A human science approach to soft computing

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A human science approach to soft computing

• Vesa A. Niskanen
• Univ. of Helsinki
• vesa.a.niskanen_at_helsinki.fi

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Application areas

• Data compression, clustering.
• Regression analysis.
• Analyzing paths, nets and graphs.
• Virtual worlds, artificial life.
• Interpretation of texts stories, narratology.

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Relation between input and output

• Goal y1/sqrt(2?)exp(-x2/2) no noise in data
• (standard normal distribution)

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Fuzzy model cluster centres

• if x then y
• -2.90 0.01
• -1.00 0.24
• 2.10 0.04
• Subclust (d0.9),
• these are rules

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Fuzzy model (Tagaki-Sugeno)

• If model unsatisfactory, we can tune it with NN.
• Goodness criteria eg. Rmse, Analysis of
  variance.
• Non-parametric non-linear models.

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Neuro-fuzzy model (Anfis)
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Model construction

• If data available, we can use fuzzy clustering or
  SOM.
• Otherwise knowledge of experts.
• We can also use both of these sources.

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Model construction
Fuzzy rules(SOM, c-means etc.) Fuzzy
reasoning
Training data
Experts
System evaluation(errors)
Tuning(NN)
Control data
New system
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Fuzzy model (Mamdani)

• Problem How much tip in restaurant in USA
  according to given criteria? (gt multi-criteria
  decision-making)
• No data gt expertise.
• Two criteria (inputs)
• quality of service
• quality of food
• Output tip.

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Decision model
Quality of service
Tipping
Quality of food
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Linguistic values of variables

• Service poor, good, excellent.
• Food rancid, delicious.
• Tip cheap, average, generous.

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Fuzzy rules

• 1 If service is poor or food is rancid, then tip
  is cheap.
• 2 If service is good, then tip is average.
• 3 If service is excellent or food is delicious,
  then tip is generous.

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Meanings of values

• The meanings of values are fuzzy sets in a given
  space.
• Then, we can use fuzzy reasoning.
• Inputs/outputs can be either crisp or fuzzy.

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Model construction (Matlab)
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Empiric data of schoolboys

• Data (SAS/STAT)
• 126 schoolboys.
• Ages in months
• Heights in inches
• Weights in pounds.
• The training data comprised 95 randomly selected
  observations, and the rest (31) were used as
  control data.

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Model (schoolboys)
Age
Weight
Height
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Sample of the data
Age / Height / Weight 159.0000 62.8000
99.0000 178.0000 63.8000 112.0000 153.0000
57.8000 79.5000 155.0000 57.3000
80.5000 178.0000 63.5000 102.5000 142.0000
55.0000 76.0000 164.0000 66.5000
112.0000 189.0000 65.0000 114.0000 164.0000
61.5000 140.0000 167.0000 62.0000
107.5000 151.0000 59.3000 87.0000
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Input space (2D)
HEIGHT
AGE
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Model space (3D)
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Linear regression analysis

• Training data
• weight0.21age2.99height-116.60
• R square 0.66
• Rmse 11.52
• Control data
• Rmse 11.97

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Generalized mean (non-linear)

• weight(w1agepw2heightp)1/p
• (w1w21)
• w10.84
• w10.16
• p3.09
• Rmse(control)10.76
• Gen. means can be neurons in NN.

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Fuzzy (Takagi-Sugeno)

• Initial rules /
• cluster centres
• IF THEN
• Age Height Weight
• 1 151 58.3 86
• 2 172 65 112
• 3 193 67.8 127.5
• 4 150 61.8 118
• (d0.4, Rmse9.99)

4 If A is young and H is medium, then W is
medium
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Fuzzy (Takagi-Sugeno)

• Actual rules
• IF THEN
• Age Height Weight
• 1 151 58.3 -0.178age - 1.910height 201.100
• 2 172 65 1.047age 3.596height - 306.300
• 3 193 67.8 0.849age 5.263height - 391.400
• 4 150 61.8 1.155age - 0.718height 5.429
• Cf. Ancova.

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Neuro-fuzzy (Anfis)

• Tune the rules if necessary.

