Authors: Huang, Y.
C., Lin, H. J., Hsu, Y. L., Lin, J. L. (20120629); recommended: YehLiang Hsu
(20120803).
Note: This paper is
published in BMC Medical Inform Decision
Making, 2012, 12:64 doi:10.1186/147269471264.
Using ngram
analysis to cluster heartbeat signals
Abstract
Background: Biological
signals may carry specific characteristics that reflect basic dynamics of the
body. In particular, heart beat signals carry specific signatures that are
related to human physiologic mechanisms. In recent years, many researchers have
shown that representations which used nonlinear symbolic sequences can often
reveal much hidden dynamic information. This kind of symbolization proved to be
useful for predicting lifethreatening cardiac diseases.
Methods: This
paper presents an improved method called the “Adaptive Interbeat Interval
Analysis (AIIA) method”. The AIIA method uses the Simple KMeans algorithm for
symbolization, which offers a new way to represent subtle variations between
two interbeat intervals without human intervention. After symbolization, it
uses the ngram algorithm to generate
different kinds of symbolic sequences. Each symbolic sequence stands for a
variation phase. Finally, the symbolic sequences are categorized by classic
classifiers.
Results: In
the experiments presented in this paper, AIIA method achieved 91% (3gram, 26
clusters) accuracy in successfully classifying between the patients with Atrial
Fibrillation (AF), Congestive Heart Failure (CHF) and healthy people. It also
achieved 87% (3gram, 26 clusters) accuracy in classifying the patients with
apnea.
Conclusions:
The two experiments presented in this paper demonstrate that AIIA method can
categorize different heart diseases. Both experiments acquired the best
category results when using the Bayesian Network. For future work, the concept
of the AIIA method can be extended to the categorization of other physiological
signals. More features can be added to improve the accuracy.
Background
Biological
signals may carry specific characteristics that reflect basic dynamics of the
body. In many studies, biological signals are mapped into symbolic sequences
for further analysis. For example, the DNAsequence, which is composed of
adenine (A), cytosine (C), guanine (G) and thymine (T), is a wellknown
biological symbolic sequence. When mapping to symbolic sequences, the essential
information of the original signals must be preserved.
The human heart
beat time series is another wellstudied example. Human cardiac autonomic
activity is affected by two different interactions: sympathetic activity
increases heart rate, and parasympathetic activity decreases heart rate. Since
these opposite effects are stimulated by many different kinds of stimuli, human
heart beat time series is highly variable and complex. Cysarz et al. [1]
demonstrated that even regular heartbeat dynamics may be associated with
cardiac health. They found that in healthy subjects, continuous adaptation to
different activities occurs during daytime, but there was erratic behavior in
Congestive Heart Failure (CHF) patients.
Regular heart
beat dynamics contains distinct alternation of acceleration and deceleration.
Some early traditional linear methods could reliably describe partial actions
in autonomic regulation, such as respiration [2, 3]. However, nonlinear
methods are needed to analyze highly variable data, such as heartbeat signals
[2, 4, 5]. In recent years, many researchers have shown that representations
which used nonlinear symbolic sequences can often reveal much hidden dynamic
information. This kind of symbolization proved to be useful for predicting
lifethreatening cardiac diseases [611].
At present,
there are three different approaches for using nonlinear symbolic sequences to
represent heart beat time series. The first approach is based on the deviation
of the heart rate time series from the local mean, and a symbol is assigned to
each heartbeat. For example, if the momentary heart rate is close to the mean
value, it is assigned a “1”; if the heart rate is lower than the mean value, it
is assigned a “2”; others are assigned a “3”. Voss et al. [7] found that there
were some specific patterns in patients after suffering myocardial infarction
using the symbolization based on deviation from the mean value. They later
improved this method to identify patients with other high risk cardiac diseases
[12].
The second
approach is to symbolize the increase or decrease of the momentary heart rate
by two different symbols. For example, Yang et al. [10] simplified the
heartbeat dynamics via mapping the output to binary sequences, where the increases
of the interbeat intervals were denoted by “1” and others were denoted by “0”.
They presented a distance method based on rank order statistics to calculate
the dissimilarity between two symbolic sequences. According to the results,
this method can robustly recognize the difference between healthy people and
patients with heart diseases. Peng et al. [11] of the same research team,
combined the distance method with a weighting function, resulting in less
overlap between groups, and more clearly distinguished classes corresponding to
the level of subjects in the CHF group. Van et al. [13] also found that
symbolization can be applied to quantify the fetal heart rate, demonstrating
that development of the autonomic nervous system and emergence of behavioral
states lead to increase in both irregular and regular heart rate patterns.
The third
approach is to divide the range between minimum and maximum heart rate into a
few equidistant intervals, or to map a time series onto a symbolic sequences of
permutation rank [1416]. Entropy and entropy rate were used to evaluate the
complexity of heart variability. Porta et al. [14] used the pattern
classification method to auto identify different physiological conditions by
the activation of different mechanisms responsible for cardiovascular
regulation. Permutation entropy and modified permutation entropy analysis have
also been studied, which maps a time series onto a symbolic sequence of
permutation rank [1516].
The second
approach described above for symbolization does not need any parameter settings
(e.g., the mean heart rate is required in the first approach), and it is
independent of any other features of heart rate variations. In contrast to the
third approach described above, it does not need to adjust the range of
intervals which might affect the results of classification. However, the second
approach used only binary symbols (e.g., 0 and 1) to represent acceleration and
deceleration of interbeat intervals, which might not be able to represent the
