1. Comparison of Adaptive Neuro-Fuzzy and Multi-Layer Perceptron with
Levenberg-Marquardt learning algorithm for Classifying EEG Signals
Damien Quinn
Quinn-D19@Email.ulster.ac.uk
Abstract- This paper compares two
inherently different approaches to classify
electroencephalogram (EEG) data from a
brain computer interface (BCI). The first
approach is a Multi-Layer Perceptron-Feed
forward (MLP-FF) neural network with
Levenberg-Marquardt learning algorithm
and secondly, a novel hybrid approach of
an Adaptive Neuro Fuzzy Inference System
(ANFIS) is implemented. ANFIS has an
advantage over many other classification
algorithms in that it provides a set of
parameters and linguistic rules derived
from the fuzzy inference system, which can
subsequently be used for interpreting
relationships between extracted features.
The performance of both ANFIS and MLP-
FF are compared and analysed.
Keywords: Electroencephalogram (EEG),
Brain Computer Interface (BCI), Multi-
Layer Perceptron Feed Forward Neural
Network, (MLP-FF NN), Adaptive Neuro-
Fuzzy Inference System (ANFIS)
1. Introduction
Brain computer Interface (BCI) is a method
of communication based on the neural
activity generated by the brain and which is
furthermore separate from its normal output
pathway of peripheral nerves and muscles.
This technology can be utilised to allow
individuals with minor and severe
movement disabilities and deficiencies to
communicate with assistive devices using
the brain signals extracted from the
individual. In order to control BCI a subject
must produce different brain activity
patterns that will be interpreted and
identified by the system and translated into
commands. In Motor Imagery (MI) based
BCI’s the subject performs a mental
imagination of a specified task or command,
whereby the MI is translated into a control
signal, using a classification algorithm
which classifies the unique
electroencephalogram (EEG) patterns of
that subjects imagined task. Imagined tasks
could range from moving ones foot,
pointing ones finger in a stipulated direction
or moving ones arm in a dictated motion.
Furthermore it has been noted that there
exists hemispheric EEG differences
between left and right hand manipulation in
the initial preparatory stage prior to
movement [3], [13], [7] and after movement
[14]. During movement the EEG displays a
bilateral desynchronization pattern. In the
pre-movement period, mu and beta event-
related desynchronization (ERD) are of
contralateral dominance and after
movement the post-movement beta
synchronization is mainly localized contra
laterally. This knowledge can be used for a
BCI by designing an EEG pattern classifier
which analyses the current EEG pattern in
real time and produces a control signal [14].
Feature extraction is also a prime
concern that will substantially affect the
accuracy of classifying MI tasks. An
effective feature extraction method helps aid
and enhances classification performance. A
great deal of extraction methods have been
proposed. Among them, the band power,
Hjorth and AAR parameter model are
popular and commonly used [2], [8].
The vast majority of BCI research
has been directed at the creation of powerful

2. signal processing techniques to enable better
and increased reliability of the interpretation
of EEG signals into coherent control
commands [9], [10], [12], [16]. Other more
contemporary research has looked at the
deployment of neural networks and self-
organising fuzzy neural networks have also
been implemented to increase feature and
signal separability in MI BCI’s [4], [6],[5],
[11]. This paper will focus on applying two
signal processing approaches namely the
application of weighted neural networks as
well as the novel hybrid approach of
ANFIS. These aforementioned techniques
will be used on EEG patterns collected, and
used to classify appropriately. The
experimental hypothesis forming the basis
of this research is whether a hybrid
approach of ANFIS can outperform the tried
and tested approach of weighted neural
networks.
2. Methods and Materials
2.1 Data used
All data extracted were from the data-set 2b
from the BCI-IV competition [1]. The data
set was comprised of 3 bipolar EEG
channels (0.5-100Hz; notch filtered), 3 EOG
channels, 250Hz sampling rate, 2 classes
based on 9 subjects. The subjects were
right-handed, had normal or corrected-to-
normal vision and were paid for
participating in the experiments. All
volunteers were sitting in an armchair,
watching a flat screen monitor placed
approximately 1 m away at eye level. For
each subject 5 sessions are provided,
whereby the first two sessions contain
training data without feedback (screening),
and the last three sessions were recorded
with feedback. Extracted features for this
experiment include [(F1=activity),
(F2=mobility), (F3=complexity), (F4=EEG
Mu Rhythm), (F5= EEG Beta Rhythm),
(F6=Hjorth), (F7=Bandpower),
(F8=Hjorth&Bandpower)].
