction
‣ “the process of reducing the number of random variables under
consideration by obtaining a set of principal variables.” (Wikipedia)
‣ Two main manifestations:
‣ Feature selection
 Select a subset of the original variables and discard the rest
 Three types: filter, wrapper, embedded
‣ Feature extraction
 Transforms the data in a high-dimensional space to a space of fewer dimensions.
 Linear transformations (PCA, ICA, SVD, etc.)
 Nonlinear transformations (autoencoders, Sammon’s mapping, Kernel PCA, etc.)
2/27/2018 17

18. Taming the Big Data Monster: Popular Solutions
‣ Instance selection
‣ “the process of reducing the number of instances (objects) in the data set.”
(Wikipedia)
‣ “the optimal outcome of IS would be the minimum data subset that can
accomplish the same task with no performance loss, in comparison with the
performance achieved when the task is performed using the whole available
data”
‣ Instance selection algorithms consider the trade-off between reduction rate and
performance degradation.
‣ Two major types:
‣ Preserve instances at the boundaries of the classes
‣ Preserve internal instances of the classes
2/27/2018 18

19. Taming the Big Data Monster: Popular Solutions
‣ Parallel/distributed architectures
2/27/2018 19

20. Taming the Big Data Monster: Popular Solutions
‣ Parallel/distributed architectures
2/27/2018 20

21. Taming the Big Data Monster: Popular Solutions
‣ Parallel/distributed architectures
2/27/2018 21

22. Taming the Big Data Monster: Popular Solutions
‣ More sophisticated algorithms (e.g. Deep Learning) that make use
of these architectures
‣ Still very numerically driven
2/27/2018 22

23. Taming the Big Data Monster: Popular Solutions
‣ Popular Deep Learning Frameworks
2/27/2018 23

24. Granular Computing: An Introduction
2/27/2018 24

25. Granular Computing: An Introduction
2/27/2018 25
‣ Three basic concepts underlying human cognition:
‣ Granulation: Decomposition of a whole into parts
‣ Organization: Integration of parts into a whole
‣ Causation: Association of causes with effects
‣ [Zadeh 1997] The granulation of an object leads to a collection of information
granules
“Informally, a granule is a clump of values of a perception (e.g., perception of age),
which are drawn together by proximity, similarity, or functionality. More
concretely, a granule may be interpreted as a restriction on the values that a
variable can take. In this sense, words in a natural language are, in large measure,
labels of granules. A linguistic variable is a variable whose values are words or,
equivalently, granules.”

26. Granular Computing: An Introduction
2/27/2018 26
‣ Granular Computing (GrC) is an umbrella term to cover any theories,
methodologies, tools and techniques that employ information granules for
problem solving purposes.
‣ An information granule is a subset of the universe.
Implicit information granules
Explicit (operational)
information granules
Humans Computer
realizations
Various points of view (models)
Fuzzy sets
Rough sets
Intervals (sets)
Clouds
Shadowed sets
Probability functions
Information granules

27. Why Granular Computing?
2/27/2018 27
1. Truthful representation of the real world
‣ GrC provides true and natural representations of multi-level systems.
2. Consistent with human thinking and problem solving
‣ Human thinking is based on levels of granularity and change between granularities
3. Simplification of problems
‣ By omitting unnecessary and irrelevant details and focusing on the right level of
abstraction
4. Economic and low-cost solutions
‣ e.g. reduced computational overhead
Yao, Yiyu. "Perspectives of granular computing" Granular Computing, 2005 IEEE International
Conference on. Vol. 1. IEEE, 2005.

28. Granular Computing in the CI/AI Family
2/27/2018 28
Granular Computing
Fuzzy sets
Neurocomputing
Evolutionary
optimization
Pedrycz, Witold “Granular Computing: Pursuing New Avenues of Computational Intelligence"

29. Granular Systems
2/27/2018 29
‣ Granular Systems (GrS) is an umbrella term that is used to describe those
complex, intelligent systems that originate from general, frequently vague and
imprecise specification and employ information granularity at their basis.
‣ They use multiple granule models as building blocks and various GrC models in
to perform inference upon them.
‣ GrC became an effective framework in the design and implementation of
intelligent systems for various real life applications.
‣ The developed systems exploit the tolerance for imprecision, uncertainty and
partial truth under the Soft Computing framework, in order to achieve
tractability, robustness and resemblance with human-like (natural) decision-
making
Szczuka, Marcin, et al. "Building granular systems: from concepts to applications" Rough Sets, Fuzzy
Sets, Data Mining, and Granular Computing. Springer International Publishing, 2015. 245-255.