degree of variations. For example, the difference between two interbeat
intervals such as +250 and +100 may both be represented as acceleration and
assigned “1”, but actually they are not the same in a detailed interpretation,
and the degree information of acceleration is lost in this binary
representation.
To address this
problem, this paper presents an improved method called the “Adaptive Interbeat
Interval Analysis (AIIA) method”. The AIIA method uses the Simple KMeans
algorithm for symbolization, which offers a new way to represent subtle
variations between two interbeat intervals without human intervention. After
symbolization, it uses the ngram
algorithm to generate different kinds of symbolic sequences. Each symbolic
sequence stands for a variation phase. Finally, the symbolic sequences are
categorized by classic classifiers.
This paper is
organized as follows. Section 2 describes the procedure of the AIIA method.
Sections 3 and 4 present two experiments to validate this method in classifying
different diseases. Finally, Section 5 concludes the paper.
Methods
Figure 1 is the
concept flow chart of the AIIA method. First, the Interbeat (RR) intervals
(RRI) from the ECG time series are extracted and the RRI differences (RRID) of
each sample are calculated. Then the RRI differences are symbolized using the
Simple KMeans algorithm. Styles and signatures are then identified using the ngram algorithm. Finally, the
probability of each signature is calculated as the input to the classic
classifiers. Details of the 5 steps are described as follows.
Figure 1. Concept flow chart of the AIIA method
(1) Preliminary
treatment – Calculating the RRI difference
Figure 2 is a
typical example of an interbeat interval time series. Consider an interbeat
interval time series where x_{i}
is the ith interbeat interval. RRI
difference (RRID_{i}_{1})
is the difference between x_{i}
and x_{i}_{1}.
Calculating each pair of successive interbeat intervals, Figure 3 demonstrates
the RR intervals and the RRI differences.
Figure 2. Typical example of interbeat interval time series
Figure 3. Values of RR intervals and RRI differences
(2) Symbolization
– Using Simple KMeans algorithm to cluster the RRI differences
Simple KMeans
is one of the most popular clustering techniques, and it has been adapted to
many problem domains because of its simplicity and efficiency. This algorithm
was voted as one of the top 10 algorithms in the data mining research area for
identifying hidden patterns and revealing underlying knowledge from large data
collections [17].
After
calculating the RRI differences for each time series, the Simple KMeans
algorithm is used to cluster the RRI differences. In this algorithm, parameter
k represents the number of clusters desired. The output of the clustering
algorithm is k clusters, which should correspond to any known classes in terms
of instance distribution.
Figure 4 is a
demonstration of the Simple KMeans algorithm with 13 data points when k = 3. The coordinates of the black
points are the mean values of the coordinates of the points of the cluster. In
this example, the distance between the centroid of the cluster 1 and the point
A was smallest, and therefore point A will be assigned to cluster 1.
Figure 4. An example to demonstrate the Simple KMeans algorithm with 13
data points when k = 3
In the AIIA
method, every RRI difference can be assigned to a cluster number. In this
paper, k = 2 to 26 were tested. Each
cluster number is then mapped to one of the 26 English letters. Figure 5 is an
example of the symbolization of a sample when k = 3.
Figure 5. Example after being mapped when the number of cluster is 3
(3) Identifying
styles and signatures – Using the ngram
algorithm
An ngram distribution computes the number
of occurrence of each “gram”. Figure 6 displays an example to generate each
2gram “ab”. Each 2gram is displayed by the underline. The occurrence of
2gram “ab” is 5. Note that strings “ab” and “ba” have exactly the same two
letters “a” and “b”, but the two strings “ab” and “ba” are clearly not the
same.
Figure 6. Example to generate each 2gram “ab”
This research
uses 26 clusters (k = 26) with
1gram, 2gram and 3gram for analysis, which includes 18,278 (18,278 = 26^{1}+26^{2}+26^{3})
different kinds of string combinations. That is to say, 18,278 different kinds
of variations in the sample are considered.
(4) Classification
– Using Classic classifiers
Prior to
classification, a probability matrix according to the occurrences of each gram
in the last step is generated. Then 6 classic classifiers, including Bayesian
Network, Logistic, Naïve Bayesian, Neural Network, Support Vector Matrix (SVM)
and TreeJ48, are used to classify the samples into different heart diseases.
In the next
section, two examples are used to demonstrate how the AIIA method is applied to
categorize different types of heart rate time series. The databases for the
examples were provided by PhysioBank, which was created under the auspices of
the National Center for Research Resources of the National Institutes of
Health, USA. It is a large and growing archive of wellcharacterized digital
recordings of physiological signals and related data for use by the biomedical
research community. The biomedical signals from healthy subjects and from
patients with a variety of diseases are included [18].
The 10fold
crossvalidation is used to assess the result. In the 10fold crossvalidation,
the original samples were randomly partitioned into 10 subsets. Of the 10
subsets, a single subset was retained as the validation data for testing the
model and the remaining 9 subsets were used as training data. This step was
then repeated 10 times. Each subset was used exactly once as the validation
data. Finally, the 10 results from the 10 subsets were averaged to produce a
single estimation. The advantage of this method was that all observations were
used for both training and validation and each observation was used for
validation exactly once.
Results
1. Example
1 – Using the AIIA method to classify heart diseases
In this first
example, the AIIA method is used to classify heart diseases from the heart rate
time series. There are 142 samples of heart rate time series data in this
example, which can be divided into 5 groups, including 43 samples with
Congestive Heart Failure (CHF), 9 samples with Atrial Fibrillation (AF), 20
samples of healthy young subjects (HY), 20 samples of healthy elderly subjects
(HE), and 50 samples of white noise (WNU). Table 1 presents detailed
information on the 5 groups.
Table 1. The 5 groups of the example 1
No.

