LINEAR DISCRIMINANT ANALYSIS VERSUS ARTIFICIAL

NEURAL NETWORK AS CLASSIFIERS FOR ELBOW

ANGULAR POSITION RECOGNITION PURPOSES

Maria Claudia F. Castro

Electrical Engineering Department, Centro Universitário da FEI

Av. Humberto de A. C. Branco, 3.972, 09850-901, São Bernardo do Campo, Brazil

Keywords: Elbow angular position, Myoelectric signal, Linear discriminant analysis, Artificial neural network, Pattern

classification.

Abstract: The increasing popularity of an Artificial Neural Network for pattern recognition and the absence of

comparative studies showing its real superiority over Discriminant Analysis Methods motivated the present

study, aiming at comparing the accuracy levels achieved for a Feed-Forward Multilayer Perceptron (MLP)

and a Linear Discriminant Analysis (RLDA) applied to myoelectric signals to classify elbow angular

positions. The results showed that there were no significant differences (t-student test p<0.05) between the

average classification accuracies achieved for both methods even with the search of configuration

parameters more appropriate to each situation. Both methods achieved average classification accuracies

above 80% for a number of classes up to 4. However, 5 subjects achieved good results in a 5-class setup,

which means a 20o shift between consecutive classes. Considering that for MLP there is an effort to define

the architecture parameters and also learning parameters, its use is only justified if there is a need of

generalization that cannot be achieved by the RLDA that does not require the predefinition of parameters, it

is practical and fast, and performs very well.

1 INTRODUCTION

An Artificial Neural Network (ANN) is a system

composed of many processing elements operating in

parallel, the neurons, that are organized in

interconnected layers. This structure allows the

knowledge acquisition through a learning process that

is built based on the mathematical function that

defines each neuron and the strengths of interneuron

connections. So, the ability to learn and to generalize

to data that it has never seen before have made ANN

an attractive tool for pattern recognition (Zhang,

2000); (Basu et al., 2010).

On the other hand, according to statisticians, a

Feed-Forward Multilayer Perceptron (MLP) can be

seen as a multiple linear or nonlinear regression or

discrimination models. In those procedures, a

functional form is imposed on the data, some

assumptions about the input-output relationship are

done, and also probabilistic models are considered in

order to define classification decision boundaries.

The effectiveness of these methods depends on the

assumptions that are made, and so, on the user

knowledge of both model and data properties.

However, if this causes some difficulties, on the other

hand, it allows you to test the relationships among

process variables (Cheng and Titterington, 1994)0;

(Sarle, 1994); (Warner and Misra, 1996).

A MLP with sigmoid activation function can be

used as a universal curve-fit, but it will never reveal

the functional relations among the variables.

Furthermore, the number of hidden layers and the

number of neurons, activation function and learning

parameters, usually are defined empirically (Warner

and Misra, 1996); (Zhang, 2000).

The increasing popularity of ANN for pattern

recognition is a fact and it is not clear its superiority

when compared with Discriminant Analysis Methods

(Parker et al., 2006); (Ahsan et al., 2010); (Scheme

and Englehart, 2011); (Peederman et al., 2011). So,

the present study aims at comparing the accuracy

levels reached for a MLP and a Linear Discriminant

Analysis (LDA) applied to myoelectric signals to

classify elbow angular positions.

351

F. Castro M..

LINEAR DISCRIMINANT ANALYSIS VERSUS ARTIFICIAL NEURAL NETWORK AS CLASSIFIERS FOR ELBOW ANGULAR POSITION RECOGNI-

TION PURPOSES.

DOI: 10.5220/0003761203510355

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2012), pages 351-355

ISBN: 978-989-8425-89-8

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

2 MATERIALS AND METHODS

2.1 Data

Seven volunteers (4 men and 3 women) keeping a

low level of contraction of biceps and triceps,

developed elbow flexion and extension movements

from 0o to 90o with 3s of steady position each 10o

shift. Myoelectric signals were sampled at 1000Hz,

filtered within the range 20-500 Hz, rectified, and

smoothed with a low pass filter to obtain the

amplitude envelope (PowerLab – AdInstruments).

This protocol was approved by COEP – USJT –

No.076/2010.

For each volunteer there were at most g=18 steady

positions or classes (9 for flexion and 9 for extension)

and Ni=15 samples of d=200ms dimensional data per

class.

2.2 Linear Discriminant Analysis

The LDA achieves class separation by means of using

linear combinations of features to maximize the

between-class scatter matrix Sb and to minimize the

within-class scatter matrix Sw. According to Fisher

criterion, this can be seen as a typical problem of

eigenvectors for (Thomaz et al., 2006).

