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Neural Network Applications Using an Improved

Performance Training Algorithm

- Annamária R. Várkonyi-Kóczy 1, 2,
- Balázs Tusor 2
- 1 Institute of Mechatronics and Vehicle

Engineering, Óbuda University - 2 Integrated Intelligent Space Japanese-Hungarian

Laboratory - e-mail varkonyi-koczy_at_uni-obuda.hu

Outline

- Introduction, Motivation for using SC Techniques
- Neural Networks, Fuzzy Neural Networks, Circular

Fuzzy Neural Networks - The place and success of NNs
- A new training and clustering algorithms
- Classification examples
- A real-world application fuzzy hand posture and

gesture detection system - Inputs of the system
- Fuzzy hand posture models
- The NN based hand posture identification system
- Results
- Conclusions

Motivation for using SC Techniques We need

something non-classical Problems

- Nonlinearity, never unseen spatial and temporal

complexity of systems and tasks - Imprecise, uncertain, insufficient, ambiguous,

contradictory information, lack of knowledge - Finite resources ? Strict time requirements

(real-time processing) - Need for optimization
- Need for users comfort
- New challenges/more complex tasks to be solved ?

more sophisticated solutions needed

Motivation for using SC Techniques We need

something non-classical Intentions

- We would like to build MACHINES to be able to do

the same as humans do (e.g. autonomous cars

driving in heavy traffic). - We always would like to find an algorithm leading

to an OPTIMUM solution (even when facing too

much uncertainty and lack of knowledge) - We would like to ensure MAXIMUM performance

(usually impossible from every points of view,

i.e. some kind of trade-off e.g. between

performance and costs) - We prefer environmental COMFORT (user friendly

machines)

Need for optimization

- Traditionally
- optimization precision
- New definition (L.A. Zadeh)
- optimization cost optimization
- But what is cost!?
- precision and certainty also carry a cost

Users comfort

Human language Modularity, simplicity,

hierarchical structures Aims of the processing

preprocessing

processing

improving the performance of the

algorithms giving more support to the processing

(new)

aims of preprocessing

image processing / computer vision

noise smoothing feature extraction (edge, corner

detection) pattern recognition, etc. 3D

modeling, medical diagnostics, etc. automatic 3D

modeling, automatic ...

preprocessing

processing

Motivation for using SC Techniques We need

something non-classical Elements of the

Solution

- Low complexity, approximate modeling
- Application of adaptive and robust techniques
- Definition and application of the proper cost

function including the hierarchy and measure of

importance of the elements - Trade-off between accuracy (granularity) and

complexity (computational time and resource need) - Giving support for the further processing
- These do not cope with traditional and AI

methods, only with Soft Computing Techniques and

Computational Intelligence

What is Computational Intelligence?

- Computer Intelligence

Increased computer facilities

Added by the new methods

L.A. Zadeh, Fuzzy Sets 1965 In traditional

hard computing, the prime desiderata are

precision, certainty, and rigor. By contrast, the

point of departure of soft computing is the

thesis that precision and certainty carry a cost

and that computation, reasoning, and decision

making should exploit whenever possible the

tolerance for imprecision and uncertainty.

What is Computational Intelligence?

- CI can be viewed as a consortium of methodologies

which play important role in conception, design,

and utilization of information/intelligent

systems. - The principal members of the consortium are

fuzzy logic (FL), neuro computing (NC),

evolutionary computing (EC), anytime computing

(AC), probabilistic computing (PC), chaotic

computing (CC), and (parts of) machine learning

(ML). - The methodologies are complementary and

synergistic, rather than competitive. - What is common Exploit the tolerance for

imprecision, uncertainty, and partial truth to

achieve tractability, robustness, low solution

cost and better rapport with reality.

Soft Computing Methods (Computational

Intelligence) fulfill all of the five

requirements(Low complexity, approximate

modelingapplication of adaptive and robust

techniquesDefinition and application of the

proper cost function including the hierarchy and

measure of importance of the elementsTrade-off

between accuracy (granularity) and complexity

(computational time and resource need)Giving

support for the further processing)

Methods of Computational Intelligence

- fuzzy logic low complexity, easy build in of the

a priori knowledge into computers, tolerance for

imprecision, interpretability - neuro computing - learning ability
- evolutionary computing optimization, optimum

learning - anytime computing robustness, flexibility,

adaptivity, coping with the temporal

circumstances - probabilistic reasoning uncertainty, logic
- chaotic computing open mind
- machine learning - intelligence