Group

Subjects

Description

Source

1.

Congestive Heart Failure (CHF)

43

15 females and 28 males, average age 55.5
years. It takes 16 to 24 hours for each sample (around 75,000 RRI).

BIDMC Congestive Heart Failure Database [19]

2.

Atrial Fibrillation (AF)

9

Takes only 2 hours for recording (around 12,000 RRI).

Albert C.C. Yang

3.

Healthy Young (HY)

20

10 females and 10 males, average age 25.9
years. It takes 2
hours for each sample (around 7,100 RRI).

Fantasia Database [2122]

4.

Healthy Elderly (HE)

20

10 females and 10 males, average age 74.5
years. It takes 2
hours for each sample (around 7,200 RRI).

5.

White Noise (WNU)

50

Uniform distribution. It takes 6 hours for each sample
(around 15,000 RRI).

Artificially generated

Total

142



The AIIA method
is first used to generate the symbolic sequences of each sample, to identify
styles and signatures, and to calculate the probability of each signature. Then
6 classic classifiers were used to classify the 142 samples into 5 groups, AF,
CHF, HY, HE, and WNU using the probability of each signature. Table 2 shows the
top 4 classified results by using 2gram analysis.
Table 2. The top 4 classified results (2gram, 26 clusters)
Classifier

Cluster Number (k)