30. Granular Systems
2/27/2018 30
‣ Granular systems are concerned with the representation, construction, and
processing of information granules
‣ In GrC we deal with calculi of granules defined by elementary granules (e.g.,
indiscernibility or similarity classes) and some operations allowing us to
construct new granules from already defined ones by their amalgamation and
aggregation.
Szczuka, Marcin, et al. "Building granular systems: from concepts to applications" Rough Sets, Fuzzy
Sets, Data Mining, and Granular Computing. Springer International Publishing, 2015. 245-255.

31. A Granular System’s Generic Architecture
2/27/2018 31
Falcon, Rafael, et al. “A review of granular cognitive maps" , submitted to Granular Computing journal

32. Types of Information Granules: Crisp Sets (e.g., Intervals)
2/27/2018 32
https://www.calvin.edu/~pribeiro/othrlnks/Fuzzy/fuzzysets.htm

33. Types of Information Granules: Fuzzy Sets
2/27/2018 33
https://www.calvin.edu/~pribeiro/othrlnks/Fuzzy/fuzzysets.htm

34. Some Membership Functions for Fuzzy Sets
2/27/2018 34
https://www.calvin.edu/~pribeiro/othrlnks/Fuzzy/fuzzysets.htm

35. Types of Information Granules: Clustering
2/27/2018 35
https://mubaris.com/2017/10/01/kmeans-clustering-in-python/
Clustering
Algorithm
Metadata
• Prototypes
• Partition matrix
• Point density
(core, boundary,
outlier)

36. Types of Information Granules: Rough Sets
2/27/2018 36
Pawlak, Zdzislaw “Rough set theory and its applications to data analysis“, Cybernetics & Systems
29:7, 661-668, 1998
Example. Predicting the loyalty of a new customer.
Identifier Member
Score
Online
Payments
City Click rate Loyalty
customer1 68 TRUE Genk 15/20 Yes
customer2 21 FALSE Hasselt 13/20 Yes
customer3 43 TRUE Brussels 0/20 No
customer4 65 FALSE Leuven 18/20 Yes
customer5 37 FALSE Hasselt 3/20 No
customer6 68 TRUE Genk 15/20 No
customer7 29 TRUE Antwerp 10/20 ?

37. Types of Information Granules: Rough Sets
2/27/2018 37
Pawlak, Zdzislaw “Rough set theory and its applications to data analysis“, Cybernetics & Systems
29:7, 661-668, 1998

38. Types of Information Granules: Rough Sets
2/27/2018 38
Pawlak, Zdzislaw “Rough set theory and its applications to data analysis“, Cybernetics & Systems
29:7, 661-668, 1998
‣ The lower and upper approximations divide the universe of
discourse into three disjoint regions:
 The positive region 𝑃𝑂𝑆 𝑋 comprises those objects certainly
related with the decision class → certainty.
 The negative region 𝑁𝐸𝐺 𝑋 comprises those objects certainly
not related with the decision class → certainty.
 The boundary region 𝐵𝑁𝐷 𝑋 comprises those objects possibly
related with the decision class → possibility.

39. Types of Information Granules: Fuzzy Rough Sets
2/27/2018 39
Dubois, Didier, and Henri Prade. "Rough fuzzy sets and fuzzy rough sets." International Journal of
General System 17.2-3 (1990): 191-209.
‣ The lower and upper approximations (crisp sets) in classical
RST are now modeled as fuzzy sets.
‣ Fuzzy tolerance relations replace the crisp equivalence relation
imposed on RST
‣ LowerApprox(Class = “Pass”) = {X1, X3, X4}
‣ FuzzyLowerApprox(Class = “Pass”) = (0.95, 0.2, 0.85, 0.90, 0.23)

40. Information Granulation: Main Avenues
2/27/2018 40
Pedrycz, Witold “Granular Computing: Pursuing New Avenues of Computational Intelligence"
Principle of justifiable information
granularity
data  single information granule
Data
Clustering
numeric data a collection of
information granules:
set-based (K-Means)
fuzzy sets (Fuzzy C-Means)
rough sets (Rough C-Means)
…

41. Designing Information Granules: Principle of Justifiable Granularity
2/27/2018 41
‣ One of the fundamental principles in Granular Computing
‣ Leads to the creation of sound information granules (IGs)
‣ Two conflicting views of an IG:
‣ Coverage: The IG should be supported by the available (often numerical) data
‣ Specificity: The IG should be specific enough, i.e., it has to exhibit a tangible
meaning
Pedrycz, Witold, and Xianmin Wang. "Designing fuzzy sets with the use of the parametric principle of
justifiable granularity" IEEE Transactions on Fuzzy Systems 24.2 (2016): 489-496.