Neural Networks

- It mimics the human brain
- (McCullogh Pitts, 1943, Hebb, 1949)
- Rosenblatt, 1958 (Perceptrone)
- Widrow-Hoff, 1960 (Adaline)

Neural Networks

- Neural Nets are parallel, distributed information

processing tools which are - Highly connected systems composed of identical or

similar operational units evaluating local

processing (processing element, neuron) usually

in a well-ordered topology - Possessing some kind of learning algorithm which

usually means learning by patterns and also

determines the mode of the information processing - They also possess an information recall algorithm

making possible the usage of the previously

learned information

Application areas where NNs are successfully used

- One and multi-dimensional signal processing

(image processing, speech processing, etc.) - System identification and control
- Robotics
- Medical diagnostics
- Economical features estimation
- Associative memory content addressable memory

Application area where NNs are successfully used

- Classification system (e.g. Pattern recognition,

character recognition) - Optimization system (the usually feedback NN

approximates the cost function) (e.g. radio

frequency distribution, A/D converter, traveling

salesman problem) - Approximation system (any input-output mapping)
- Nonlinear dynamic system model (e.g. Solution of

partial differential equation systems,

prediction, rule learning)

Main features

- Complex, non-linear input-output mapping
- Adaptivity, learning ability
- distributed architecture
- fault tolerant property
- possibility of parallel analog or digital VLSI

implementations - Analogy with neurobiology

Classical neural nets

- Static nets (without memory, feedforward

networks) - One layer
- Multi layer
- MLP (Multi Layer Perceptron)
- RBF (Radial Basis Function)
- CMAC (Cerebellar Model Articulation Controller)
- Dynamic nets (with memory or feedback recall

networks) - Feedforward (with memory elements)
- Feedback
- Local feedback
- Global feedback

Feedforward architectures

One layer architectures Rosenblatt perceptron

Feedforward architectures

One layer architectures

Input

Output

Tunable parameters (weighting factors)

Feedforward architectures

Multilayer network (static MLP net)

Approximation property

- universal approximation property for some kinds

of NNs - Kolmogorov Any continuous real valued N

variable function defined over the 0,1N compact

interval can be represented with the help of

appropriately chosen 1 variable functions and sum

operation.

Learning

- Learning structure parameter estimation
- supervised learning
- unsupervised learning
- analytic learning
- Convergence??
- Complexity??

Supervised learning

estimation of the model parameters by x, y, d

n (noise)

x

d

Input

CC(e)

y

Parameter tuning

Supervised learning

- Criteria function
- Quadratic
- ...

- Minimization of the criteria
- Analytic solution (only if it is very simple)
- Iterative techniques
- Gradient methods
- Searching methods
- Exhaustive
- Random
- Genetic search

Parameter correction

- Perceptron
- Gradient methods
- LMS (least means square algorithm)
- ...

Fuzzy Neural Networks

- Fuzzy Neural Networks (FNNs)
- based on the concept of NNs
- numerical inputs
- weights, biases, outputs fuzzy numbers

Circular Fuzzy Neural Networks (CFNNs)

- based on the concept of FNNs
- topology realigned to a circular shape
- connection between the hidden and input layers

trimmed - the trimming done depends on the input data
- e.g., for 3D coordinates, each coordinate can be

connectedto only 3 neighboring hidden layer

neurons - dramatic decrease in the required
- training time

Classification

- Classification the most important unsupervised

learning problem it deals with finding a

structure in a collection of unlabeled data - Clustering assigning a set of objects into

groups whose members are similar in some way and

are dissimilar to the objects belonging to

other groups (clusters) - (usually iterative) multi-objective optimization

problem - Clustering is a main task of explorative data

mining, statistical data analysis used in machine

learning, pattern recognition, image analysis,

information retrieval, bioinformatics, etc. - Difficult problem multi-dimensional spaces,

time/data complexity, finding an adequate

distance measure, non-unambiguous interpretation

of the results, overlapping of the clusters, etc.

The Training and Clustering Algorithms

- Goal
- To further increase the speed of the training of

the ANNs used for classification - Idea
- During the learning phase, instead of directly

using the training data the data should be

clustered and the ANNs should be trained by using

the centers of the obtained clusters

- u input
- u centers of the appointed clusters
- y output of the model
- d desired output
- c value determinedby the criteria function

The Algorithm of the Clustering Step (modified

K-means alg.)