Total number of
instances

Correctly
classified instances

Incorrectly classified
instances

Accuracy

Best Performance

Bayesian Network

20

142

126

16

88.7%

20 clusters, 88.7%

SVM

20

142

124

18

87.3%

24 clusters, 88.7%

TreeJ48

20

142

121

21

85.2%

24 clusters, 88.0%

Naïve
Bayse

20

142

113

29

79.6%

24 clusters, 81.7%

Accuracy at k = 20 and the best accuracy of
each classifier are presented for comparison.
From the results
in Table 2, the Bayesian Network had the best performance with 88.7% accuracy
in classifying the samples from patients with different heart diseases when the
cluster number k = 20. The Support
Vector Matrix (SVM) and the TreeJ48 also had over 88.0% accuracy, but both of
them needed 24 clusters. On the other hand, the classification results using
the other classifiers were unstable. Figure 7 shows the relationship between
accuracy rates and cluster numbers by using the Bayesian Network for
classification. When the cluster number was over 16, the performance of the
classifier became stable.
Figure 7. Relationship between the number of clusters and accuracy rate of
2gram analysis
Table 3 shows
details for the classification results by using the Bayesian Network. The
Bayesian Network has 77.8% accuracy for classifying the AF, 88.4% accuracy for
classifying the CHF, 85.0% accuracy for classifying the HE, 65.0% accuracy for
classifying the HY, and 100% accuracy for classifying the WNU. The best
performance was in classifying the CHF group, which had profoundly abnormal
heart function. This function was associated with pathological alterations in
both the parasympathetic and sympathetic control mechanisms.
Table 3. Detailed classification results form using Bayesian Network
Group

AF

CHF

HE

HY

WNU

Total

9

43

20

20

50

Correct

7

38

17

13

50

Incorrect

2

5

3

7

0

Accuracy

77.8%

88.4%

85.0%

65.0%

100%

Figure 8 shows
the comparison between the results from 1gram, 2gram and 3gram by using the
Bayesian Network. When cluster numbers are more than 7, the accuracies by using
3gram analysis are better than the classified results by using 1gram and 2gram
analysis. AIIA method achieved 91% (3gram, 26 clusters) accuracy in
successfully classifying between the patients with Atrial Fibrillation (AF),
Congestive Heart Failure (CHF) and healthy people. The same sample data was
also studied by [10]. However, no accuracy data was presented and therefore
cannot be compared.
Figure 8. The comparison result between 1gram, 2gram and 3gram by using
Bayesian Network
2. Example
2 – Using the AIIA method to classify patients with apnea
Apnea is a term
for breathing suspension. There is no movement of patient’s muscles of
respiration and it leads to lack of oxygen in the blood circulation. Thus,
patients with sleep apnea may have an increased cardiac risk [20]. In the
second example, the AIIA method is used to classify the patients with apnea
from the heart rate time series. There are 4 groups in this example, including
20 samples with Apnea, 20 samples of healthy young subjects (HY), 20 samples of
healthy elderly subjects (HE), and 20 samples of white noise (WNU) for a total
of 80 samples. Table 4 presents detailed information on the 4 groups.
Table 4. The 4
groups of the example 2
No.

Group

Subject

Description

Source

1.

Apnea (APNEA)

20

This experiment
uses the class ‘A’ set which includes 20 records for the target set of Apnea.
These records meet all Apnea criteria. Recordings in class A contain at least
one hour with an apnea index of 10 or more, and at least 100 minutes with
apnea during the recording. It takes 8 hours for each sample (around 35,000
RRI).

ApneaECG database
[23]

2.

Health Young (HY)

20

10 females and 10
males, average age 55.5 years. It takes 2 hours for each sample (around 7,100
RRI).

Fantasia Database [2122]

3.

Health Elderly
(HE)

20

10 females and 10
males, average age 74.5 years. It takes 2 hours for each sample (around 7,200
RRI).

4.

White Noise (WNU)

20

Uniform
distribution. It takes 6 hours for each sample (around 15,000 RRI).