However, in practical applications, may not

exist, and in order to overcome this limitation, a

Regularized LDA (RLDA) adds a constant  to the

diagonal elements of the Sw, where 0< <1 is known

as the regularization parameter (Guo et al., 2007).

The method Leave One Out was chosen as the

classification algorithm, due to the small sample size.

This was applied for each class, in order to ensure the

same number of samples in each class. So, there is a

training matrix with N-g samples and a test matrix

with g samples, one of each class. Finally, class

assignment was done based on Euclidean distances.

2.3 Feed-forward MLP

A MLP with sigmoid, as activation function, was

used. The number of hidden layers and the number of

neurons were empirically investigated, and the results

will be discussed. Back propagation was the learning

algorithm chosen, with a learning rate of 0.3,

momentum rate of 0.9 and a maximum number of

epochs of 10000. The generalized delta rule with

gradient descent was utilized in each network’s

learning process.

Prior to the application of the MLP,

dimensionality reduction was done using Principal

Components Analysis. The number of components

defined the number of neurons in the input layer

while the number of neurons in the output layer was

coincident with the number of classes to be

recognized. The method Leave One Out was also

applied for MLP as the classification algorithm.

3 RESULTS

The 2-class setup matches the extreme positions 0o

and 90o and the 3-class setup matches 10o, 50o and

90o positions. In the 4-class setup, positions differ by

30o shift while in the 5 and in the 10 classes setup

they differ by 20o and by 10o respectively.

Table 1: Average classification accuracies.

RLDA MLP

g Phase Rate(%) Rate(%)

2 Flex. 96.19 95.24

Ext. 97.14 98.10

3 Flex. 79.36 80.63

Ext. 86.35 88.89

4 Flex. 77.14 77.14

Ext. 77.62 79.05

5 Flex. 61.71 59.05

Ext. 66.86 70.29

10 Flex. 43.90 39.14

Ext. 46.10 42.19

Table 2: Best classification accuracies for volunteers A and

RLDA MLP

g Phase Rate(%) Rate(%)



2 Flex. 100 83.33 100 76.67

Ext. 100 90.00 100 90.00

3 Flex. 100 64.44 100 68.89

Ext. 100 57.78 100 66.67

4 Flex. 88.33 53.33 90.00 51.67

Ext. 85.00 58.33 83.33 56.67

5 Flex. 89.33 41.33 85.33 49.33

Ext. 80.00 36.00 82.67 48.00

10 Flex. 66.67 22.00 61.33 21.33

Ext. 55.33 26.00 52.00 24.67

(g - number of classes, Flex. - flexion, Ext. - extension, Rate (%) -

classification rate, V

- V

– Volunteers A and B).

Average classification accuracies are presented in

Table 1, showing rates above 80% for 2 and 3 classes.

The rates achieved for both methods were almost the

same and for all configurations they were higher

during the extension phase. However, as the number

of classes increases, the effect was the decrease of

classification accuracies. This occurred even for

different regularization parameters for RLDA and

different network parameters such as the number of

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352

hidden layers and the number of neurons.

Table 2 shows individual results, corresponding to

the best and to the worst results, for each method.

Volunteer A reached high classification accuracies

until 5 classes, and the results for flexion phase were

better than those for extension phase. Other five

volunteers had classification accuracies similar to this

volunteer and only one had results similar to the

volunteer B.

4 DISCUSSION

Despite the increasing popularity of ANN in pattern

recognition applications due to the belief of better

performance and better generalization ability, the

results showed a different situation. Table 1 showed

in 50% of the cases classification accuracies of MLP

greater than those obtained with RLDA and in 40%

of the cases classification accuracies of RLDA

greater than those obtained with MLP. The other 10%

the result was the same for both methods. However,

the differences are not significant for the classes setup

(t-student test p<0.05). The fact that the classification

accuracies were the same for both methods can be

explained due to the linearity between class

boundaries as shown in a previous work (Castro,

2011) that used RLDA in order to separate up to 18

classes. What was surprising is that it was possible to

linearly separate those classes, while the results here

showed that the classifiers, based on the same feature,

did not achieve a good performance for the same

number of classes.

In Englehart et al. (1999), LDA showed in some

cases using time-frequency features better

performance than MLP, however using time domain

features MLP exhibited better performance.

According to them, the difference was due to the fact

that as the feature set dimensionality grows, the

degree of nonlinearity between class boundaries

diminishes, and so decreases the advantage that a

MLP may have over an LDA. Oskoei and Hu (2006)

found similar results investigating the discriminant

information provided for many features in time and

frequency domain, using LDA and MLP as

classifiers. Hargrove, Englehart and Hudgins (2007)

in other work comparing surface and intramuscular

myoelectric signal, the performance of the LDA was

again better than the MLP. In a more recent work

showing the state of the art, Scheme and Englehart

(2011) mentioned a comparative study aiming at

investigating the performance of various classifiers in

11-class motion setup, with nondisabled subjects and

transradial-amputation subjects, which also showed

the superiority of LDA over ANN in both cases.

