Permutation Entropy of the Electroencephalogram Background

Activity in Alzheimer’s Disease

Investigation into the Incidence of Repeated Values

Samantha Simons and Daniel Abásolo

Centre for Biomedical Engineering, Department of Mechanical Engineering Sciences, Faculty of Engineering and Physical

Sciences, University of Surrey, Guildford, U.K.

Keywords: Alzheimer’s Disease, Electroencephalogram, Non-Linear Analysis, Permutation Entropy.

Abstract: This pilot study applied Permutation Entropy (PE), a non-linear symbolic measure, and a novel modification

(modPE), to investigate the regularity of electroencephalogram (EEG) signals from 11 Alzheimer’s disease

(AD) patients and 11 age-matched controls given input parameters n (embedding vector), τ (coarse graining)

and slide (difference between the start of two concurrent embedding vectors). PE discriminated better than

modPE with controls showing reduced regularity over AD patients. Increasing τ identified the greatest

differences between EEG signals. Longer embedding vectors were also more able to identify differences.

The greatest difference between groups was at Fp1 with n,τ,slide = 3,10,1 (p=0.0112 Kruskal Wallis with

Bonferroni). Subject and epoch based leave-one-out cross validation was carried out with thresholding from

Receiver Operating Characteristic Curves. The greatest ability to correctly identify AD patients and

controls were 81.82% (Fp2 n,τ,slide = 7,4,4, PE and modPE, F7 n,τ,slide = 3,10,1, PE and modPE) and

90.91% (Fp1 n,τ,slide = 3,10,1, PE and modPE), respectively. The maximum accuracy (both groups

correctly identified) was 81.82% seen at many electrode and input combinations. All are with subject based

analysis. This suggests that PE can identify changes in EEG signals in AD, given appropriate variables.

However, modPE makes little improvement over PE.

1 INTRODUCTION

Alzheimer’s Disease (AD) is a neurological

condition of complex aetiology producing

progressive symptoms of memory and function loss

caused by modification of amyloid β and

hyperphosphorated tau in neurons, modifying

information transition in the brain (Pieyani et al,

2011). The ‘preclinical’ phase of the disease, where

the AD patient is undiagnosed, can be as long as 20

years (Reiman et al, 2012) due to the slow symptom

onset and possible misdiagnosis, caused by the range

of symptoms which can be presented (McKann et al,

2011). With the development of more effective

treatments for AD and the increase in the number of

patients suffering from this disease, the need for

early, accurate diagnosis is imperative to ensure that

treatments can be utilised effectively.

There is evidence that the progress of the disease

can be detected through changes of brain signals

measured with an electroencephalogram (EEG)

(Dauwels, Vialatte and Cichocki, 2010). The

disease must be highly progressed for visual

identification from EEG signals but signal

processing techniques may improve the ease at

which changes due to AD can be seen in the early

stages of the disease.

Non-linear signal processing has been shown to

reliably identify changes in EEG signals in AD

patients including the slowing of EEG signals and

increased signal regularity and decreased signal

complexity (e.g. Abásolo et al, 2006; Dauwels,

Vialatte and Cichocki, 2010; Escudero et al, 2006).

Permutation Entropy (PE) is a symbolic, non-linear

method that calculates the complexity of a signal by

identifying different patterns in it (Bandt and

Pompe, 2002). However, information is lost about

the magnitude of the patterns (Zanin et al, 2012) and

so a number of modifications have been proposed to

improve results when used with biological signals

(Bian et al, 2012; Xiao-Feng and Yue, 2009).

In this pilot study PE and a novel modification of

PE (modPE) are tested for investigating the

Simons S. and Abásolo D..

Permutation Entropy of the Electroencephalogram Background Activity in Alzheimer’s Disease - Investigation into the Incidence of Repeated Values.

DOI: 10.5220/0004721000970103

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2014), pages 97-103

ISBN: 978-989-758-011-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

regularity of EEG signals of AD patients in

comparison to age-matched controls. It is

hypothesised that the modPE method will show clear

differences between the two groups, while PE will

show reduced differences between the two groups.