42. ‣ These two requirements are in conflict and a compromise must be achieved
Designing Information Granules: Principle of Justifiable Granularity
2/27/2018 42
Pedrycz, Witold, and Xianmin Wang. "Designing fuzzy sets with the use of the parametric principle of
justifiable granularity" IEEE Transactions on Fuzzy Systems 24.2 (2016): 489-496.
‣ The principle of Justifiable Granularity can be formulated as an optimization
problem:
‣ generate initial representatives (IG) of the underlying data
‣ adjust the IGs (stretch, shrink) so the two requirements can be met to a
significant extent

43. Traditional Machine Learning Models
2/27/2018 43
Pedrycz, Witold “Granular Computing: Pursuing New Avenues of Computational Intelligence"

44. Granular Machine Learning Models
2/27/2018 44
Pedrycz, Witold “Granular Computing: Pursuing New Avenues of Computational Intelligence"

45. Granular Models: Two Key Principles
2/27/2018 45
‣ The model is built as a network of associations among information
granules.
‣ This supports interpretability of the model, which becomes easily translated
into a collection of rules with condition and conclusion parts being formed by
the constructed information granules.
‣ Information granules form conceptually sound building blocks
(supported by data) and in light of their functionality, can be used in the
formation of a variety of relationships among input and output variables.
Reyes-Galaviz, Orion and Pedrycz, Witold “Granular fuzzy models: analysis, design and
evaluation" International Journal of Approximate Reasoning 64 (2015): 1-19.

46. Example: A Granular Neural Network
2/27/2018 46
Reyes-Galaviz, Orion and Pedrycz, Witold “Granular fuzzy models: analysis, design and
evaluation" International Journal of Approximate Reasoning 64 (2015): 1-19.
intervals
clusters

47. Example: Traditional Fuzzy Rule-based System
2/27/2018 47
-if x is Ai then y = Li(x, ai), i=1, 2, …,c
Ai – fuzzy set in the input space Li(x, ai) – local model (linear)
Data-driven design process
condition parts developed through fuzzy clustering (e.g., Fuzzy C-Means, FCM)
conclusion part – estimation of parameters a1, a2, …, ac
Pedrycz, Witold “Granular Computing: Pursuing New Avenues of Computational Intelligence"

48. Example: Granular Fuzzy Rule-based System
2/27/2018 48
Pedrycz, Witold “Granular Computing: Pursuing New Avenues of Computational Intelligence"
-if x is G(Ai) then y = Li(x, ai), i=1, 2, …,c
G(Ai )– type-2 fuzzy set in the input space (granular prototypes)
Li(x, ai) – local model (linear)
Granular condition space

49. Example: Granular Fuzzy Rule-based System
2/27/2018 49
Pedrycz, Witold “Granular Computing: Pursuing New Avenues of Computational Intelligence"
Granular conclusion space
-if x is Ai then y = Li(x, G(ai)), i=1, 2, …,c
Ai –fuzzy set in the input space
Li(x, G(ai)) – local model (linear) with granular parameters

50. Example: Granular Fuzzy Rule-based System
2/27/2018 50
Pedrycz, Witold “Granular Computing: Pursuing New Avenues of Computational Intelligence"
Granular condition and conclusion spaces
-if x is G(Ai) then y = Li(x, G(ai)), i=1, 2, …,c
G(Ai) –fuzzy set of type-2 in the input space
Li(x, G(ai)) – local model (linear) with granular parameters

51. Example: From Traditional Decision Trees …
2/27/2018 51

52. … to Granular Decision Trees
2/27/2018 52
Balamash, A., Pedrycz, W., Al-Hmouz, R., & Morfeq, A. (2017). “Granular classifiers and their design
through refinement of information granules”. Soft Computing, 21(10), 2745-2759.
Idea: Granulate the input space by producing an initial number of granular
prototypes (IGs). Then subsequently refine these prototypes according to their
diversity until a certain homogeneity level is reached
Granular prototypes formed
via FCM-based clustering

53. Example: … to Granular Decision Trees
2/27/2018 53
Balamash, A., Pedrycz, W., Al-Hmouz, R., & Morfeq, A. (2017). “Granular classifiers and their design
through refinement of information granules”. Soft Computing, 21(10), 2745-2759.

