This document describes self-organizing maps and adaptive resonance theory neural networks. It discusses how self-organizing maps use competitive learning and weight adjustment to have neurons represent different input classes. Adaptive resonance theory networks combine self-organizing maps with associative (outstar) networks so the input layer finds the most similar stored pattern and the output layer recalls the full pattern. The adaptive resonance algorithm compares input and output patterns using an AND operation and vigilance threshold to determine if the weight adjustments should be made or if a new neuron is needed to represent the input.
1
The Perceptron and its Learning Rule
Carlo U. Nicola, SGI FH Aargau
With extracts from publications of :
M. Minsky, MIT, Demuth, U. of Colorado,
D.J. C. MacKay, Cambridge University
WBS WS06-07 2
Perceptron
(i) Single layer ANN
(ii) It works with continuous or binary inputs
(iii) It stores pattern pairs (Ak,Ck) where: Ak = (a1
k, …, an
k)
and Ck = (c1
k, …, cn
k) are bipolar valued [-1, +1].
(iv) It applies the perceptron error-correction procedure, which
always converges.
(v) A perceptron is a classifier.
Bias b is sometimes called θ
Inroduction to Perceptron and how it is used in Machine Learning and Artificial Neural Network.
This presentation is prepared by Zaid Al-husseini, as a lectur for third stage of undergraduate students in Softwrae department - faculity of IT - University of Babylon, Iraq.
It is publicly availabe for the beginners to learn in theory and mathmatically how the Perceptron is working.
Notice: the slides are not detailed. And need a teacher to explain them deeply.
1
The Perceptron and its Learning Rule
Carlo U. Nicola, SGI FH Aargau
With extracts from publications of :
M. Minsky, MIT, Demuth, U. of Colorado,
D.J. C. MacKay, Cambridge University
WBS WS06-07 2
Perceptron
(i) Single layer ANN
(ii) It works with continuous or binary inputs
(iii) It stores pattern pairs (Ak,Ck) where: Ak = (a1
k, …, an
k)
and Ck = (c1
k, …, cn
k) are bipolar valued [-1, +1].
(iv) It applies the perceptron error-correction procedure, which
always converges.
(v) A perceptron is a classifier.
Bias b is sometimes called θ
Inroduction to Perceptron and how it is used in Machine Learning and Artificial Neural Network.
This presentation is prepared by Zaid Al-husseini, as a lectur for third stage of undergraduate students in Softwrae department - faculity of IT - University of Babylon, Iraq.
It is publicly availabe for the beginners to learn in theory and mathmatically how the Perceptron is working.
Notice: the slides are not detailed. And need a teacher to explain them deeply.
Neural network analysis can be used to predict the performance characteristics of formulations or multi-step processes -- even when there are a large number of variables with complex interactions.
The slide covers the basic concepts and designs of artificial neural networks. It explains and justifies the use of McCulloh Pitts Model, Adaline network, Perceptron algorithm, Backpropagation algorithm, Hopfield network and Kohonen network; along with its practical applications.
Deep learning is a technique that basically mimics the human brain. So, the Scientist and Researchers taught can we make machines learn in the same way so, there is where the deep learning concept came that lead to the invention called Neural Network
Deep neural networks & computational graphsRevanth Kumar
To improve the performance of a Deep Learning model. The goal is to reduce the optimization function which can be divided based on the classification and the regression problems.
Deep learning is a technique that basically mimics the human brain. So, the Scientist and Researchers taught can we make machines learn in the same way so, there is where the deep learning concept came that led to the invention called the neural network
Abstract: This PDSG workshop introduces basic concepts of the grandfather of neural networks - the Perceptron. Concepts covered are history, algorithm and limitations.
Level: Fundamental
Requirements: No prior programming or statistics knowledge required.
Contains description of CPN.
CP algorithm consists of a input, hidden and output layer.
In this case the hidden layer is called the Kohonen layer & the output layer is called the Grossberg layer.
Neural network analysis can be used to predict the performance characteristics of formulations or multi-step processes -- even when there are a large number of variables with complex interactions.
The slide covers the basic concepts and designs of artificial neural networks. It explains and justifies the use of McCulloh Pitts Model, Adaline network, Perceptron algorithm, Backpropagation algorithm, Hopfield network and Kohonen network; along with its practical applications.
Deep learning is a technique that basically mimics the human brain. So, the Scientist and Researchers taught can we make machines learn in the same way so, there is where the deep learning concept came that lead to the invention called Neural Network
Deep neural networks & computational graphsRevanth Kumar
To improve the performance of a Deep Learning model. The goal is to reduce the optimization function which can be divided based on the classification and the regression problems.