2.2 Experimental Paradigm
The aforementioned data set was obtained
utilising the following experimental cue-
based paradigm which consists of two
classes, namely MI of the left hand (class 1)
and MI of the right hand (class 2).
Three EEG channels (C3, Cz, and C4) were
recorded in bipolar mode with a sampling
frequency of 250 Hz and were bandpass-
filtered between 0.5 Hz and 100 Hz, and a
notch filter at 50 Hz was enabled. However,
here only two channels C3 and C4 are to be
utilized. Depicted in figure 1 illustrates the
entire process to which a subject was
exposed. Initially at 0 s there was a small
grey smiley on the centre of the screen. This
is to indicate no activity. On the onset of 2
s, a small warning noise (1 kHz, 70ms) rang
to indicate that some activity was imminent.
Next a cue was presented from 3 s to 7.5 s,
and the subject was expected to perform a
directed imagination in specific relation to
the cue. At 7.5 s the screen went blank and a
random interval of between 1 s and 2 s was
utilised in order to prevent user adaption.
Figure 1 Timing scheme of the paradigm. (a) The first
two sessions (01T, 02T) contain training data without
feedback, and (b) the last three sessions (03T, 04E, 05E)
with smiley feedback.

3. Figure 2 Electrode placement
2.3 EEG Classification: Multi-Layer -FF NN
(MLP-FF)
Initially ANN’s and more specifically MLP
were employed as a classification technique
on EEG patterns, as they provide a well-
established framework for pattern
recognition problems and furthermore
serves as a good benchmark to compare the
hybrid approach of ANFIS against. Figure 3
illustrates the general architecture in which
the ANN was composed.
Figure 3 General Architecture of MLP with hidden
layers
An MLP is composed of several layers of
neurons: an input layer, possibly one or
several hidden layers, and an output layer.
Each neuron’s input is connected with the
output of the previous layer’s neurons
whereas the neurons of the output layer
determine the class of the input feature
vector.
Neural Networks and thus MLP are
universal approximators, i.e., when
composed of enough neurons and layers,
they can approximate any continuous
function. Added to the fact that they can
classify any number of classes, this makes
ANN’s very flexible classifiers that can
adapt to a great variety of problems.
Consequently, MLP, which are the most
popular NN used in classification, have
been applied to almost all BCI problems
such as binary or multiclass synchronous or
asynchronous BCI. However, the fact that
MLP are universal approximators makes
these classifiers sensitive to overtraining,
especially with such noisy and non-
stationary data as EEG.
In this particular instance, MLP-FF
NN with two hidden layers trained by the
Levenberg-Marquardt (LM) algorithm was
used to classify different combinations of
two mental tasks represented by the
different EEG features. Originally the LM
algorithm was developed to act as an
intermediate and address the inherent
shortcomings of the more established
Gauss-Newton and Gradient Descent. LM is
relatively more robust than Gauss-Newton
and Gradient Descent, which means in most
cases it finds a solution even if it starts very
far off the final minimum.
Furthermore in this instance the
MLP-FF applies a tan sigmoid
and pure linear
activation function. Also the hidden layers
are applied values of 10-12.

4. Figure 4 Typical FeedForward network composed of
three layers
2.4 EEG Classification: Adaptive Neuro Fuzzy
Inference System
The hybrid approach chosen to classify
EEG signals appropriately is the Adaptive
Neuro-Fuzzy Inference System known more
popularly as ANFIS. It takes on the
structure of an artificial neural network
integrated with a Takagi-Sugeno fuzzy
inference system. As it integrates the merits
of both fuzzy logic and neural network
principles, it has the potential to avail of the
advantages of both in a single framework.