Further, it is hypothesised that the AD patients will

show an increased EEG regularity when compared

to the control subjects.

The paper is arranged as follows. Section 2

introduces the test database and the methods used in

this study. Section 3 contains results and a

discussion is held in section 4. Section 5 contains

the conclusion of this study.

2 METHODS

2.1 EEG Signals Database

This database has been described in a number of

different studies (e.g. Escudero et al, 2009). The

pertinent points are repeated here for completeness.

The sample group contained 22 subjects, 11

probable AD patients (6 men and 5 women, 72.5 ±

8.3 years, mean ± standard deviation (SD)), who had

a Mini-Mental State Examination (MMSE) score of

13.1 ± 5.9 (mean ± SD) and 11 age-matched controls

(4 women and 7 men, 72.8 ± 6.1 years, mean ± SD)

with a MMSE score of 30 ± 0 (mean ± SD). The

MMSE is a long established method of measuring

the level of cognitive function of a patient (Folstein,

Folstein and McHugh, 1975). Full ethical approval

was obtained for the collection and use of this

database.

Signals were recorded at 256Hz with a 12-bit

analogue to digital converter using the international

10-20 electrode placement system (electrodes Fp1,

Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4,

T5, T6, Fz, Cz and Pz) with subjects in an awake but

resting state with closed eyes. In excess of 5

minutes of data were recorded from each subject.

This data was then reviewed by a clinician who

selected 5 second epochs (1280 data points) with

minimal electromyographic activity and no

movement and electrooculographic artefacts. These

epochs were copied for off-line analysis and were

then further filtered using a Hamming window finite

impulse band-pass filter with cut-off frequencies at

0.5 and 40Hz to remove DC components and

residual noise. For each subject, 30.0 ± 12.5 (mean

± SD) epochs were collected. All epochs were

tested with the methods described in this paper.

2.2 Permutation Entropy

PE is a symbolic dynamics non-linear method which

has been shown to be robust to noise and can be

applied to short time series (Bandt and Pompe,

2002). The method is as follows (Bandt and Pompe,

2002):

 Take the first embedding vector of the dataset n

data points long, skipping τ data points between

each data point selected to join the embedding

vector. I.e. given time series {x(i), i = 1,2,…},

embedding vector = x(i), x(i+τ), …, x(i+(n-1)τ).

 Assign the lowest data point in the embedding

vector 0, the second lowest 1 and on until all data

points in the embedding vector have been replaced

with their ranking order.

 Collect a new embedding vector from the original

dataset. The first data point is slid further along

the original dataset from the first data point of the

previous embedding vector. The subsequent data

points of the embedding vector are found using the

same pattern as the first embedding vector from its

first data point. The movement of vectors along

the dataset is shown in Figure 1.

Figure 1: Two graphs showing how different combinations

of n,τ,slide move along the same dataset with a) showing

3,1,2 and b) showing 3,2,4. In figure b) the dashed line

between points indicate the pattern of the embedding

vector created by τ=2.

 Again replace this with the ranking of the new

vector as detailed in the previous point.

 Continue this until all possible embedding vectors

BIOSIGNALS2014-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

have been created and ranked. Then calculate the

PE with equation 1.







PPslidenPE

log),,(



(1)

where k is the number of different sub-sequence

ranked vectors and P

is the fraction of the sub-

sequence ranked vectors. Equation 1 is similar to

Shannon’s Entropy (Shannon, 1948). A less regular

signal will have a greater range of embedding

vectors and, therefore, a higher PE. Given the

pattern recognition method in PE, where the ranking

of each data point in order of assent is mapped back

to their position in the original vector, {0.2 0.5 0.1

0.4 0.7} would create the ranking {1 3 0 2 4}.