54. Example: … to Granular Decision Trees
2/27/2018 54
Balamash, A., Pedrycz, W., Al-Hmouz, R., & Morfeq, A. (2017). “Granular classifiers and their design
through refinement of information granules”. Soft Computing, 21(10), 2745-2759.

55. Example: Granular clustering
2/27/2018 55
Rubio, Elid, and Oscar Castillo. "A new proposal for a granular fuzzy C-Means algorithm" Design of
Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Springer
International Publishing, 2015. 47-57.
Goal: Granulate the output of the Fuzzy C-Means (FCM) clustering algorithm in
order to produce region-based granular prototypes representing the clusters,
not just numerical prototypes as done in FCM.
Idea: Granulation-degranulation mechanism

56. Example: Granular clustering
2/27/2018 56
Rubio, Elid, and Oscar Castillo. "A new proposal for a granular fuzzy C-Means algorithm" Design of
Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Springer
International Publishing, 2015. 47-57.
Based on the reconstruction error
computed by the granulation-
degranulation mechanism,
two approximations of the original data
can be built.
(Interval-based) granular prototypes and
membership matrices can be derived
from this information

57. Example: Granular clustering
2/27/2018 57
Rubio, Elid, and Oscar Castillo. "A new proposal for a granular fuzzy C-Means algorithm" Design of
Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization. Springer
International Publishing, 2015. 47-57.
Original FCM Granular FCM

58. Example: Granular cognitive mapping
2/27/2018 58
 Goal: augment Fuzzy Cognitive Maps (FCMs) with information granules
 Fuzzy cluster prototypes
 Rough-set-based regions
 positive, negative and boundary regions
Step 1
• Information
granulation
Step 2
• Topology
construction
Step 3
• Network
exploitation
Fuzzy sets
Rough sets
Fuzzy Cognitive Maps:
concepts, weights
Activation of the
granular concepts

59. Fuzzy Cognitive Maps
2/27/2018 59
A type of recurrent neural network denoting system concepts and their
causal connections modeled via fuzzy sets

60. Granular Time Series Modeling
2/27/2018 60
Wojciech Froelich, Witold Pedrycz (2017) “Fuzzy cognitive maps in the modeling of granular time
series”, Knowledge-Based Systems, Vol. 115, pp. 110 – 122

61. Granular FCM for Graded Multilabel Classification
2/27/2018 61
Gonzalo Nápoles, Rafael Falcon, Elpiniki Papageorgiou, Rafael Bello and Koen Vanhoof (2016)
“Partitive Granular Cognitive Maps to Graded Multilabel Classification”, 2016 IEEE International
Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, Canada, July 24-29, 2016, pp. 1363-1370
‣ Graded Multilabel Classification (GMLC) = predict the membership
degree of an input pattern to multiple class labels
‣ Automatic construction of the granular FCM
‣ FCM input concepts = set of fuzzy cluster prototypes generated
through Fuzzy C-Means clustering
‣ FCM output concepts = set of decision classes
‣ FCM weights = learned from data using Particle Swarm Optimization
(PSO); three underlying topologies were explored

62. Granular FCM for Graded Multilabel Classification
2/27/2018 62
Gonzalo Nápoles, Rafael Falcon, Elpiniki Papageorgiou, Rafael Bello and Koen Vanhoof (2016)
“Partitive Granular Cognitive Maps to Graded Multilabel Classification”, 2016 IEEE International
Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, Canada, July 24-29, 2016, pp. 1363-1370
GCM-1: input neurons are fully connected with each other and with each
decision label; only recurrent connections allowed in the output layer

63. Granular FCM for Graded Multilabel Classification
2/27/2018 63
Gonzalo Nápoles, Rafael Falcon, Elpiniki Papageorgiou, Rafael Bello and Koen Vanhoof (2016)
“Partitive Granular Cognitive Maps to Graded Multilabel Classification”, 2016 IEEE International
Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, Canada, July 24-29, 2016, pp. 1363-1370
GCM-2: input neurons are fully connected with each other and with each
decision label; fully connected output layer to capture inter-label correlations

64. Granular FCM for Graded Multilabel Classification
2/27/2018 64
Gonzalo Nápoles, Rafael Falcon, Elpiniki Papageorgiou, Rafael Bello and Koen Vanhoof (2016)
“Partitive Granular Cognitive Maps to Graded Multilabel Classification”, 2016 IEEE International
Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, Canada, July 24-29, 2016, pp. 1363-1370
GCM-3: fully connected topology

