adaptive resonance theory report
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Adaptive Resonance TheoryMohamad Dankar
AUL
hamra
Abstract — The reason behind ART model is that the
identification of the objects and there recognition are the result
of top-down interaction when observed with bottom-up sensory
information. When compared with real object features as by the
senses , ART model says that Top-down expectations are
memory template form.
It s̀ a description of a number of neural network models in
which we use supervised and unsupervised learning methods,
and where the address problems are pattern recognition and
prediction..
I. I NTRODUCTION
Adaptive resonance theory is developed by Carpenter and
Grossberg . It`s aim is for clustering binary vectors were
different models are found ART1 and ART2. ART1 accepts
continuous-valued vectors .ART2 uses unsupervised learning
method recognition and prediction inputs are in any order
weights are considered as code vectors for the cluster pattern.
The difference between sensation and expectation should not
exceed a set of threshold called the "vigilance parameter".
If not exceeded , sensed object is considered as a member
of the expected class. As mentioned before , ART system is an
unsupervised learning model of a comparison field and a
recognition field both composed of neurons, a vigilance
parameter, and finally a reset module. The Vigilance
parameter is highly influenceable on the system .
For that , with high vigilance , highly detailed memories
will be produced. while with lower vigilance , the results will
be more general for the memories .The comparison field takes
a one-dimensional array of values input vector and transfers it
to its best match in the recognition field. Recognition field
neuron , (1) each generates a negative signal to each of the
other recognition field neurons and inhibits their output
accordingly. In this way the recognition field exhibits lateralinhibition, allowing each neuron in it to represent a category
to which input vectors are classified.
After classifiying the input vector, reset module is compared
to the strength of the recognition match to the vigilance
parameter.If vigilance threshold is met, training starts.If not,
we see if the match level does not meet the vigilance
parameter, than firing recognition neuron will be inhibited
until a new input vector is applied; the training will start only
when search procedure is done.
Talking about the seach procedure,reset function will disable
neurons recognition one by one until the vigilance parameter
is satisfied by a recognition match.
If not committed recognition neuron’s match meets the
vigilance threshold, then an uncommitted neuron is committed
and adjusted towards matching the input vector.
II. TRAINING
We have two training methods :
A. Slow
B. Fast
In the Slow learning method ,the training degree of the
recognition neuron`s weights towards input vector will be
calculated with differential equations to continuous values
and so it is dependent on the length of time where the input
vector is presented.
With fast learning, we use algebraic equations to calculate
degree of weight adjustments while using the binary
values.Though fast learning effectivness and efficiency are
for a variety of tasks,the slow learning method is more
biologically reasonable and is used with continuous-time
networks.
III. ART1
Stands for Adaptive Resonance Theory 1. An Unsupervised
Clustering of binary input vectors.It is the simplest variety of
ART networks, accepting only binary inputs. The architecture
for the ART1 consists of F1 units , F2 units and a unit for
reset that will implement user to control similarity degree
placed on the same cluster.
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FIGURE I
ART1 ARCHITECTURE
So ART1 is comprised of the following component
1. The short term memory layer: F1 .The recognition
layer: F2 .
2. F2 Contains the long term memory of the system.
3. The Vigilance Parameter : ρ. It̀ s a parameter
controlling the principles of the memory.
Larger ? means more detailed memories, smaller ?
produces more general memories.
Figure II
IV Training ART1 MODEL
Training method is consisted of 4 steps:
1. Step1
2. Step2
3. Step3
4. Step4
1 . Input sended from layer F1 to layer F2 for processing.
The first node within the F2 layer is chosen to be the closest
match for the input and than a hypothesis is formed.It
represents what the node will look after the learning, assumingupdate is for the correct node .
Figure III
Diagramatic Representation
2 . After the hypothesis has been formed, it will be sent back
to the layer F1 for matching. Let Tj(I*) represent the level of
matching between I and I* for node j (“minimum fraction of
the input that must remain in the matched pattern for
resonance to occur”) .
Then Tj(I*)= (I^I*)/I; where A^B=min(A,B)
If Tj(I*)>= Vigilance Parameter, then the hypothesis is
accepted & assigned to that node , else move to Step 3. (2)
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Figure IV
3 . If we have a rejection of the hypothesis, a command
called "RESET" will be sent back to the later F2. Here the jth
node within F2 is no longer a candidate so the process repeats
for node j+1.