The outcome of PE will be influenced by the

choice of n, τ and slide. A greater value of n, the

embedding dimension, will give a greater possible

range of ranking vectors and, therefore a greater

resolution. Bandt and Pompe (2002) recommended

n=3 to 7 but n! must be less than the length of the

original time series. However, testing with epilepsy

patients showed n=3 and 4 were too small to be of

use (Cao et al, 2004). In this study this range will be

adhered to along with testing of n=10 to identify if

values greater than n=7 may also identify

statistically significant differences between the two

study groups.

Coarse-graining of the recorded EEG signal for

creation of the sub-sequence vectors is carried out

by τ. Initially Bandt and Pompe (2002) used τ=1 but

it was identified that this may not be the optimum

value for signal analysis (Cao et al, 2004). No

studies have been completed to identify the most

reliable range of τ and there is little consensus in the

studies already completed using PE on the value(s)

chosen for τ. The maximum τ seen in biological

studies is 50, used to investigate EEGs of AD

patients (Frantzidis et al, 2012) though this study

produced results showing AD patients with more

irregular EEGs, a finding inconsistent with the large

body of other, already published results from similar

studies. In this study, τ=1 to 4 was chosen with a

further test of τ=10.

There is another variable that has not yet been

investigated by previous work on PE. This is the

movement of the sub-sequence vector along the

original data set and will be denoted by slide in this

paper. All previous papers have used slide=1 but

this may not be the optimal choice of variable and

could have a significant effect on the PE calculation

given its interaction with the other two input

variables. Therefore, this study looked at slide=1 to

The combinations of n,τ,slide tested in this study

are summarised in Table 1, chosen to investigate the

influence of each input variable and variable

combinations and to compare how low and high

input variable combinations interact:

Table 1: Combinations of input variables tested.

n τ slide

3 to 7, 10 1 1

3 2 to 4, 10 1

3 1 2 to 4

7 4 1, 4

The results were normalised to allow for direct

comparison between different variations in n, τ and

slide. Equation 2 shows the normalisation

procedure:

)!ln(

),,(

slidenPE





(2)

with ln(n!) the maximum number of ranking

permutations given the length of the ranking vector.

Note that the number of possible permutations is not

dependent on τ or slide as these do not directly affect

the theoretical maximum of possible permutations.

2.3 Modified Permutation Entropy

As previously mentioned, PE loses information

which relates to the relative magnitude of the sub-

sequence vector data points, including ignoring any

repeated values, giving the first repeated value in the

vector (the value to the left of the vector) a lower

integer than subsequent repeats and so on until all

repeats are accounted for (Bandt and Pompe, 2002).

With biological datasets this can cause a significant

loss of information due to the level of sampling

applied in the data collection phase or the

information needed being held in the signal

amplitude (Bian et al, 2012).

A number of methods have been proposed to

improve the PE algorithm when applied to biological

datasets, Fine-grained PE (FGPE) (Xiao-Feng and

Yue, 2009), Weighted permutation entropy (WPE)

(Fadlallah et al, 2013) and index-modified PE

(imPE- identified as mPE in the seminal paper)

(Bian et al, 2012). FGPE adds a further argument to

the sub-sequence ranking vector which relates

mathematically to the specific values contained in

the sub-sequence vector but maintains the PE

method in all other aspects. WPE creates a

multiplication factor of each logarithmic calculation

which are created using amplitude information from

each embedding vector. However, imPE allows for

PermutationEntropyoftheElectroencephalogramBackgroundActivityinAlzheimer'sDisease-Investigationintothe

IncidenceofRepeatedValues

repeated values to be given the same ranking value.

The created ranking vector from imPE does not

follow the same method as PE, unlike FGPE. The

ranking of each data point in order of increasing

value is not mapped back to their position in the

original embedding vector, as in PE. Instead the

ranking denotes the position of the data point in the

embedding vector in an order that describes

ascending value of each of those data points. The

vector {0.2 0.5 0.1 0.4 0.7} described before with

PE as pattern {1 3 0 2 4} would now be {2 0 3 1 4}

with imPE. This is because as, when reordered, the

lowest value 0.1 comes from the third position,

denoted as two when starting from zero rather than

one, the next lowest 0.2 is from position one,

denoted zero in the ranking, and so on (Bian et al,

2012).