Deep learning is a technique that basically mimics the human brain. So, the Scientist and Researchers taught can we make machines learn in the same way so, there is where the deep learning concept came that led to the invention called the neural network
Abstract: This PDSG workshop introduces basic concepts of the grandfather of neural networks - the Perceptron. Concepts covered are history, algorithm and limitations.
Level: Fundamental
Requirements: No prior programming or statistics knowledge required.
Contains description of CPN.
CP algorithm consists of a input, hidden and output layer.
In this case the hidden layer is called the Kohonen layer & the output layer is called the Grossberg layer.
An artificial neuron network (neural network) is a computational model that mimics the way nerve cells work in the human brain. Artificial neural networks (ANNs) use learning algorithms that can independently make adjustments - or learn, in a sense - as they receive new input
Boundness of a neural network weights using the notion of a limit of a sequenceIJDKP
feed forward neural network with backpropagation le
arning algorithm is considered as a black box
learning classifier since there is no certain inter
pretation or anticipation of the behavior of a neur
al
network weights. The weights of a neural network ar
e considered as the learning tool of the classifier
, and
the learning task is performed by the repetition mo
dification of those weights. This modification is
performed using the delta rule which is mainly used
in the gradient descent technique. In this article
a
proof is provided that helps to understand and expl
ain the behavior of the weights in a feed forward n
eural
network with backpropagation learning algorithm. Al
so, it illustrates why a feed forward neural networ
k is
not always guaranteed to converge in a global minim
um. Moreover, the proof shows that the weights in t
he
neural network are upper bounded (i.e. they do not
approach infinity). Data Mining, Delta
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We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
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moisture, it could reduce its total cooling water intake
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Additionally, harmful acids released from the stack can be
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Condensation of vapors in flue gas is a complicated
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Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
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6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
2. 2
Self-Organizing Networks (Maps)
Properties:
The weights in the neurons should be representative
of a class of patterns. So each neuron represents a
different class.
Input patterns are presented to all of the neurons,
and each neuron produces an output. The value of
the output of each neuron is used as a measure of
the match between the input pattern and the pattern
stored in the neuron.
A competitive learning strategy which selects the
neuron with the largest response.
A method of reinforcing the largest response.
4. 4
Like other neural networks, take inputs, xj, and
produce a weighted sum called netj. This
weighted sum is the output of the neuron,
which means that there is no non-linear output
function in the neurons.
The weighted sum can be expressed in vector
form as:
where |X| means the magnitude of X. In other
words netj is the product of two vectors and
therefore can be expressed as the “length” of
one vector multiplied by the projection of the
other vector along the direction of the first
vector.
θ===∑=
cosYX]W][X[xwnet ji
n
0i
ijj
5. 5
If the two vectors X and Wj are normalized,
which means scaling them so that they each
have a length of 1, the product ends up being
equal to cos(θ), where θ is the angle between
the two vectors.
If the two vectors are identical, θ will be zero,
and cos(θ) = 1.
The further apart the two vectors become, the
greater the angle (positive or negative) and the
smaller the value of the product.
In the extreme, where the input pattern is the
inverse of the stored weight, θ is ±1800
and
cos(θ) = -1.
6. 6
If the assumption is made that patterns that are
similar will be close together in pattern space,
then normalizing the input vector means that
the output of a neuron is a measure of the
similarity of the input pattern and and its
weights.
If a network is set up initially with random
weights, when an input pattern is applied, each
of the neurons will produce an output which is
a measure of the similarity between the weights
and input pattern. The neuron with the largest
response will be the one with the weights that
are most similar to the input pattern.
7. 7
Normalizing the input vector means dividing the
magnitude of the vector which is the square
root of the sum of square of all the elements in
the vector.
Example:
Assume that a neuron has been trained with the
pattern: 011
and that the weights are normalized. The
magnitude of X is
and the weights are therefore
w1 = 0, w2 = w3 = 1/1.412 ≈ 0.7
∑=
=
n
1i
2
ixX
412.12110xX 222
n
1i
2
i ==++== ∑=
8. 8
The following table shows the value of the output of this
neuron when other input patterns are applied. It can be
seen that the output ranges from 0 to 1, and that the
more the input pattern is like the stored pattern the
higher the output score.
Input
0 0 0 0 0 0 0
0 0 1 0 0 1 0.7
0 1 0 0 1 0 0.7
0 1 1 0 0.7 0.7 1
1 0 0 1 0 0 0
1 0 1 0.7 0 0.7 0.5
1 1 0 0.7 0.7 0 0.5
1 1 1 0.6 0.6 0.6 0.8
Normalized input output
9. 9
The next step is to apply a learning rule so that
the neuron with the largest response is selected
and its weights are adjusted to increase its
response. The first part part is described as a
“winner takes all” mechanism and can be
simply stated as
yj = 1 if netj > neti for all i≠j.
yj = 0 otherwise
The learning rule for adjusting the weights is
different to the Hebbian rules that have been
described in the previous lectures.
