This document discusses self-organizing neural networks, including Kohonen networks and Adaptive Resonance Theory (ART). Kohonen networks use competitive learning to form topological mappings between input and output layers. Neighboring units respond to similar inputs, and learning updates weights of both the winning unit and its neighbors. ART networks learn stable recognition codes in response to input sequences and address the stability-plasticity dilemma by resetting matches that fail a vigilance test.
Tensor representations in signal processing and machine learning (tutorial ta...Tatsuya Yokota
Tutorial talk in APSIPA-ASC 2020.
Title: Tensor representations in signal processing and machine learning.
Introduction to tensor decomposition (テンソル分解入門)
Basics of tensor decomposition (テンソル分解の基礎)
An image can be seen as a matrix I, where I(x, y) is the brightness of the pixel located at coordinates (x, y). In the Convolutional neural network, the kernel is nothing but a filter
that is used to extract the features from the images.
Tensor representations in signal processing and machine learning (tutorial ta...Tatsuya Yokota
Tutorial talk in APSIPA-ASC 2020.
Title: Tensor representations in signal processing and machine learning.
Introduction to tensor decomposition (テンソル分解入門)
Basics of tensor decomposition (テンソル分解の基礎)
An image can be seen as a matrix I, where I(x, y) is the brightness of the pixel located at coordinates (x, y). In the Convolutional neural network, the kernel is nothing but a filter
that is used to extract the features from the images.
On Approach to Increase Integration Rate of Elements of a Current Source CircuitBRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a current source circuit.
Framework the approach, we consider a heterostructure with special configuration. Several specific
areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/
or radiation defects should be optimized.
BINARY TREE SORT IS MORE ROBUST THAN QUICK SORT IN AVERAGE CASEIJCSEA Journal
Average case complexity, in order to be a useful and reliable measure, has to be robust. The probability distribution, generally uniform, over which expectation is taken should be realistic over the problem domain. But algorithm books do not certify that the uniform inputs are always realistic. Do the results hold even for non uniform inputs? In this context we observe that Binary Tree sort is more robust than the fastand popular Quick sort in the average case.
constant strain triangular which is used in analysis of triangular in finite element method with the help of shape function and natural coordinate system.
AN APPROACH TO OPTIMIZE MANUFACTURE OF AN ACTIVE QUADRATURE SIGNAL GENERATOR ...antjjournal
In this paper we introduce an approach to increase density of field-effect transistors framework an active
quadrature signal generator. Framework the approach we consider manufacturing the generator in heterostructure
with specific configuration. Several required areas of the heterostructure should be doped by diffusion
or ion implantation. After that dopant and radiation defects should by annealed framework optimized
scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered
heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures
during manufacturing of integrated circuits with account mismatch-induced stress.
https://arxiv.org/abs/2011.04370
A concept of quantum computing is proposed which naturally incorporates an additional kind of uncertainty, i.e. vagueness (fuzziness), by introducing obscure qudits (qubits), which are simultaneously characterized by a quantum probability and a membership function. Along with the quantum amplitude, a membership amplitude for states is introduced. The Born rule is used for the quantum probability only, while the membership function can be computed through the membership amplitudes according to a chosen model. Two different versions are given here: the "product" obscure qubit in which the resulting amplitude is a product of the quantum amplitude and the membership amplitude, and the "Kronecker" obscure qubit, where quantum and vagueness computations can be performed independently (i.e. quantum computation alongside truth). The measurement and entanglement of obscure qubits are briefly described.
Exploring temporal graph data with Python: a study on tensor decomposition o...André Panisson
Tensor decompositions have gained a steadily increasing popularity in data mining applications. Data sources from sensor networks and Internet-of-Things applications promise a wealth of interaction data that can be naturally represented as multidimensional structures such as tensors. For example, time-varying social networks collected from wearable proximity sensors can be represented as 3-way tensors. By representing this data as tensors, we can use tensor decomposition to extract community structures with their structural and temporal signatures.
The current standard framework for working with tensors, however, is Matlab. We will show how tensor decompositions can be carried out using Python, how to obtain latent components and how they can be interpreted, and what are some applications of this technique in the academy and industry. We will see a use case where a Python implementation of tensor decomposition is applied to a dataset that describes social interactions of people, collected using the SocioPatterns platform. This platform was deployed in different settings such as conferences, schools and hospitals, in order to support mathematical modelling and simulation of airborne infectious diseases. Tensor decomposition has been used in these scenarios to solve different types of problems: it can be used for data cleaning, where time-varying graph anomalies can be identified and removed from data; it can also be used to assess the impact of latent components in the spreading of a disease, and to devise intervention strategies that are able to reduce the number of infection cases in a school or hospital. These are just a few examples that show the potential of this technique in data mining and machine learning applications.
