Title: A human science approach to soft computing
1A human science approach to soft computing
- Vesa A. Niskanen
- Univ. of Helsinki
- vesa.a.niskanen_at_helsinki.fi
2Application areas
- Data compression, clustering.
- Regression analysis.
- Analyzing paths, nets and graphs.
- Virtual worlds, artificial life.
- Interpretation of texts stories, narratology.
3Relation between input and output
- Goal y1/sqrt(2?)exp(-x2/2) no noise in data
- (standard normal distribution)
4Fuzzy 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
5Fuzzy model (Tagaki-Sugeno)
- If model unsatisfactory, we can tune it with NN.
- Goodness criteria eg. Rmse, Analysis of
variance. - Non-parametric non-linear models.
6Neuro-fuzzy model (Anfis)
7Model construction
- If data available, we can use fuzzy clustering or
SOM. - Otherwise knowledge of experts.
- We can also use both of these sources.
8Model construction
Fuzzy rules(SOM, c-means etc.) Fuzzy
reasoning
Training data
Experts
System evaluation(errors)
Tuning(NN)
Control data
New system
9Fuzzy 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.
10Decision model
Quality of service
Tipping
Quality of food
11Linguistic values of variables
- Service poor, good, excellent.
- Food rancid, delicious.
- Tip cheap, average, generous.
12Fuzzy 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.
13Meanings 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.
14Model construction (Matlab)
15Empiric 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.
16Model (schoolboys)
Age
Weight
Height
17Sample 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
18Input space (2D)
HEIGHT
AGE
19Model space (3D)
20Linear regression analysis
- Training data
- weight0.21age2.99height-116.60
- R square 0.66
- Rmse 11.52
- Control data
- Rmse 11.97
21Generalized 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.
22Fuzzy (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
23Fuzzy (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.
24Neuro-fuzzy (Anfis)
- Tune the rules if necessary.
25Interpretation 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
26Interpretation
- 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).
27Conventional 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.
28Hypertext 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
29Atlas Semantic network
30Fuzzy 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.
31Fuzzy 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.
32South African apartheid politics (Kosko)
33NN 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.
34NN structure of FCM
(0,1,0) o
(x,y,z)
Transformation /thresholding
35FCM
- 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
36South African politics (Kosko)
1"positive correlation"0"no correlation"-1"ne
gative correlation"
37South 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.
38Linguistic FCM
- We can use linguistic inputs and outputs.
- The relations between nodes are described by
linguistic rules.
Node
Node
Linguistic rules
39Fuzzy 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.
40Virtual undersea world (Kosko)
shark
fish school
dolphin herd
41Node matrix for undersea world
We may link animations to these maps
42References
R. Axelrod, Structure of decision the cognitive
maps of political elites. Princeton Univ. Press,
1976. H. Bandemer W. Näther, Fuzzy data
analysis (Kluwer, Dordrecht, 1992). S. Chiu,
Fuzzy model identification based on cluster
estimation, Journal of Intelligent and Fuzzy
Systems, 2 (1994) 267-278. H. Dyckhoff W.
Pedrycz, Generalized means as model of
compensative connectives, Fuzzy Sets and Systems
14 (1984) 143-154. R. Jang, ANFIS
Adaptive-network-based fuzzy inference system,
IEEE Transactions on Systems, Man and Cybernetics
23/3 (1993) 665-685. Kacprzyk, J. and Fedrizzi,
M. (Eds.), Fuzzy Regression Analysis (Physica
Verlag, Heidelberg, 1992). W. Kickert, Fuzzy
Theories on Decision Making (M. Nijhoff, Boston,
1978). B. Kosko, Neural networks and fuzzy
systems, (Prentice-Hall, Englewood Cliffs,
1992). V.A. Niskanen, A brief logopedics for the
data used in a neuro-fuzzy milieu, Lecture Notes
in Artificial Intelligence, 1566, Springer
Verlag, Berlin, 1999, pp. 222-233. I. Rojas
al., Statistical analysis of the main parameters
in the fuzzy inference process, Fuzzy Sets and
Systems,102/2 (1999) 157-173. M. Smithson, Fuzzy
set analysis for behavioural and social sciences
(Springer Verlag, New York, 1987). T. Takagi M.
Sugeno, Fuzzy identification of systems and its
applications to modeling and control, IEEE
Transactions on Systems, Man and Cybernetics,
SMC-15/1 (1985) 116-132. R. Yager D. Filev,
Generation of fuzzy rules by mountain clustering,
Journal of Intelligent and Fuzzy Systems 2 (1994)
209-219. L. Zadeh, Fuzzy logic Computing with
words, IEEE Transactions on Fuzzy Systems, vol.
2, pp. 103-111, 1996. L. Zadeh, From Computing
with Numbers to Computing with Words -- From
Manipulation of Measurements to Manipulation of
Perceptions, IEEE Transactions on Circuits and
Systems, 45, 1999, 105-119. L. Zadeh, Toward a
theory of fuzzy information granulation and its
centrality in human reasoning and fuzzy logic,
Fuzzy Sets and Systems 90/2 (1997) 111-127.