Figure 5General overview of ANFIS architecture
In ANFIS the parameters can be estimated
in such a way that both the Sugeno and
Tsukamoto fuzzy models are represented by
the ANFIS architecture. Again with minor
constraints the ANFIS model resembles the
Radial basis function network (RBFN)
functionally. This ANFIS methodology
comprises of a hybrid system of fuzzy logic
and neural network technique. The fuzzy
logic takes into account the imprecision and
uncertainty of the system that is being
modelled while the neural network gives it a
sense of adaptability. Using this hybrid
method, at first an initial fuzzy model along
with its input variables are derived with the
help of the rules extracted from the input
output data of the system that is being
modelled. Next the neural network is used
to fine tune the rules of the initial fuzzy
model to produce the final ANFIS model of
the system.
Figure 6 Learning fuzzy sets
Figure 7 Learning fuzzy rules
Figure 8 Learning rule weights
ANFIS enhances fuzzy parameter
tuning with self-learning capability for
achieving optimal prediction objectives. An

5. ANFIS network is a multilayer feed-forward
network where each node performs a
particular node function on incoming
signals. It is characterized with a set of
parameters pertaining to that node. To
reflect different adaptive capabilities, both
square and circle node symbols are used. A
square node (adaptive node) has parameters
needed to be trained, while a circle node
(fixed node) has none. The parameters of
the ANFIS network consist of the union of
the parameter sets associated to each
adaptive node. To achieve a desired input–
output mapping, these parameters are
updated according to given training data and
a recursive least square (RLS) estimate.
One of the prime concerns when
utilising ANFIS for classifying data is its
inherent ability to generalise when
confronted with a small element of data.
The generating of a fuzzy inference system
in turns leads to a large number of fuzzy
rules being extracted which subsequently
leads to a large number of ANFIS
parameters that need fine tuning. These
parameters will not be adjusted accurately if
using a small number of training data. For
example if you had 8 features for every trail
and you had 140 trials, if three fuzzy
membership functions were defined for each
input feature, that would provide a possible
total of 6561 rules which subsequently
cannot be trained given a small number of
training patterns.
To overcome this problem,
subtractive clustering was used and more
accurately Genfis2 was invoked to generate
a limited number of rules. Genfis2 was used
to initially create that Sugeno-type fuzzy
inference system and uses subtractive
clustering and furthermore requires separate
sets of inputs and output data as arguments.
Genfis2 was implemented as opposed to
Genfis1 as there was more than 6 inputs and
a large amount of training data. Furthermore
Genfis1 differs from Genfis2 as Genfis1
produces grid partitioning of the input space
and thus is more likely to have the problem
of the curse of dimensionality while as
mentioned previously, Genfis2 uses
subtractive clustering. Subtractive clustering
aims to uncover pertinent pattersn from
within the data by identifyig optimal data
points in which to locate cluster centres.
These cluster are next used to extract
meaningful fuzzy rules.
3. Performance Evaluation
3.1 MLP-FF Performance Evaluation
The experiments were carried out on data
ascertained from nine subjects. All data
obtained were taken from the BCI
experiment mentioned in section 2.1. It is
only logical to first interpret the results of
implementing neural networks on the EEG
sample. Table 1 to Table 9 shows
classification results when implementing
MLP-FF utilising 2 hidden layers given
values of 10-12 respectively. As explained
above 8 features have used in the MLP-FF
classifier. Extracted features for this
experiment include [(F1=activity),
(F2=mobility), (F3=complexity), (F4=EEG
Mu Rhythm), (F5= EEG Beta Rhythm),
(F6=Hjorth), (F7=Bandpower),
(F8=Hjorth&Bandpower)]. As features 1-5
have inherently similar qualities, they have
been grouped together and an average
computed. .
Subject1 F1-F5
Avg.
F6 F7 F8
Correct
Classification
51.5% 60.62% 54.37% 55.62%
Incorrect
Classification
48.5% 39.38% 45.63% 44.37
Table 1
Subject2 F1-F5
Avg.
F6 F7 F8
Correct
Classification
50.16% 52.5% 53.33% 44.16%
Incorrect
Classification
49.84% 47.5% 46.67% 55.84%
Table 2
Subject3 F1-F5
Avg.