The method proposed in this paper, modPE,

combines the ability to cope with repeated values

within the embedding vector suggested by Bian et al

(2012) with the ranking mapping used in the original

PE method. The method will be described as PE

though repeated values will retain the same ranking

index, rather than being given differing ranking

indexes. Retention of information pertaining to

repetition of data points in an embedding vector of

two or more instances with one or more values will

be incorporated into the method. For example sub-

sequence vector {0.2 0.5 0.1 0.2 0.7} will create the

ranking {1 3 0 1 4}. Note position 2 is not recorded

in the ranking vector as there are two 1’s.

The variables for n, τ and slide will be the same

as those tested for PE to allow for easy comparison.

Again the results will also be normalised to allow for

direct comparison by the method identified by

equation 2, though the denominator for this method

will be calculated differently due to the increased

numbers of possible permutations. For modPE, this

was calculated by summing the number of different

combinations given different repeated values.

2.4 Statistical Analysis

Results given PE and modPE analysis from all

epochs were averaged for each electrode from each

subject. Normality of these average values was

tested using Lilliefors test. Statistically significant

differences were identified between the 11 AD

patients and the 11 controls using Student’s t test if

the data were found to be normally distributed and

Kruskal Wallis if not. Statistical significance was

indicated with p<0.05 in both cases with a

Bonferroni correction for the 16 electrodes. This

correction leads to an uncorrected statistical

significance of 0.0031.

Statistically significant combinations were

further investigated using Receiver Operating

Characteristic (ROC) curves (Fawcett, 2006) with a

leave-one-out cross-validation procedure.

Sensitivity is defined as the proportion of correctly

identified AD patients and specificity is defined as

the proportion of correctly identified controls, while

accuracy identifies the total number of correctly

identified AD and control subjects combined.

3 RESULTS

Controls have a higher PE and modPE value than

AD patients, suggesting an increase of EEG

regularity due to this form of dementia. At low n, τ

and slide combinations, electrodes F7, T3 and T4 do

not follow this trend. At n = 5 to 7 with τ and slide

= 1 electrodes Fp1, Fp2, F7, F8, C4, T3, T4, T5 do

not follow this trend though all these cases show a

difference between values of less than 2%. At these

values of n, increasing τ reduces the number of

electrodes not following the trend but the modPE is

less able to distinguish between the two groups, with

almost all electrodes showing an increased modPE

for patients as τ increases. With n,τ,slide = 10,1,1

electrodes T3, T4 and T5 show increased irregularity

in AD patients. In total, 75.21% of calculations

showed increased irregularity in controls over AD

patients, but this was not equally distributed; some

input parameters showed increased irregularity in

EEG signals of AD patients in all electrodes and

others increased regularity in EEG signals of AD

patients in all electrodes. Results were found to be

predominately normally distributed except for when

τ=10. All electrodes showing statistically significant

differences between the two groups are presented in

Table 2.

With low values of n with slide and τ both equal

to 1 both methods were unable to distinguish with

statistical significance between the two test groups at

any electrode. The ability to distinguish between the

two groups increased as n increased. The choice of τ

was found to be the most critical in distinguishing

between the two test groups. Slide values had little

effect on distinguishing between the two groups.

However, a greater significance was seen between

the two groups as slide increased though this did not

reach statistical significance.

All statistically significant electrode

combinations were then subjected to leave-one-out

cross-validation analysis with the threshold

identified through ROC plots. The results are also

BIOSIGNALS2014-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

100

Table 2: Statistical results for PE and modPE. Statistical significance calculated with Student’s t Test is identified by S

while statistical significance calculated with Kruskal Wallis is denoted KW. P values in this table have already been

corrected with a Bonferroni correction. As such, statistical significance is denoted as p<0.05. Leave-one-out with subject

based analysis is denoted SB and with epoch based analysis is denoted EB.