65. Granular FCM for Graded Multilabel Classification
2/27/2018 65
Gonzalo Nápoles, Rafael Falcon, Elpiniki Papageorgiou, Rafael Bello and Koen Vanhoof (2016)
“Partitive Granular Cognitive Maps to Graded Multilabel Classification”, 2016 IEEE International
Conference on Fuzzy Systems (FUZZ-IEEE), Vancouver, Canada, July 24-29, 2016, pp. 1363-1370
‣ Experimental Results
‣ Generated GMLC datasets from UCI ML repositories via
Random Forests
‣ Performance metric: Normalized Mean Squared Error (NMSE)
‣ All three granular models perform comparably
‣ Not compared to other GMLC classifiers as they predict the ordinal
relation of labels instead of their exact membership grade

66. Rough Cognitive Networks (RCNs)
2/27/2018 66
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
‣ Granular FCMs whose input concepts are derived from the three regions
in Rough Set Theory

67. Rough Cognitive Networks (RCNs)
2/27/2018 67
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
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2/27/2018 68
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
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2/27/2018 69
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
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70. Rough Cognitive Networks (RCNs)
2/27/2018 70
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
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2/27/2018 71
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
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72. Rough Cognitive Networks (RCNs)
2/27/2018 72
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
𝐷1 𝐷2
𝑃1 𝑃2
𝑁1
𝐵1
𝑁2
𝐵2
1.0
1.0
1.0
1.0
1.0
1.0
-1.0
-1.0
-1.0 -1.0 -1.0-1.0
1.0 1.0
0.5
0.5
0.5
0.5

73. Rough Cognitive Networks (RCNs)
2/27/2018 73
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
‣ To activate the neurons we compute the intersection between
the similarity class 𝑅 𝑥 and each granule.
𝑅 𝑥 𝑃𝑂𝑆(𝑋 𝑘)
𝐴𝑖
0
=
𝑅 𝑥 ∩ 𝑃𝑂𝑆(𝑋 𝑘)
𝑃𝑂𝑆 𝑋 𝑘

74. Rough Cognitive Networks (RCNs)
2/27/2018 74
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
‣ Experimental takeaways
‣ RCNs are capable of outperforming standard ML classifiers
‣ User intervention in the RCN learning process relegated only to the
selection of a single input parameter: the similarity threshold used to
build the similarity classes in the input space
‣ RCN topology not depending on the number of input features
 Rather it depends on the number of decision classes (C << M)

75. RCN Limitations
2/27/2018 75
Nápoles, Gonzalo, Isel Grau, Elpiniki Papageorgiou, Rafael Bello, and Koen Vanhoof.
"Rough cognitive networks" Knowledge-Based Systems 91 (2016): 46-61.
‣ Building the similarity relation requires specifying the proper
granularity degree. That is to say:
‣ Evaluating a threshold value requires building the lower and
upper approximations from scratch.
𝑅: 𝑦𝑅𝑥 ⟺ 𝑆𝑖𝑚𝑖𝑙𝑎𝑟𝑖𝑡𝑦 𝑥, 𝑦 ≥ 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑

76. Two Ways To Overcome RCN Limitations
2/27/2018 76
Gonzalo Nápoles, Rafael Falcon, Elpiniki Papageorgiou, Rafael Bello and Koen Vanhoof (2017)
“Rough Cognitive Ensembles”, Int’l Journal of Approximate Reasoning, Vol 85, June 2017, pp. 79-96
Gonzalo Nápoles, Carlos Mosquera, Rafael Falcon, Isel Grau, Rafael Bello and Koen Vanhoof (2017)
“Fuzzy-Rough Cognitive Networks”, Neural Networks, to appear
High prediction rates, complex and
difficult to understand
High prediction rates, simpler and
comprehensible
Rough Cognitive Ensembles Fuzzy-Rough Cognitive Networks

77. Conclusions
2/27/2018 80
‣ Granular Computing is a promising approach to tackle the
multifaceted challenges posed by Big Data and Internet of
Things
‣ The development of granular models is still in its infancy
‣ and certainly confined to academic circles
‣ not aware of any commercially available implementation
‣ Lots to do in this field!

78. 2/27/2018 81
Thank you for your time!
Questions?
Rafael Falcon, Ph.D., SMIEEE
Research Scientist, Larus Technologies
Adjunct Professor, University of Ottawa
rfalcon@ieee.org