F6 F7 F8
Correct
Classification
50.37% 53.75% 50% 51.87%
Incorrect
Classification
49.63% 46.25% 50% 48.13%
Table 3

6. Subject4 F1-F5
Avg.
F6 F7 F8
Correct
Classification
72.37% 84.37% 96.87% 97.50%
Incorrect
Classification
27.63% 15.63% 3.13% 2.5%
Table 4
Subject5 F1-F5
Avg.
F6 F7 F8
Correct
Classification
58.25% 76.87% 72.50% 78.12%
Incorrect
Classification
41.75% 23.13% 27.50% 21.88%
Table 5
Subject6 F1-F5
Avg.
F6 F7 F8
Correct
Classification
55.5% 68.75% 63.12% 60%
Incorrect
Classification
45.5% 31.25% 36.88% 40%
Table 6
Subject7 F1-F5
Avg.
F6 F7 F8
Correct
Classification
48.37% 56.25% 55.62% 56.87%
Incorrect
Classification
51.63% 43.75% 44.38% 43.13%
Table 7
Subject8 F1-F5
Avg.
F6 F7 F8
Correct
Classification
67.12% 82.5% 73.75% 79.37%
Incorrect
Classification
32.88% 17.50% 26.25% 20.63%
Table 8
Subject9 F1-F5
Avg.
F6 F7 F8
Correct
Classification
59.5% 78.75% 73.75% 70.62%
Incorrect
Classification
40.5% 21.25% 26.25% 29.38
Table 9
The architecture of the MLP-FF is based on
a straight forward approach with two hidden
layers of 10 and 12 nodes respectively, with
two outputs and 100 epochs training. For
validation purposes, the data was divided
into the following ratios to enhance
classification- initial training ratio 70/100,
initial validation ratio 15/100 and finally
test ratio 15/100. The results obtained from
implementing MLP-FF with Levenberg-
Marquardt training algorithm were
comparatively mixed. As seen in the tabled
data, the classification accuracy for the two
class problem performed better on subject 4.
Furthermore it can be seen that the
classification accuracy for subject 3 and
subject 7 was the worst amongst all other
classification scores. Classification accuracy
performed as expected in all subjects when
applied to feature set 6 (f6) with an average
correct classification accuracy of 68.26%.
This is to be contrasted against F1-F5 which
had a correct classification accuracy of
57.02% which generally classified as many
instances incorrectly as correctly. A further
aspect to be noted is the quicker time in
classification than the hybrid model of
ANFIS which will be discussed in the next
section.
Figure 9 Validation Performance on Subject 4 F8
Figure 9 above depicts the best
classification performance of 97.5% ran
over the first 8 initial epochs.
Figure 10 ROC graph on best classification
performance (Subject 4 F8)

7. 3.2 ANFIS Performance Evaluation
As seen previously, all experiments were
carried on data ascertained from nine
subjects. All data obtained were taken from
the BCI experiment mentioned in section
2.1. During execution of ANFIS on the
mentioned data set, there was quite a lot of
results extracted. Too much to be
adequately illustrated on this report. All
graphs and execution results as well as
source code will be found on disc submitted
with this report.
On implementation of ANFIS on the data
set a collection of radii were selected as to
centre clusters that ranged from 0.5– 1.2
respectively. These radii were selected
along with all available features ranging
from F1-F8 on all subjects. During the
training phase, ANFIS by default utilises a
hybrid learning algorithm to identify
parameters for the fuzzy inference system
(FIS). It utilises a combination of least
squares method along with back
propagation gradient descent for training
FIS membership function parameters to
copy a given training data set.
These identified clusters will generate the
formation of fuzzy rules. Furthermore it was
noted that as the specified cluster radius
increased, the number of generated
associated rules decreased. The Genfis2.m
function in Matlab has been utilised to
generate and extract rules. This function
extracts rules by first using the results of the
subtractive clustering in order to generate
the number of rules and antecedent
membership functions and then uses linear
least squares estimation to determine each
subsequent rules consequent equations.