Illustration Clamor Echelon Evaluation via Prime Piece PsychotherapyIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
Cornell University’s Hod Lipson is seeking to understand if machines can learn analytical laws automatically. For centuries, scientists have attempted to identify and document analytical laws underlying physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. Lipson has developed machines that take in information about their environment and discover natural laws all on their own, even learning to walk.
On Approach to Increase Integration Rate of Elements of a Current Source CircuitBRNSS Publication Hub
In this paper, we introduce an approach to increase integration rate of elements of a current source circuit.
Framework the approach, we consider a heterostructure with special configuration. Several specific
areas of the heterostructure should be doped by diffusion or ion implantation. Annealing of dopant and/
or radiation defects should be optimized.
BINARY TREE SORT IS MORE ROBUST THAN QUICK SORT IN AVERAGE CASEIJCSEA Journal
Average case complexity, in order to be a useful and reliable measure, has to be robust. The probability distribution, generally uniform, over which expectation is taken should be realistic over the problem domain. But algorithm books do not certify that the uniform inputs are always realistic. Do the results hold even for non uniform inputs? In this context we observe that Binary Tree sort is more robust than the fastand popular Quick sort in the average case.
constant strain triangular which is used in analysis of triangular in finite element method with the help of shape function and natural coordinate system.
AN APPROACH TO OPTIMIZE MANUFACTURE OF AN ACTIVE QUADRATURE SIGNAL GENERATOR ...antjjournal
In this paper we introduce an approach to increase density of field-effect transistors framework an active
quadrature signal generator. Framework the approach we consider manufacturing the generator in heterostructure
with specific configuration. Several required areas of the heterostructure should be doped by diffusion
or ion implantation. After that dopant and radiation defects should by annealed framework optimized
scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered
heterostructure. We introduce an analytical approach to analyze mass and heat transport in heterostructures
during manufacturing of integrated circuits with account mismatch-induced stress.
https://arxiv.org/abs/2011.04370
A concept of quantum computing is proposed which naturally incorporates an additional kind of uncertainty, i.e. vagueness (fuzziness), by introducing obscure qudits (qubits), which are simultaneously characterized by a quantum probability and a membership function. Along with the quantum amplitude, a membership amplitude for states is introduced. The Born rule is used for the quantum probability only, while the membership function can be computed through the membership amplitudes according to a chosen model. Two different versions are given here: the "product" obscure qubit in which the resulting amplitude is a product of the quantum amplitude and the membership amplitude, and the "Kronecker" obscure qubit, where quantum and vagueness computations can be performed independently (i.e. quantum computation alongside truth). The measurement and entanglement of obscure qubits are briefly described.
Exploring temporal graph data with Python: a study on tensor decomposition o...André Panisson
Tensor decompositions have gained a steadily increasing popularity in data mining applications. Data sources from sensor networks and Internet-of-Things applications promise a wealth of interaction data that can be naturally represented as multidimensional structures such as tensors. For example, time-varying social networks collected from wearable proximity sensors can be represented as 3-way tensors. By representing this data as tensors, we can use tensor decomposition to extract community structures with their structural and temporal signatures.
The current standard framework for working with tensors, however, is Matlab. We will show how tensor decompositions can be carried out using Python, how to obtain latent components and how they can be interpreted, and what are some applications of this technique in the academy and industry. We will see a use case where a Python implementation of tensor decomposition is applied to a dataset that describes social interactions of people, collected using the SocioPatterns platform. This platform was deployed in different settings such as conferences, schools and hospitals, in order to support mathematical modelling and simulation of airborne infectious diseases. Tensor decomposition has been used in these scenarios to solve different types of problems: it can be used for data cleaning, where time-varying graph anomalies can be identified and removed from data; it can also be used to assess the impact of latent components in the spreading of a disease, and to devise intervention strategies that are able to reduce the number of infection cases in a school or hospital. These are just a few examples that show the potential of this technique in data mining and machine learning applications.
Illustration Clamor Echelon Evaluation via Prime Piece PsychotherapyIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
Cornell University’s Hod Lipson is seeking to understand if machines can learn analytical laws automatically. For centuries, scientists have attempted to identify and document analytical laws underlying physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. Lipson has developed machines that take in information about their environment and discover natural laws all on their own, even learning to walk.
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1. Self Organising Neural Networks
Kohonen Networks.
A Problem with Neural Networks.
ART.
Beal, R. and Jackson, T. (1990). Neural Computing: An Introduction.
Chapters 5 & 7. Adam Hilger, NY.
Hertz, J., Krogh, A. and Palmer, R. (1991). Introduction to the Theory
of Neural Computation. Chapter 9. Addison–Wesley. NY.
Grossberg, S. (1987). Competitive Learning: from interactive acti-
vation to adaptive resonance. Cognitive Science, 11: 23–63.