These results disagree with the current assumption

that an ANN is always better than a statistical

approach.

Another observation is that the classification

accuracy decreased with the increase of the number

of classes in the same way for both methods, even

with the use of different configuration parameters

aimed to better adapt to the data. The generalization

ability of the classifier depends not only to its own

characteristics but also to the data characteristics,

number of input components and the number of

classes. Data characteristics are represented by

features extracted from the original raw data. This

study used amplitude envelope that, for a small

number of classes was adequate, however with the

increase of the number of classes this feature has not

provided sufficient discriminant information for both

classifiers. Some authors have studied the duo

feature-classifier, feature of providing discriminant

information and the classifier in recognizing this

information, showing that for each classifier there is a

feature or subset of features that is more adequate to

it and so, resulting in better classification accuracies

(Englehart et al., 1999; Oskoei and Hu, 2006;

Hargrove, Englehart and Hudgins, 2007).

Table 2 showed the classification accuracies for

two volunteers, that reached the best and the worst

scores. Other five volunteers had similar distribution

of classification rates from the Volunteer A and

another one had results close to the volunteer B. And

for all of them the performance of both methods was

the same. The poor results obtained for two

volunteers were due to electrode positioning

problems and a poor skin electrode interface. If those

data were eliminated, the average classification

accuracy would improve above 80% for at most 4-

class setup. However, there were volunteers that

reached good classification accuracies for 5-class

setup, which positions differ by 20o between

consecutive ones.

It is important to note that besides to the great

similarity between classes, which occurs mainly from

the configuration of 4 classes, the contraction level

was kept at low levels during the movements, making

them close to the normal way to perform them, and

so, making SME hardly discernible from background

activity. Itakura et al. (1996) in a similar experiment

using 4 classes of wrist angular positions classified by

a MLP achieved averages of discrimination rates

from 70.3% to 76.0% that were smaller than those

obtained here.

This configuration differs from the other works

which use very different positions in each class and to

LINEAR DISCRIMINANT ANALYSIS VERSUS ARTIFICIAL NEURAL NETWORK AS CLASSIFIERS FOR ELBOW

ANGULAR POSITION RECOGNITION PURPOSES

353

reach each one some muscle strength is applied.

Another difference is the use of amplitude envelope

instead of some other feature combination in time or

frequency domain. This may be the reasons to the

smaller classification accuracies for a number of

classes greater than 5 compared to the results

obtained from other authors, which continue with

classification rates above 90 for these class

configurations (Hargrove, Englehart and Hudgins,

2007; Ahsan, Ibrahimy and Khalifa, 2010; Basu,

Bhattacharyya and Kim, 2010; Scheme and

Englehart, 2011). However, considering the type of

movement and distinctive classes, the low level of

contraction and the use of the amplitude envelope,

which require a minimum processing effort, for a

small number of classes, the systems had performed

well.

On the other hand, the process based on RLDA

was very fast, while the process based on MLP was

time consuming as much to define adequate

parameters as for as network training. There was no

pattern for the number of hidden layers and the

number of neurons. These parameters varied for each

volunteer and for each class configuration, aimed at

obtaining the best classification accuracies. Usually, 2

or 3 hidden layers were enough, but the number of

neurons varied from 9 to 100 depending on the case.

Englehart et al. (1999) and other researchers such as

Basu, Battacharyya and Kin (2010) and Zhang (2000)

defend that MLP, as long as properly trained and with

an appropriate configuration will always match, if not

exceed, the performance of an RLDA. But usually,

due to the need to automate MLP training over a large

number of interactions, the number of hidden layers

and also the number of neurons are fixed. For a given

subject and a specific number of classes however, the

configuration may be inappropriate, and will be

inhibit the generalization performance of the MLP.

The RLDA, on the other hand does not require these

specifications, and performs very well.

5 CONCLUSIONS

This study showed the same performance for RLDA

and MLP in a problem of elbow angular position

classification, based on the SME amplitude envelope.

Both methods achieved average classification

accuracies above 80% for a number of classes until 4

but individually, 5 subjects achieved similar results in

a 5-class setup, which means a 20o shift between

consecutive classes. May be a better classification

accuracy can be reached with another feature instead

of amplitude envelope that was used. However, this

probably will also change the comparative

performance between the methods. Considering that

for MLP there is a great effort to define the

architecture and also learning parameters, its use is

only justified if there is a need of generalization that

cannot be achieved by the RLDA that does not

require the predefinition of parameters, it is practical

and fast.

ACKNOWLEDGEMENTS

The author thanks FEI and FAPESP for sponsoring.

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