Computing with Students from LIS

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Computing with Students from LIS

ECE 1001

• Prof. Marian S. Stachowicz
• Laboratory for Intelligent Systems
• ECE Department, University of Minnesota, USA
• November 7, 2006

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• Professor Marian S. Stachowicz
• 273 MWAH
• M and W from 1400 to 1530
• http//www.d.umn.edu/ece/lis

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Courses

• ECE 5831 Fuzzy Sets Theory
• ECE 3151 Control Systems

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Outline

• LIS
• Computing with Words
• Fuzzy Logic - Mathematica Package
• Soft Computing
• Color Mining

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LIS

• LABORATORY FOR INTELLIGENT SYSTEMS
• http//www.d.umn.edu/ece/lis

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Laboratory for Intelligent Systems
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LIS has been founded in cooperation with
Minnesota Power and 3M.
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Undergraduate and graduate students concentrate
on methods and algorithms for soft computing and
their applications in - image processing, -
multi-objective optimization, - color
recognition.
RESEARCH
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Computing with Words

• Computing with Words (CW) is a methodology in
  which words are used in place of numbers for
  computing and reasoning.

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LEXICAL IMPRECISION

• DALLAS STAR
• PRICESS OF CRUDE OIL, WHICH HAVE EDGED HIGHER IN
  RECENT WEEKS AFTER BEING REMARKABLY STABLE
  THROUGH MUCH OF THE YEAR, MAY FLUCTUATE AS MUCH
  AS A DOLLAR A BARREL IN THE MONTHS AHEAD,
• BUT ABRUPT CHANGES ARE NOT LIKELY, MANY ANALYSTS
  BELIEVE.

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Computing with Words

• CW is a necessity when the available information
  is too imprecise to justify the use of numbers.
• When there is tolerance for imprecision which can
  be exploited to achieve tractability, robustness,
  low solution cost, and better rapport with
  reality.

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A key aspect of CW is that it involves a fusion
of natural languages and computation with fuzzy
variables.
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A linguistic variable AGE

• T(AGE) YOUNG, NOT YOUNG, VERY YOUNG, NOT VERY
  YOUNG, , OLD, NOT OLD, VERY OLD, NOT VERY OLD,
  , MIDDLE AGED, NOT MIDDLE AGED,, NOT OLD AND
  NOT MIDDLE AGED,, EXTREMELY OLD,

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Fuzzy Partition

• Fuzzy partitions formed by the linguistic values
  young, middle aged, and old

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What are Fuzzy Sets?
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Problem 1 Given the set U 1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, describe the set of prime
numbers.
A u in U u is a prime number
The elements of the set are defined unequivocally
as A 2, 3, 5, 7, 11
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Problem 2 Now using the same set U,
suppose we want to describe the set of small
numbers.
M u in U u is a small number
Now, it is not so easy to define the set. We
can use a sharp transition like the following,
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An alternative way to define the set would be to
use a smooth transition.
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Fuzzy Sets

• A fuzzy set A defined in the universal space U is
  a function defined in U which assumes values in
  the range 0,1 .
• A U ? 0, 1

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Characteristic Function

A U ? 0, 1

Membership Function
M U ? 0, 1
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Areas of Applications 1

• Approximate Reasoning
• Fuzzy Decision Making
• Fuzzy Arithmetic
• Fuzzy Modeling
• Fuzzy Logic Control

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Fuzzy Modeling
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Fuzzy Sets

• The human brain interprets imprecise and
  incomplete sensory information provided by
  perceptive organs.
• Fuzzy sets theory provides a systematic calculus
  to deal with such information linguistically, and
  it performs numerical computation by using
  linguistic labels stipulated by membership
  functions.

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Fuzzy sets theory provides a strict mathematical
framework in which vague conceptual
phenomena can be precisely and rigorously studied.
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Where is Fuzzy System Used?

• Linear and Nonlinear Process Control
• Robotics, Automation, Tracking
• Consumer Electronics
• VCRs, Digital High Definition Television,
  Microwave Ovens, Cameras, etc.
• Pattern Recognition
• Image Processing, Machine Vision
• Decision Making

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Where is Fuzzy System Used?

• Sensor Fusion, Risk Analysis
• Financial Systems
• Information Systems
• Data Base Management
• Information Retrieval
• Data Analysis
• Meteorology
• Art and Music

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Fuzzy Systems

• Why fuzzy systems?
• What are fuzzy systems?
• Where are fuzzy systems used and how?

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Fuzzy Systems

• Fuzzy systems are knowledge-based or
• rules-based systems.
• A fuzzy systems is constructed from a collection
  of fuzzy IF-THEN rules.

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A fuzzy IF-THEN rule is statement in which some
words are characterized by membership function
(MF).
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Two kinds of justification for fuzzy system
theory

• We need a theory to formulate human knowledge in
  a systematic manner and put it into engineering
  systems.

• The real world is too complicated for precise
  descriptions to be obtained.

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Example 1. 2

• Problem
• We want to design a controller to automatically
  control the speed of a car.

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Two approaches to designing such a controller

• use conventional control theory,
• for example, designing a PID controller.

• to emulate human drivers, that is, converting the
  rules used by human drivers into an automatic
  controller.

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Knowledge-based or rules-based.

• IF speed is low, THEN apply more force to the
  accelerator,
• IF speed is medium, THEN apply normal force to
  the accelerator,
• IF speed is high, THEN apply less force to the
  accelerator.
• Where the words low, medium, high and more,
  normal, less
• are characterized by membership functions (MF).

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Where Are Fuzzy Systems Used ?