The ANNs

- Feedforward MLP, BP algorithm
- Number of neurons 2-10-2
- learning rate 0.8
- momentum factor 0.1
- Teaching set 500 samples, randomly chosen from

the clusters - Test set 1000 samples, separately generated

Examples Problem 1

- Easily solvable problem
- 4 classes, no overlapping

The Resulting Clusters and Required Training Time

in the First Experiment with Clustering Distances

A 0.05, B 0.1, and C 0.25

Clustering distance Clustering distance Time Spent on Training (minsec) Quantity of Appointed Clusters Quantity of Appointed Clusters Quantity of Appointed Clusters Quantity of Appointed Clusters S

Unclustered Unclustered 207 (100) 113 127 127 133 500

Clustered A1 200 (94,5) 30 30 8 14 82

Clustered B1 153 (89) 11 13 3 4 31

Clustered C1 053 (41,7) 3 2 1 1 7

- (First experiment)

Comparison between the Results of the Training

using the Clustered and the Cropped Datasets of

the 1st Experiment

Clustering distance Clustering distance Accuracy of the Training Accuracy of the Training Decrease in quality Decrease in Required Time

Clustered A1 1000/1000 100 no decrease 5.5

Clustered B1 1000/1000 100 no decrease 11

Clustered C1 1000/1000 100 no decrease 58.3

Cropped A1 1000/1000 100 no decrease 18

Cropped B1 1000/1000 100 no decrease 62.99

Cropped C1 965/1000 96.5 3.5 decrease 63.78

Examples Problem 2

- Moderately hard problem
- 4 classes, slight overlapping

The Resulting Clusters and Required Training Time

in the Second Experiment with Clustering

Distances A 0.05, B 0.1, and C 0.25

Clustering distance Clustering distance Time Spent on Training (hourminsec) Quantity of Appointed Clusters Quantity of Appointed Clusters Quantity of Appointed Clusters Quantity of Appointed Clusters S

Unclustered Unclustered 33802 (100) 127 125 137 111 500

Clustered A2 04451 (20,57) 28 31 14 2 78

Clustered B2 01135 (5,31) 11 10 5 2 28

Clustered C2 00300 (1,38) 2 3 1 1 7

Comparison between the Results of the Training

using the Clustered and Cropped Datasets of the

2nd Experiment

Clustering distance Clustering distance Accuracy of the Training Accuracy of the Training Decrease in Accuracy Decrease in Required Time

Clustered A2 997/1000 99.7 0.3 79.43

Clustered B2 883/1000 88.3 11.7 94.69

Clustered C2 856/1000 85.6 14.4 98.62

Cropped A2 834/1000 83.4 16.6 96.32

Cropped B2 869/1000 86.9 13.1 96.49

Cropped C2 834/1000 83.4 16.6 96.68

Comparison of the Accuracy and Training Time

Results of the Clustered and Cropped Cases of the

2nd Experiment

Group Decrease in Accuracy Decrease in Accuracy Decrease in Required Time Decrease in Required Time

Group Clustered Cropped Clustered Cropped

A2 A2 0.3 16.6 79.43 96.32

B2 B2 11.7 13.1 94.69 96.49

C2 C2 14.4 16.6 98.62 96.68

Examples Problem 3

- Hard problem
- 4 classes, significant overlapping

The Resulting Clusters and Required Training Time

in the Third Experiment with Clustering Distances

A 0.05, B 0.1, and C 0.2

Clustering distance Clustering distance Time Spent on Training (minsec) Quantity of Appointed Clusters Quantity of Appointed Clusters Quantity of Appointed Clusters Quantity of Appointed Clusters S

Unclustered Unclustered N/A 127 125 137 111 500

Clustered 0.05 5229 28 30 33 6 97

Clustered 0.1 2413 12 10 12 3 37

Clustered 0.2 735 3 4 4 1 12

Comparison between the Results of the Training

using the Clustered and Cropped Datasets of the

3rd Experiment

Clustering distance Clustering distance Accuracy of the Training Accuracy of the Training Decrease in quality

Clustered A3 956/1000 95.6 4.4

Clustered B3 858/1000 85.8 14.2

Clustered C3 870/1000 87 13

Cropped A3 909/1000 90.9 9.1

Cropped B3 864/1000 86.4 13.6

Cropped C3 773/1000 77.3 22.7

Comparison of the Accuracy Results of the

Clustered and Cropped Cases of the 3rd Experiment

Group Decrease in quality Decrease in quality

Group Clustered Cropped

A3 A3 4.4 9.1

B3 B3 14.2 13.6

C3 C3 13 22.7

Examples Problem 4

- easy problem
- 4 classes, no overlapping

d 0.2 0.1

0.05

The original dataset

The trained networks classifying ability

Clustering Distance Clustering Distance Accuracy on the test set Number of samples Required time for training Relative speed increase