Electrode n,τ,slide Method Normalised

control

(mean±SD)

Normalised

(mean±SD)

Statistical

method

P with

Bonferroni

correction

Leave-

one-out

method

Sensitivity

(%)

Specificity

(%)

Accuracy

(%)

Fp1 3,10,1 PE 0.9957

±0.0016

0.9886

±0.0058

KW 0.0112 SB 72.73 90.91 81.82

EB 60.93 69.55 65.04

modPE 0.6588

±0.0011

0.6541

±0.0039

KW 0.0224 SB 72.73 90.91 81.82

EB 61.52 71.47 66.26

Fp2 7,4,1 PE 0.7981

±0.0071

0.7860

±0.0082

S 0.0224 SB 63.64 81.82 72.73

EB 76.61 69.86 73.56

7,4,4 PE 0.6654

±0.0020

0.6609

±0.0033

S 0.0144 SB 63.64 81.82 72.73

EB 67.54 73.05 70.03

F7 3,10,1 PE 0.9964

±0.0023

0.9927

±0.0034

KW 0.0368 SB 81.82 81.82 81.82

EB 58.09 70.68 64.18

modPE 0.6593

±0.0015

0.6568

±0.0023

KW 0.0368 SB 81.82 81.82 81.82

EB 56.36 64.51 60.30

held in Table 2. For subject-based analysis, the

greatest sensitivity of 81.82% was obtained at

electrode F7 with n,τ,slide = 3,10,1 and the greatest

specificity was 90.91% at electrode Fp1 with

n,τ,slide = 3,10,1. In both cases this is the same for

both PE and modPE. The greatest accuracy,

81.82%, was seen at a number of electrode and

calculation combinations with subject based

methods. Epoch based results were less sensitive to

differences between the two groups, with a

maximum sensitivity of 76.61% with Fp2 at n,τ,slide

= 7,4,1, a maximum specificity of 73.05% with Fp2

at n,τ,slide = 7,4,4, and an accuracy of 73.56% with

Fp2 at n,τ,slide = 7,4,1. This shows a significant

ability to distinguish between controls and AD

patients at this electrode.

4 DISCUSSION

In this study we tested PE and a novel version of PE,

denoted modPE, to analyse the EEG signals of 11

AD patients and 11 age-matched controls. PE is a

symbolic non-linear method and other symbolic

non-linear methods, such as Lempel-Ziv

Complexity, have been shown to discriminate

between the EEG signals of AD patients and

controls with statistical significance (Abásolo et al,

2006). While PE is not a new method, little research

has been carried out into its behaviour with EEG

signals from AD patients.

The increased signal irregularity of control

subjects when compared to AD patients EEG signals

supports the hypothesis stated in section 1 that

controls show a less regular signal than AD patients.

Morabito et al (2011; 2012) tested AD and MCI

subjects using PE and multivariate multi-scale PE

with n=3 and τ=1, also finding increased irregularity

in control subject EEGs in comparison to AD

patients. However, modPE did not perform

significantly better than PE as hypothesised, a

hypothesis which was based on the work by Bian et

al (2012) where imPE was used with input

parameters n,τ = 3-7,1 and 3,1-4 on R-R intervals

from ECG signals rather than complete EEG signals.

The inability of small n (n < 5) to identify

changes in signals caused by pathological changes in

the brain was identified by Cao et al (2004) testing

combinations of input parameters which included

n=3-7 and τ=2,3 and 10. This is supported by our

results, with low values of n unable to discriminate

between control subjects and AD patients. Further,

ranges of n outside those suggested by Bandt and

Pompe (2002) can be utilised successfully with this

method, shown by the support of the trend of

reduced regularity in AD EEG signals seen with the

lower values of n. These findings suggest that the

differences in EEG signals between AD patients and

controls only manifest themselves in larger patterns

and similar smaller patterns are seen in both signal

types.