1
2. Kohonen Self Organising Networks
Kohonen, T. (1982). Self–organized formation of topologically cor-
rect feature maps., Biological Cybernetics, 43: 59–69.
An abstraction from earlier models (e.g. Malsburg,
1973).
The formation of feature maps (introducing a geo-
metric layout).
Popular and useful.
Can be traced to biologically inspired origins.
Why have topographic mappings?
– Minimal wiring
– Help subsequent processing layers.
Example: Xenopus retinotectal mapping (Price & Will-
shaw 2000, p121).
2
3. Basic Kohonen Network
Geometric arrangement of units.
Units respond to “part” of the environment.
Neighbouring units should respond to similar parts
of the environment.
Winning unit selected by:
Ü Û min Ü Û
where Û is the weight vector of winning unit, and
Ü is the input pattern.
and Neighbourhoods...
3
4. Neighbourhoods in the Kohonen Network
Example in 2D.
Neighbourhood of winning unit called Æ .
4
5. Learning in the Kohonen Network
All units in Æ are updated.
dÛ ´ µ ´ µ Û ´Øµ
« Ø Ü Ø for ¾ Æ
dØ ¼ otherwise
where
dÛ
dØ = change in weight over time.
´µ
« Ø = time dependent learning parameter.
Ü ´Øµ = input component at time Ø.
Û ´Øµ = weight from input to unit at time Ø.
¯ Geometrical effect: move weight vector closer to in-
put vector.
¯ « is strongest for winner and can decrease with dis-
tance. Also decreases over time for stability.
5
7. Biological origins of the Neighbourhoods: Mals-
burg
Excitatory connections:
Excitatory units
Inhibitory units
Inhibitory connections:
Excitatory units
Inhibitory units
Implements winner-take-all processing.
7
14. Example Application of Kohonen’s Network
The Phonetic Typewriter
MP Filter A/D
FFT
Rules
Kohonen
Network
Problem: Classification of phonemes in real time.
Pre and post processing.
Network trained on time sliced speech wave forms.
Rules needed to handle co-articulation effects.
14
15. A Problem with Neural Networks
Consider 3 network examples:
Kohonen Network.
Associative Network.
Feed Forward Back-propagation.
Under the situation:
Network learns environment (or I/O relations).
Network is stable in the environment.
Network is placed in a new environment.
What happens:
Kohonen Network won’t learn.
Associative Network OK.
Feed Forward Back-propagation Forgets.
called The Stability/Plasticity Dilemma.
15
16. Adaptive Resonance Theory
Grossberg, S. (1976a). Adaptive pattern classification and univer-
sal recoding I: Feedback, expectation, olfaction, illusions. Biological
Cybernetics, 23: 187–202.
a “neural network that self–organize[s] stable pat-
tern recognition codes in real time, in response to
arbitrary sequences of input patterns”.
ART1 (1976). Localist representation, binary patterns.
ART2 (1987). Localist representation, analog patterns.
ART3 (1990). Distributed representation, analog pat-
terns.
Desirable properties:
plastic + stable
biological mechanisms
analytical math foundation
16
17. ART1
Attentional subsystem
F2 units ( )
Orienting subsystem
+ (Ø ) +( )
-
+ F1 units (Ü ) - r
G
+ +
+
Input (Ü )
F1 F2 fully connected, excitatory ( ).
F2 F1 fully connected, excitatory (Ø ).
Pattern of activation on F1 and F2 called Short Term
Memory.
Weight representations called Long Term Memory.
Localist representations of binary input patterns.
17
18. Summary of ART 1
(Lippmann, 1987). N = number of F1 units.
Step 1: Initialization
Ø ½ ½
½·Æ
Set vigilance parameter ¼ ½
Step 2: apply new input (binary Ü )
Step 3: compute F2 activation
Æ
Ü
½
Step 4: find best matching node , where .
Step 5: vigilance test
Æ Æ
Ü Ì ¡ Ø Ü
½ ½
Ì ¡
Is
If no, go to step 6. If yes go to step 7.
Step 6: mismatch/reset: set ¼ and go to step 4.
Step 7: resonance — adapt best match
Ø Ø Ü
Ø
·
È Æ
½Ø Ü
Step 8: Re-enable all F2 units and go to step 2
18
19. ART1: Example
INPUT F2 UNITS REPRESENT:
UNIT 1 UNIT 2 UNIT 3 UNIT 4 UNIT 5
resonance
resonance
1st choice resonance
reset
2nd choice 1st choice resonance
reset reset
3rd choice 1st choice 2nd choice resonance
reset reset reset
1st choice
resonance
1st choice 2nd choice
reset resonance
1st choice 4th choice 3rd choice 2nd choice resonance
reset reset reset reset
19
20. Summary
Simple?
Interesting biological parallels.
Diverse applications.
Extensions.
20