Original Original 100 500 2 minutes 38 seconds -

Clustered 0.2 89.8 7 6 seconds 96

Clustered 0.1 95.6 21 22 seconds 86

Clustered 0.05 99.7 75 44 seconds 72

Cropped 0.2 96.8 7 5 seconds 96.8

Cropped 0.1 97.1 21 11 seconds 93

Cropped 0.05 98.7 75 23 seconds 85

Clustering Distance Clustering Distance Accuracy of the training on the original training set Accuracy in percentage Accuracy of the training on the test set Accuracy in percentage

Clustered 0.2 450/500 90 898/1000 89.8

Clustered 0.1 481/500 96.2 956/1000 95.6

Clustered 0.05 499/500 99.8 997/1000 99.7

Cropped 0.2 447/500 89.4 898/1000 89.8

Cropped 0.1 488/500 97.6 971/1000 97.1

Cropped 0.05 498/500 99.6 987/1000 98.7

Accuracy/training time

Clustering Distance Clustered Cropped Clustered to cropped relation

0.2 89.8 89.8 equals

0.1 95.6 97.1 1.5 better

0.05 99.7 98.7 1 better

Clustering Distance Clustered Cropped Clustered to cropped relation

0.2 6 seconds 5 seconds 16.6 slower

0.1 22 seconds 11 seconds 50 slower

0.05 44 seconds 23 seconds 47.7 slower

Examples Problem 5

- Moderately complex problem
- 3 classes, with some overlapping
- The network could not learn the original training

data with the same options

d 0.2 0.1

0.05

The original dataset

Clustering Distance Clustering Distance Accuracy on the original training set Number of clusters Required time for training

Clustered 0.2 80.6 16 35 seconds

Clustered 0.1 91 44 1 minute 47 seconds

Clustered 0.05 95.2 134 17 minutes 37 seconds

Cropped 0.2 80.2 16 32 seconds

Cropped 0.1 93.4 44 1 minute 20 seconds

Cropped 0.05 91.4 134 1 hour 50 minutes 9 seconds

Clustering Distance Clustering Distance Accuracy of the training on the original training set Accuracy in percentage Accuracy of the training on the test set Accuracy in percentage

Clustered 0.2 403/500 80.6 888/1000 88.8

Clustered 0.1 455/500 91 977/1000 97.7

Clustered 0.05 476/500 95.2 971/1000 97.1

Cropped 0.2 401/500 80.2 884/1000 88.4

Cropped 0.1 467/500 93.4 974/1000 97.4

Cropped 0.05 457/500 91.4 908/1000 90.8

Clustering Distance Clustered Cropped Clustered to cropped relation

0.2 35 seconds 32 seconds 8.6 slower

0.1 1 minute 47 seconds 1 minute 20 seconds 25 slower

0.05 17 minutes 37 seconds 1 hour 50 minutes 9 seconds 625 faster

A Real-World Application Man-machine cooperation

in ISpace

- Man-machine cooperation in ISpace using visual

(hand posture and gesture based) communication - Stereo-camera system
- Recognition of hand gestures/ hand tracking and

classification of hand movements - 3D computation of feature points /3D model

building - Hand model identification
- Interpretation and execution of instructions

The Inputs The 3D coordinate model of the

detected hand

- The method uses two cameras
- From two different viewpoint
- The method works in the following way
- It locates the areas in the pictures of the two

cameras where visible human skin can be detected

using histogram back projection - Then it extracts the feature points in the back

projected picture considering curvature extrema - peaks and
- valleys
- Finally, the selected feature points are matched

in a stereo image pair.

The results The 3D coordinate model of the hand,

15 spatial points

Fuzzy Hand Posture Models

- describing the human hand by fuzzy hand feature

sets - theoretically 314 different hand postures

- 1st set four fuzzy features describing the

distance between the fingertips of - each adjacent finger (How far are finger X

and finger Y from each other?) - 2nd set five fuzzy features describing the

bentness of each finger - (How big is the angle between the lowest joint

of finger W and the plane of the palm?) - 3rd set five fuzzy features describing the

relative angle between the bottom finger - joint and the plane of the palm of the given

hand (How bent is finger Z?)