The influence of τ was the greatest of all input

variables on the ability of PE and modPE in

distinguishing between the two groups. This input

variable effectively coarse-grains the signal before

calculating PE or modPE. It has been found that

coarse-graining of signals can provide a greater

understanding of those signals under investigation

and in some cases has increased the ability to

distinguish between differing groups such as AD

PermutationEntropyoftheElectroencephalogramBackgroundActivityinAlzheimer'sDisease-Investigationintothe

IncidenceofRepeatedValues

101

patients and controls (Escudero et al, 2006; Simons,

Abásolo and Escudero, 2012a; 2012b). The ability

of this method to improve understanding and

discrimination and the link between coarse-graining

and τ supports the findings of this study.

It was found in the range of slide variables tested

in this study that this had no influence on the ability

of the methods to distinguish between the two

groups, though a trend was seen in the resulting p

values that suggests that increasing slide may

improve resolution for investigation of EEG signals.

However, significantly increasing slide reduces the

data investigated directly in the calculation of PE.

Given the findings of this pilot study, it is

suggested that n,τ,slide = 3,10,1 is the optimum

selection of parameters for discriminating between

AD patients and controls. However, there may be

another combination with higher n and τ values

which has not been tested in this study which is

more able to discriminate between the two groups.

The novel method of modPE was introduced to

investigate the improvement over PE by retaining

the information contained in the appearance of

repeated values, identified as a key component of the

changing R-R intervals from ECG signals

investigated in the paper by Bian et al (2012) and

vital to distinguish between the data from patients

and healthy controls. This study does not confirm

their findings, both as PE identified statistically

significant differences in the EEG signals of AD

patients and controls and that modPE, while also

identifying statistically significant differences, did

not provide a large increase in the ability of the

methodology to distinguish between signals from

healthy controls and patients.

This change in the abilities of the two methods to

distinguish between the two groups is thought to be

due to significant differences in the signal types

analysed and, therefore, the appearance of repeated

values. An ECG is more prone to repeatability than

signals from other, more complex neuronal systems

such as the EEG from the brain. This means that the

probability of repeated values within a given pattern

from an ECG trace is significantly higher than that

from an EEG signal. Furthermore, the focus of a

particular metric from a signal, such as the R-R

interval, rather than the entirety of a signal further

increases the possibility of repeated values.

While PE is currently undergoing wide ranging

testing (e.g. Fadlallah et al, 2013; Li et al, 2013;

Riedl, Müller and Wessel, 2013), there are few

studies applying this method to AD diagnosis. The

differences in signal regularity found by a majority

of PE and modPE calculations with this dataset are

comparable to those found with Multi Scale Entropy

(Escudero et al, 2006), historically the most accurate

method with this database.

Some limitations of this study should be

mentioned. The small sample size of this dataset

leads the findings of this work to be a pilot study.

Furthermore, a greater range of input variables must

be trialled to understand the optimum combination

of input variables to discriminate between these two

groups and other groups with similar pathologies

such as Mild Cognitive Impairment (Albert et al,

2011). In addition, recent evidence suggests that the

increased regularity observed in AD patients’ EEGs

with non-linear methods might be closely linked

with the slowing found with traditional spectral

techniques (Dauwels et al, 2011). Therefore, further

research looking at possible correlations between

different implementations of PE and spectral

techniques is needed. One possible option might

include synthetic signal analysis (Riedl, Müller and

Wessel, 2013). In spite of these shortcomings, PE

and modPE are able to distinguish changes in the

EEG signal of AD patients with a range of input

parameters.

5 CONCLUSIONS

This work has shown the application of PE and a

novel modified version of PE to the analysis of EEG

in AD patients in comparison to age-matched

controls. The findings with PE corroborate other

studies with this dataset and others with similar

methods, in that control subject’s EEGs were found

to be more irregular than those of AD patients. The

choices of input parameters were found to be a key

component in identifying the changes in the signal.

However, caution must be taken due to the small

size of the dataset studied.

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PermutationEntropyoftheElectroencephalogramBackgroundActivityinAlzheimer'sDisease-Investigationintothe

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