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Interpretation of stories and texts

• Plot / intrigue of a story, report, an interview
  or a historical event.
• Plot / intrigue of a picture or movie.
• Internet / WWW gt

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Interpretation

• In a wide sense, interpretation (hermenuein in
  the Ancient Greek) means (i) delivering messages,
  (ii) explanation, (iii) exegesis or (iv)
  translation.
• At the core of the interpretative approach is
  hermeneutics.
• Interpretation is based on the foreknowledge
  (Vorverständnis) of the researcher. The
  foreknowledge will be modified according to our
  study.
• The whole of the object or phenomenon may be
  understood according to its parts, and vice
  versa. This is a continuous process (hermeneutic
  circle).

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Conventional qualitative tool Atlas

• ATLAS.ti is a powerful workbench for the
  qualitative analysis of large bodies of textual,
  graphical, audio and video data.
• It offers a variety of tools for accomplishing
  the tasks associated with any systematic approach
  to "soft" data, e.g., material which cannot be
  analyzed by formal, statistical approaches in
  meaningful ways.
• ATLAS.ti's unique network building feature allows
  you to visually "connect" selected passages,
  memos, and codes by means of diagrams. This
  feature allows you to construct concepts and
  theories based on visible relations - often
  bringing to light yet other relations. You may
  instantly revert back to your notes or primary
  document selection at any time.
• Networks open up a "context of discovery" and new
  approaches to theory building.

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Hypertext our materials or data constitute
pieces of information and we may construct
networks in which their constituents are
interconnected
Linear
Non-linear
Classic examples I Ching, Homer's Odysseia,
several Aristotle's writings
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Atlas Semantic network
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Fuzzy cognitive maps (FCM)

• A complex society is like a water balloon.
  Squeeze it here, and the water moves over there.
  Anything that makes big changes in one sector
  will affect other sectors.
• For example, What happens under health care
  reform? The problem is how to model complex
  feedback dynamical systems.
• What happens when, for example, the reform
  movement starts? The fuzzy cognitive maps (FCM)
  are expressly designed for this kind of
  high-level modeling.

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Fuzzy cognitive maps (FCM)

• FCM are fuzzy signed graphs with possible
  feedback.
• The nodes are causal concepts.
• They can model events, actions, values, goals,
  stories etc.

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South African apartheid politics (Kosko)
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NN approach

• Edge matrix lists the connections of causal
  links.
• The inputs and outputs are state vectors, and
  matrix multiplication is used.
• Outputs are modified with transformation function
  if necessary.

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NN structure of FCM
(0,1,0) o
(x,y,z)
Transformation /thresholding
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FCM

• Matrix cells can contain bivalent 0,1,
  trivalent -1,0,1 or real valued values.
• The values in each node can oscillate, be chaotic
  or they can finally obtain stable values.
• Adaptive FCMs learn from training data. They
  modify the edge matrix according this data. (gt
  NN)
• Fuzzy Thought Amplifier

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South African politics (Kosko)
1"positive correlation"0"no correlation"-1"ne
gative correlation"
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South African politics (simulation)
Start Support foreign investment policy(keep
c11 constantly)
Transformation xlt0 gt x0xgt0 gt x1
In1(1,0,0,0,0,0,0,0,0), out1(0,1,1,0,0,0,0,1,1),
transformgt in2(1,1,1,0,0,0,0,1,1),
out2(0,1,2,1,-1,-1,-1,4,1), transformgt
in3(1,1,1,1,0,0,0,1,1), out3(0,1,2,1,-1,0,0,4,1)
, transformgt in4(1,1,1,1,0,0,0,1,1)out3 gt
system is stable, and mining, black employment,
strength of gov. and nat. party constituency are
on. Hence, sustained foreign investment maintains
a balance of government stability and racism.
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Linguistic FCM

• We can use linguistic inputs and outputs.
• The relations between nodes are described by
  linguistic rules.

Node
Node
Linguistic rules
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Fuzzy virtual worlds (Kosko)

• A virtual world (cyberspace) is a dynamical
  system which changes with time as the user moves
  through.
• It links humans and computers in a medium that
  can trick the mind and senses.

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Virtual undersea world (Kosko)
shark
fish school
dolphin herd
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Node matrix for undersea world
We may link animations to these maps
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References
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