Instead of the weights being adjusted so that
the actual output matches some desired output,
the weights are adjusted so that they become
more like the incoming patterns.
10. 10
Mathematically, the learning rule, which is
often referred to as Kohonen learning is:
∆wij = k(xi – wij)y
In the extreme case where k = 1, after
being presented with a pattern, the
weights in a particular neuron will be
adjusted so that they are identical to the
inputs, that is wij = xi. Then for that
neuron, the output is maximum for that
input pattern. Other neurons are trained
to be maximum for other input patterns.
11. 11
With k < 1 the weights change in a way that
makes them more like the input patterns
but not necessarily the identical. After
training the weights should be
representative of the distribution of the
input pattern.
The term yj is included so that, during
training, only the neuron with the largest
response will have an output of 1 after
competitive learning, while all other
outputs are set to zero. Therefore, only
this neuron will adapt its weights.
12. 12
The combination of finding the weighted
sum of normalized vectors, Kohonen
learning and competition means that the
instar network has the ability to organize
itself such that individual neurons have
weights that represent particular
patterns or classes of patterns. When a
pattern is presented at its input, a single
neuron, which has weights that are the
closest to the input pattern, produces a 1
output while all the other neurons
produce a 0. Learning in the instar is
therefore unsupervised.
13. 13
Outstar Networks:
An outstar network consists of neurons which finds the
weighted sum of inputs.
Its function is to convert the input pattern, xi, into a
recognized output pattern and is therefore supervised.
14. 14
The learning rule for the outstar network is often
referred to as Grossberg learning and can be
stated mathematically as
∆wij = k(yi – wij)xi
It is possible to combine instar and outstar
together as shown below:
15. 15
A property of this network is that if a new
pattern is presented, the stored pattern
that is most similar to it will produce the
maximum output in the first layerand
then recall the stored pattern in the
second layer. So the instar/outstar
network can generalize and recall perfect
data from imperfect data.
17. 17
This theorem works as follows:
Step1: Input pattern X directly to the instar network.
Step2: Find the neuron with the maximum response –
neuron i
Step3: Make the output of neuron i equal to 1, and all
others zero.
Step4: Feed the output of the instar to the input of the
outstar to generate an output pattern, Y.
Step5: Feed Y to create a new pattern which equals X
AND Y.
Step 6: calculate the vigilance, ρ.
Step 7: if ρ is greater than some predetermined threshold,
modify the weights of neuron i in the instar network so
that the output produced equals the new pattern X
AND Y. Go back to step 1.
Step8: If ρ is less than the threshold, supress the output of
neuron i
, and find the neuron with the next largest output value –
neuron j. Go to step 3.
18. 18
The vigilance ρ equals the number of 1s in
the pattern produced by finding X AND
Y, divided by the number of 1s in the
input pattern, X. This can be written as
where yi is the stored pattern in 0/1
notation and Λ is the AND function.
In this algorithm, the weights are
normalized as
∑
∑
=
=
∧
=ρ n
0i
i
n
0i
ii
x
yx
( )∑=
∧+−
∧
= n
1i
ii
ii
i
yx1L
)yx(L
w where weights must be greater than 1.
19. 19
A typical solution is to let L = 2 so that the
equation becomes
In the second layer, weights in each of the
neurons are adjusted so that they too
correspond to the AND of the two patterns and
therefore have values of either 0 or 1. The effect
is that the patterns ‘resonate’, producing a
stable output.
( )
( )∑=
∧+
∧
= n
1i
ii
ii
i
yx1
yx2
w
20. 20
Example:
Consider the following diagram. Assume that an input pattern
Of 0 1 0 is presented to the network. The response of the three
neurons is 0 0.7 and 0 respectively, therefore the second neuron
gives the largest response indicating that its stored pattern is
the closest to the Input pattern. The winner takes all neuron
produces a 1 at the output of neuron 2, and 0 at each of the
outputs of neuron 1 and 3. Thus the pattern 110 is produced at
21. 21
the output of the ART network.This is fed back, and the
AND of the two patterns calculated:
input pattern X 0 1 0
output pattern Y 1 1 0
XΛY 0 1 0
The number of 1s in X is 1 and the number of 1s in X ΛY
is also 1, so the vigilance of this match is 1/1 = 1.
Assume a typical value for the threshold of say 0.8,
then as vigilance is larger than this, the pattern is
accepted into the class and the new exampler pattern
stored. The weights in neuron 2 are modified so that
they now represent the AND of the two patterns after
normalization. The weights in the output layer are also
modified so that if neuron 2 produces a 1 output than
the exampler pattern will be produced at the output of
the neuron.