Fuzzy Hand Posture Models

Example Victory

Feature group Feature Value

Relative distance between adjacent fingers a Large

Relative distance between adjacent fingers b Medium

Relative distance between adjacent fingers c Small

Relative distance between adjacent fingers d Small

Relative angle between the lowest joint of each finger and the plane of the palm A Medium

Relative angle between the lowest joint of each finger and the plane of the palm B Small

Relative angle between the lowest joint of each finger and the plane of the palm C Small

Relative angle between the lowest joint of each finger and the plane of the palm D Large

Relative angle between the lowest joint of each finger and the plane of the palm E Large

Relative bentness of each finger A Medium

Relative bentness of each finger B Large

Relative bentness of each finger C Large

Relative bentness of each finger D Small

Relative bentness of each finger E Small

Fuzzy Hand Posture and Gesture Identification

System

- ModelBase
- GestureBase
- Target Generator
- Circular Fuzzy Neural Networks (CFNNs)
- Fuzzy Inference Machine (FIM)
- Gesture Detector

Fuzzy Hand Posture and Gesture Identification

System

- ModelBase

Stores the features of the models as linguistic

variables

- GestureBase

Contains the predefined hand gestures as

sequences of FHPMs

Fuzzy Hand Posture and Gesture Identification

System

- Target Generator

Input parameters

Calculates the target parameters for the CFNNs

and the FIM.

d - identification value (ID) of the model in

the ModelBase. SL - linguistic variable for

setting the width of the triangular fuzzy sets

Fuzzy Hand Posture and Gesture Identification

System

- Fuzzy Inference Machine (FIM)
- Max (Min(ßi)) ßi - intersection

of the fuzzy feature sets - Gesture Detector

Identifies the detected FHPMs by using fuzzy

min-max algorithm

Searches predefined hand gesture patterns in the

sequence of detected hand postures

Circular Fuzzy Neural Networks (CFNNs)

- 3 different NNs for the 3 feature groups
- 15 hidden layer neurons
- 4/5 output layer neurons
- 45 inputs ( 15 coordinate triplets)
- but only 9 inputs connected to each
- hidden neuron

Convert the coordinate model to a FHPM

The Experiments

- Six hand models
- Separate training and testing sets
- Training parameters
- Learning rate 0.8
- Coefficient of the momentum method 0.5
- Error threshold 0.1
- SL small
- 3 experiments
- First and second experiments compare the speed of

the training using the clustered and the original

unclustered data and the accuracy of the trained

system - for given clustering distance (0.5)
- Third experiment compares the necessary training

time and the accuracy of the trained system for

different clustering distances

- The first two experiments have been conducted on

an average PC (Intel Pentium 4 CPU 3.00 GHz, 1

GB RAM, Windows XPSP3 operating system), while

the third experiment has been conducted on

another PC (Intel CoreTM 2 Duo CPU T5670 1.80

GHz, 2 GB RAM, Windows 7 32-bit operating

system).

Experimental Results The Result in Required

Training Time

Network type Time Required for Error Threshold Intervals Time Required for Error Threshold Intervals Time Required for Error Threshold Intervals Time Required for Error Threshold Intervals

Network type 0.5-0.25 0.25-0.2 0.2-0.15 0.15-0.12

Unclustered A 28 mins 39 minutes 1 hour17 minutes 2 hour 24 minutes

Unclustered B 50 mins 2 hours 14 minutes 2 hours 14 minutes 2 hour 28 minutes

Unclustered C 53 mins 52 minutes 52 minutes 2 hour 40 minutes

Clustered A 16 minutes (42.86) 25 minutes (35.9) 1 hour 14 minutes (3.9) 1 hour 18 minutes (45.8)

Clustered B 32 minutes (36) 1 hour 3 minutes (52.9) 1 hour 3 minutes (52.9) 1 hour 1 minutes (58.8)

Clustered C 31 minutes (41.5) 46 minutes (11.5) 46 minutes (11.5) 58 minutes (63.75)

- (First experiment)

Experimental Results Another Training Session

with only One Session

Network type Error Threshold Intervals Speed Increase

Network type 0.5-0.12 Speed Increase

Unclustered A 4 hours and 27 minutes 51.6

Clustered A 2 hours and 9 minutes 51.6

Unclustered B 3 hours and 8 minutes 27.1

Clustered B 2 hour and 22 minutes 27.1

Unclustered C 4 hours and 5 minutes 18

Clustered C 3 hours and 21 minutes 18

- (Second experiment)

