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A Self-Organizing CMAC Network With Gray Credit Assignment

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Title: A Self-Organizing CMAC Network With Gray Credit Assignment


1
A Self-Organizing CMAC Network With Gray Credit
Assignment
  • Ming-Feng Yeh and Kuang-Chiung Chang
  • IEEE, Vol. 36, No. 3, 2006, pp. 623-635.
  • Presenter Cheng-Feng Weng
  • 2008/8/14

2
Outline
  • Motivation
  • Objective
  • Methods
  • CMAC
  • SOCMAC
  • Experimental results
  • Summary and conclusion
  • Comments

3
Motivation
  • Limitions of the SOM
  • The neighborhood relations between neurons have
    to be defined in advance.
  • The dynamics of the SOM algorithm cannot be
    described as a stochastic gradient on any energy
    function.

4
Objective
  • To incorporate the structure of the
    cerebellar-model-articulation-controller (CMAC)
    network into the SOM to construct a
    self-organizing CMAC (SOCMAC) network.

5
Methods
  • CMAC
  • SOCMAC
  • Performance Index(PI)

6
CMAC Model
  • Properties
  • Using a supervised learning method
  • The information of the state is distributively
    stored in Ne memory elements
  • Fast learning speed(by table-lookup)
  • Good generalization ability

7
CMAC Example
block
hypercube
8
CMAC Concept
  • The stored data yk for the state sk
  • The updating rule

Memory content
index
Desired value of the state
Memory elements
Learning error
9
Gray Relational Analysis
  • It can be viewed as a similarity measure for
    finite sequences.
  • The fray relational coefficient between x and wi
    at the jth element as
  • the reference vector x (x1,x2,,xn)
  • The comparative vector wi (wi1,wi2,,win)
  • ?ij xj-wij, ?maxmaximaxj?ij,
    ?minminiminj?ij, 0lt?lt1
  • Gray relational grade
  • The weighting factor a 0
  • 0g1

Control factor
10
SOCMAC
  • Viewing as the SOM
  • The input space of the CMAC can be viewed as a
    topological structure similar to the output layer
    of the SOM.
  • The output vector of that state is as the
    corresponding connection weight of the SOM.
  • The output of the state
  • The ck,h of the state those addressed are 1, and
    the other are 0.
  • The winner state selected

11
SOCMAC (con.)
  • The updating rule for the corresponding memory
    contents of the winning state is
  • Gray credit assignment
  • The original function cannot determine which
    memory content is more responsible for the
    current error.

Learning error
12
SOCMAC Procedure
  1. Initialize the memory contents and necessary
    parameters.
  2. Present an input training vector x(t) to the
    SOCMAC.
  3. Calculate all state outputs by using (8).
  4. Determine the winning state by using (10).
  5. Update the memory contents by using (12).
  6. If every value of the input training data is
    presented to the SOCMAC, then go to step 7
    otherwise, go to step 2.
  7. Reduce the learning rate by a small and fixed
    amount.
  8. Go to step 2 if the selected termination
    criterion is not satisfied.

13
Memory Size
  • There are mxmy states in the input space of the
    SOCMAC.
  • The entire memory size Nh is therefore smaller
    than mx my, i.e., Nh lt mx my.
  • Ne represents the generalization parameter
  • (number of layers) and Ne 2.

Example Nh Ne Nb2 3 32 27.
14
Neighborhood Region
  • the neighborhood function, denoted by O(k, k),
    of the winning state is defined by

15
Simulations
  • To solve clustering problems for two artificial
    datasets and classification problems for five
    University of California at Irvine (UCI)
    benchmark datasets.
  • A performance index(PI)

Center of the dth cluster
Overall patterns
16
Experiment 1
21 artificial data
17
Experiment 1 - Result
18
Experiment 2
150 artificial data
19
Experiment 2 - Result
20
Experiment 3 - Result
21
Conclusions
  • The new scheme simultaneously has the features of
    both the SOM and the CMAC.
  • The neighborhood region need not be defined in
    advance.
  • It distributes the learning error into the
    addressed hypercubes.
  • The convergence of the learning process has been
    proved.
  • Simulation results showed the effectiveness and
    feasibility of the proposed network.

22
Comments
  • Advantage
  • Drawback
  • ...
  • Application
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