• Fuzzy washing machine
• Digital image stabilizer
• Fuzzy systems in cars
• Fuzzy control of a cement kiln
• Fuzzy control of subway train

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Digital image stabilizer.

• IF all the points in the picture are moving in
  the same direction, THEN the hand is shaking.
• IF only some points in the picture are moving,
  THEN the hand is not shaking.

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Mitsubishi Heating/Cooling

• 25 Heating Rules
• 25 Cooling Rules
• Heats/Cools 5x faster
• Reduces power consumption by 24

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Maytag Dishwasher

• Measures soil in water, adjusts wash accordingly
• Adjusts for dried-on foods
• Determines optimum wash cycle

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Sony Palmtop

• Used directly for character recognition
• Each person writes letters slightly differently
• Fuzzy rules account for these differences

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Soft Computing

• The research of fuzzy systems, neural network,
  and genetic algorithms are categorized into a
  same computer paradigm, so-called Soft Computing.

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Evolutionary Computation

• Genetic algorithms (GAs) are based on the
  evolutionary principle of natural selection.
• GAs are derivative-free stochastic optimization
  method.
• The GAs offers the capacity for population-based
  systematic random searches.

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Global maximum
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Tuning the PID Controller

• The generic algorithm helps us avoid random
  searches by evolving meaningful variables from a
  seemingly infinity number of possibilities for
  the parameters of P, I and D which determine the
  performance of a PID controller 21.

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Performance specifications

• ITAE ? t ? e(t)? d t for 0 ? t lt ?

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Example 1 A FIRST ORDER UNSTABLE SYSTEM
System Characteristics and Design Results
GA Method
Kp 35.0 Ki 148.4 Kd 1.2 ITAE Index
0.0377
Unit Step Response
Traditional Method
Kp 9.4 Ki 36.0 Kd 0.0 ITAE Index
0.0553

• Note
• Red reference input
• Blue system output
• Green error

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Soft computing

• Soft computing uses the human mind as a role
  model and, at the same time, aims at a
  formalization of the cognitive processes humans
  employ so effectively in the performance of daily
  task.
• - Lotfi A. Zadeh

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Acknowledgments

• Jonathan Andersh
• Lance Beall
• Cheng Tong
• Chaohui Yang
• Dan Yao

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Purpose of research
Color and Computer
To explore the ways how color can be used in
computer.
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Color and Computer Images

• Three main color schemes used with computers
• - CMYK cyan, magenta, yellow, black
• used by printers
• - HSB hue, saturation, brightness
• similar to human vision
• - RGB red, green, blue
• most common system
• computer images are generally stored in this
  format
• used in this research

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Color and Computer Images

• The Basic Image Element Pixel
• Pixels are described by two features
• Location in the x-y plane
• Color - in the from R, G, B,
• where R, G, B 0 to 255

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Spatial and Intensity Resolutions

• An image with M pixels can be represented by a
  spatial-chromatic hybrid vector
• Xi (xi, yi, Ri, Gi, Bi )T (i 1, 2,
  , M)
• where
• xi, yi are the spatial
  coordinates
• Ri, Gi, Bi are the color components.

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The spatial resolution

• The spatial resolution describes how many pixels
  are possible within a certain distance such as
  150 dots per inch (DPI).

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24-bit color

• Almost always, each of the R G B numbers is a
  single byte, so the red, green, and blue
  components can take on integer values from 0 to
  255.
• 255, 255, 255 would represents white,
• 0, 0, 0 would represent black,
• 255, 0, 0 would represent red, and so on.

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COLOR MINING

• 256 x 256 x 256 16 777 216 colors per one pixel
  

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Color Recognition Method

• - Using only color information
• - Two main steps

Feature Extraction
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COLOR CUBE
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National Flags Identification
A system which can identify national flags by
comparing an input flag to a known database.
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The intensity resolution

• The intensity resolution describes how many
  different intensities or colors are possible for
  a particular pixel.

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Stamps Identification
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Grab.exe
I-35 near 4th Ave. West, Duluth, MN
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Heart Murmur Classification
normal
pathology
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T(COLOR)RED, GREEN, BLUE, CYAN, MAGENTA,
YELLOW, WHITE, BLACK
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Acknowledgments

• Sonny Zhan
• David Lemke
• Lucas May
• David Olsen
• Nicholas Andrisevic
• Adilbek Karaguishiyev
• Glenn Nordehn, M.D.

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References

• 1 L.A. Zadeh, Fuzzy sets, Information and
  Control,
• vol.8, pp. 338-353, 1965.
• 2 George S. Klir and Bo Yuan, Fuzzy Sets,
  Uncertainty, and Information. Prentice Hall,
  Englewood Cliffs, New Jersey, 1995.
• 3 M.S. Stachowicz and Lance E. Beall, Fuzzy
  Logic Package for use
• with Mathematica, Wolfram Research, Inc.
  Champaign, IL 61820, 2003
• http//www.wolfram.com/fuzzylogic
• 4 C.M. Charlton, Strange Attractor, CD Album
  of Piano Improvisations, Orange Moon Production,
  Inc. 19672 Stevens Creek Blvd., 178, Cupertino,
• CA 95014, http//www.catherinemariecharlton.com/

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Laboratory for Intelligent Systems
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AG-H Krakow, Poland 22-26 May, 2006
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Palma De Mallorca - Spain, 30 August, 2006
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ECE 5831-F-2006
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Professor Lotfi Zadeh and Professor Marian S.
Stachowicz Vienna, Austria, 28
November 2005
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THANK YOU.