Experimental Results Comparative Analysis of the

Result of the Trainings of the Two Sessions

Measured attribute Input data for the training Input data for the training Difference in ratio

Measured attribute Unclustered Clustered Difference in ratio

First Experiment Total time spent on Training 14 hours and 38 minutes 8 hours and 8 minutes 44.4 decrease

First Experiment Classification accuracy 98.125 95.2 2.9 decrease

Second Experiment Total time spent on training 11 hours and 41 minutes 7 hour and 52 minutes 32.5 decrease

Second Experiment Classification accuracy 98.125 95.83 2.3 decrease

Experimental Results The quantity of Clusters

Resulting from Multiple Clustering Steps for

Different Clustering Distances

Clustering distance Number of clusters for each hand type Number of clusters for each hand type Number of clusters for each hand type Number of clusters for each hand type Number of clusters for each hand type Number of clusters for each hand type Number of clusters for each hand type

Clustering distance Open hand Fist Three Point Thumb-up Victory S

Unclustered 20 20 20 20 20 20 120

d 0.5 10 13 4 7 4 5 42

d 0.4 13 16 5 9 5 8 55

d 0.35 13 17 5 12 10 8 65

- (Third experiment)

Experimental Results Comparative Analysis about

the Characteristics of the Differently Clustered

Data Sets

Measured attribute Measured value Difference in ratio

Unclustered Total time spent on training 6 hours and 30 minutes -

Unclustered Average classification accuracy 97 -

d 0.5 Total time spent on training 3 hour and 57 minutes 39 decrease

d 0.5 Average classification accuracy 95.2 1.8 decrease

d 0.4 Total time spent on training 4 hour and 22 minutes 32.8 decrease

d 0.4 Average classification accuracy 97 0 decrease

d 0.35 Total time spent on training 5 hour and 46 minutes 11.1 decrease

d 0.35 Average classification accuracy 97 0 decrease

- (Third experiment)

Experimental Results Clustered Data Sets

Hand posture type Clustering distance Clustering distance Clustering distance Clustering distance

Hand posture type UC 0.5 0.4 0.35

Open hand 77/80 76/80 76/80 76/80

Fist 72/80 77/80 76/80 76/80

Three 78/80 74/80 79/80 80/80

Point 80/80 77/80 78/80 79/80

Thumb-up 80/80 78/80 80/80 78/80

Victory 79/80 75/80 77/80 77/80

Average (in ratio) 97 95.2 97 97

Number of correctly classified samples / number

of all samples

- (Third experiment)

References to the examples

- Tusor, B. and A.R. Várkonyi-Kóczy, Reduced

Complexity Training Algorithm of Circular Fuzzy

Neural Networks, Journal of Advanced Research in

Physics, 2012. - Tusor, B., A.R. Várkonyi-Kóczy, I.J. Rudas, G.

Klie, G. Kocsis, An Input Data Set Compression

Method for Improving the Training Ability of

Neural Networks, In CD-ROM Proc. of the 2012

IEEE Int. Instrumentation and Measurement

Technology Conference, I2MTC2012, Graz, Austria,

May 13-16, 2012, pp. 1775-1783. - Tóth, A.A., Várkonyi-Kóczy, A.R., A New Man-

Machine Interface for ISpace Applications,

Journal of Automation, Mobile Robotics

Intelligent Systems, Vol. 3, No. 4, pp. 187-190,

2009. - Várkonyi-Kóczy, A.R., B. Tusor, Human-Computer

Interaction for Smart Environment Applications

Using Fuzzy Hand Posture and Gesture Models,

IEEE Trans. on Instrumentation and Measurement,

Vol. 60, No 5, pp. 1505-1514, May 2011.

Conclusions

- SC and NN based methods can offer solution for

many unsolvable cases however with a burden of

convergence and complexity problems - New training and clustering procedures which can

advantageously be used in the supervised training

of neural networks used for classification - Idea reduce the quantity of the training sample

set in a way that does little (or no) impact on

its training ability - Clustering based on the k-means method with the

main difference in the assignment step, where the

samples are assigned to the first cluster that is

near enough. - As a result, for classification problems, the

complexity of the training algorithm (and thus

the training time) of neural networks can

significantly be reduced - Open questions
- dependency of the decrease of classification

accuracy and training time of different types of

ANNs - optimal clustering distance
- generalization of the method towards other types

of NNs, problems, etc.