Giving 8 input features, each rule will
compose of 8 antecedents and one
consequent. The radius of each cluster
specifies the range of influence of the
cluster centre. Hence as mentioned
previously, a smaller cluster radius will
generate more smaller clusters in the data
and inevitable more rules. The analysis of
the generated rules can provide pertinent
information about the relationship and
interaction of selected features.
Furthermore it was noted during execution
trials that as the specified cluster radius
increased the training error increased while
the checking error decreased as shown in
figure 11 and figure 12. This also led to less
rules being generated.
Figure 11Training error subject 7 radius cluster size
0.5
Figure 12Training error subject 7 radius cluster 1.2
Also noted was, as the setting of the radius
was set smaller, generated a higher
classification. For example, using subject 7,
F6 and setting radius to 1.2 gave a
classification accuracy of 58.75%, whereas
using the same subject, same feature but a
smaller radius of 0.5 elicited a higher
classification accuracy of 67.87%.
Furthermore it was noted that ANFIS
performed classification better when
compared with MLP-FF. One example is

8. when ANFIS was executed on Subject 7’s
data, on F6 at radius 0.5, it gave a correct
classifcation of 67.87% which is to be
contrasted against MLP-FF’s correct
classification on the same subject of
56.25%. A demerit of implementing
ANFIS is the generally slower execution
times as compared against MLP-FF. In most
probability this may be due to the excessive
functions in which ANFIS must create in
order to execure as compared against the
computationally simpler model of MLP-FF.
Figure 13 ROCgraph using ANFIS on same subject as
previous MLP-FF ROC graph as performance comparison
Generally for the majority of executions,
ANFIS performed more accurately in terms
of correct classification across all 9 subjects
and features as further depicted when
comparing Figure 13 and Figure 10
respectively.
4. Evaluation & Conclusions
In this paper, the findings of both MLP-FF
with Levenberg-Marquardt learning
algorithm and ANFIS when deployed on the
data set mentioned in section 2.1 were
collated and interpreted.
Firstly, it was noticed that MLP-FF
performed quite mediocrely eliciting an
average correct classification of just under
70%. This is to be contrasted against ANFIS
which performed better across most subjects
depending on specified parameters set. This
performance gulf could be offset by perhaps
utilising a different learning algorithm other
than Levenberg-Marquardt. An alternative
is put forward by [15] which shows
promising results. Furthermore the
parameters could also be modified in future
endeavours to elicit hopefully better
classification accuracy. For example extra
hidden layers with varying amount of nodes
could be implemented in order to extract
better results.
It was noted that during the implementation
of ANFIS, it proved useful in that it elicited
pertinent information about the interaction
of input features and their relationship with
the associated class labels. As a whole, the
ANFIS classifier using fuzzy subtractive
clustering and which is trained to modify
membership parameters of the inputs and
the output has been thoroughly analysed and
interpreted. It was noted that by modifying
clustering radii, elicited varying amount of
rules and hence different classification
accuracies. The results obtained from
ANFIS were found to be better than those
elicited from MLP-FF on most subjects
across all features while also providing
meaningful linguistic rules to further
explain relationships between input features
and their associated class labels.
Further investigation using ANFIS could be
to compare against other classification
methods such as the linear support vector
machine, and perhaps to implement ANFIS
on a multiclass classification problem and
evaluate the associated results and

9. ultimately the correct classification
performance.
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http://www.bbci.de/competition/iv/desc_2b.pdf
Figure 2 obtained from http://en.wikipedia.org/wiki/10-
20_system_(EEG)
Figure 3 obtained from
https://learning.ulster.ac.uk/week6/pg7
Figure 4 obtained from http://www.ijser.org/paper/A-
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Figure 5 obtained from http://omicsonline.org/2157-
7048/images/2157-7048-3-124-g002.gif
Figure 6 obtained from
https://learning.ulster.ac.uk/week11/pg6
Figure 7 obtained from
https://learning.ulster.ac.uk/week11/pg6
Figure 8 obtained from
https://learning.ulster.ac.uk/week11/pg6
Figure 9 obtained from this research
Figure 10 obtained from this research
Figure 11 obtained from this research
Figure 12 obtained from this research
Figure 13 obtained from this research