Figure V
4 . If we have acceptance of the hypothesis,winning node
assigns its values to it. Else, the nodes accepted the
hypothesis,and a there will be creation of a new node withinF2. In addition, the system creates a new memory.
Figure VI
V ART2
It extends network capabilities to support continuous inputs.
It`s an Unsupervised Clustering for :
– Real-valued input vectors
– Binary input vectors that are noisy
The fast learning is done in order that Weights reach
equilibrium in each learning trial.we have some of the same
characteristics as the weight found by ART1 and the more
appropriate for data in which the primary information is
contained in the pattern of components that are ‘small’ or
‘large.
The slow learning is done when Only one weight update
iteration performed on each learning trial .We have the needfor more epochs than in the fast learning.
Finally , it`s more appropriate for data in which the relative
size of the nonzero components is important .
VI Fuzzy ART
The Learning Algorithm Of Modified Fuzzy ART (3)
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Step 1: Initialize the vigilance parameter and weight vector of
each uncommitted node j as follows:
where and are the 2N -dimensional weight vector and
vigilance parameter respectively, and N is the dimension of
input vector before transformation.
Step 2: Transform the N -dimensional input vector , whose
components are in the interval [0,1], to 2N -dimensional
vector as follow before presenting it to .
Step 3. The winning node (or category), say j, is the node with
the weight vector ( ) most similar to input in terms of the minimum difference of grayscale value between the
input and category j, that is, , in
layer where 2N is the dimension of . In case of tie, one
of them is to be selected arbitrarily.
Step 3: The selected category j is said to meet the vigilance
criterion if the following inequality stand.
Step 4: If resonance, go to Step 5; otherwise, the reset occurs
and a new category (node) is added to layer C unless there is
no new node available. In that case, the operation terminates.
Step 5: Update only the weight vectors associated with the
selected category J (either the winner or new added
category) as follows.
where is the fuzzy min operator.
Step 6: If no new input vector, terminate the process;
otherwise, get the next input vector and go back to Step 2.
The Measure Criteria
The following criteria are used in this work mean absolute
error (MAE), mean square error (MSE), single-to-noise-ratio
(SNR), bit-per-pixel (BPP, compression ratio). They are
defined as follows:
where and are the subimage in the original and
reconstructed pictures respectively, N is the dimension of the
input vector I or subimages M , and F is the total number of
subimages
where G is the maximum grayscale value of picture.
where B is the bits per pixel in the original picture and C is the
total number of categories formed during training.
VII THE CONTROL MECHANISM OF FUZZY
CONTROLLER
Fuzzy logic is a successful way of the application to automatic
control . So, we have proposed to include a fuzzy controller
into the MFART to accomplish an automatic control during
the process of compression. MFART relation and fuzzy
controller are both shown in Figure V.
Its two inputs, and , to the fuzzy controller are
shown below :
where G is the maximum grayscale value.
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Generally , the membership function of the fuzzy set A, ,
is prescribed as follows:
where X is the universal set. In this paper, seven
sets of fuzzy models are used--PB (positive big), PM (positive medium), PS (positive small), ZE (zero), NS (negative small), NM (negative medium), and NB (negative big)for those inputs andoutput of fuzzy controller. (5)
Figure VI
VIII Conclusion
We can not predict a proper vigilance value, with the help of
fuzzy controller, the ART1 network might be insensitive for
given initial vigilance values. Plus , a Modified Fuzzy ART
has advantages over the ART1 that are a minimum processing
time and a low implementation cost.
References
(1) http://en.wikipedia.org/wiki/Adaptive_reson
ance_theory#Learning_model
(2) http://www.google.com/url?
sa=t&source=web&cd=1&ved=0CBUQFjAA&url=h
ttp%3A%2F%2Fwww.cs.csi.cuny.edu%2F~natacha
%2FTeachFall_20 08%2FGradCenter
%2FStudentProjects%2FFinal
%2FPresentation.ppt&rct=j&q=This%20hypothesis
%20represents%20what%20the%20%20node
%20will
%20look&ei=rF7qTYn0OdKxhQfJkq26Bg&usg=AF
QjCNEmLjFq1qoegUfWwyhZg4B00QwzYw
(3) http://dimes.lins.fju.edu.tw/pub/iasted-
icmscpi-94c/iasted-icmscpi94c.htm