Artificially
generated

Total

80



The AIIA method
is first used to generate the symbolic sequences of each sample, identify
styles and signatures, and calculate the probability of each signature. Then 6
classic classifiers were used to classify the 80 samples into 4 groups, APNEA,
HY, HE, and WNU using the probability of each signature. Table 5 shows the top
4 classified results by using the 2gram analysis.
Table 5. Top 4 classification results (2gram, 26 clusters)
Classifier

Cluster Number (k)

Total number of instances

Correctly classified instances

Incorrectly classified instances

Accuracy

Best Performance

Bayesian Network

11

80

68

12

85.0%

11 clusters, 85.0%

TreeJ48

11

80

63

17

78.6%

17 clusters,
81.3%

Logistic

11

80

55

25

68.8%

17 clusters, 83.8%

SVM

11

80

54

26

67.5%

23 clusters, 83.8%

Accuracy at k = 11 and the best accuracy of each
classifier are presented for comparison
From the results
in Table 5, the Bayesian Network again had the best performance with 85.0%
accuracy in classifying the samples from patients with different heart diseases
when the cluster number k = 11. The
Logistic method and the SVM had 83.8% accuracy in classifying the data. Figure
9 shows the relationship between accuracy rates and cluster numbers by using
the Bayesian Network for classification. From Figure 9, there is a big
difference between clusters 5 to 7, and when the cluster number was over 16, the
performance of the classifier became stable.
Figure 9. Relationship between the number of clusters and accuracy rate of
2gram analysis
Table 6
describes the detailed classification results using the Bayesian Network. The Bayesian
Network provides 95% accuracy in classifying the Apnea, 85% accuracy in
classifying the HE, 60% accuracy in classifying the HY, and 100% accuracy in
classifying the WNU. Its best performance was classifying the Apnea group.
Table 6. Detailed classification results using Bayesian Network
Group

Apnea

HE

HY

WNU

Total

20

20

20

20

Correct

19

17

12

20

Incorrect

1

3

8

0

Accuracy

95.0%

85.0%

60.0%

100%

Figure 10 shows
the comparison results between 1gram, 2gram and 3gram by using the Bayesian
Network. Obviously, the classification results by using 3gram analysis are
better than those by using 1gram and 2gram analysis because more variations
are considered in 3gram analysis. The AIIA method achieved 87% (3gram, 26
clusters) accuracy in classifying the patients with apnea.
Figure 10. The comparison result between1gram, 2gram and 3gram by using
Bayesian Network
Discussion
As interest
continues to grow in analyzing heart diseases, symbolic analysis will clearly
remain an important research tool. It offers advantages such as computational
efficiency, ease of visualization, as well as the ability to combine with other
algorithms, information theories and language that may not be matched by any
other approach. The most significant issue in the application of symbolic
analysis is how to develop an algorithm to appropriately define symbols in the
absence of generating partitions. Although some information is always lost
during the symbolic transformation process and it involves some degree of
imprecision, many associated applications have proved it to be viable and
realistic.
The AIIA method
presented here also cannot assure that no information is lost, but it tries to
capture small variations when doing the symbolic transformation. First, the
method uses up to 26 symbols (a to z) to represent variations between interbeat
intervals to show the increase or decrease phases and the degree of variation.
Second, the symbols are not generated by artificial experiences or functions,
but by the Simple KMeans algorithm, which is one of the most popular
clustering techniques that supplies clusters with minimal total variance [17].
The criterion of minimal total variance yields the most closed clusters. That
is, if variations belong to the same cluster, they are similar. This step is
totally different from previous studies. Finally, it uses the ngram algorithm to generate symbolic
sequences. Closely associated with the problem of symbol definition, there
always needs to be an efficient algorithm for defining the appropriate length
of symbolic sequences. The ngram
algorithm can automatically change the lengths of sequences according to the
experimental performance. The complexity of calculating the occurrence of each
“gram” is, where n is the number of clusters and m is the number of grams. In
general, more clusters and grams may lead to better performance, but it
requires a large amount of computation and takes a long CPU time. It also may lead
to an overfitting problem.
Conclusions
Biological
signals may carry specific characteristics that reflect basic dynamics of the
body. Therefore, finding and analyzing the hidden signals of dynamical structures
which raise a lot of clinical interests. The AIIA method presented here uses
the Simple KMeans algorithm for symbolization, which offers a new way to
represent subtle variations between two interbeat intervals without human
intervention.
The two experiments
presented in this paper demonstrate that AIIA method can categorize different
heart diseases. Both experiments acquired the best category results when using
the Bayesian Network. For future work, the concept of the AIIA method can be
extended to the categorization of other physiological signals. Further study is
required to show robustness of the AIAA method, and more features can be added
to improve its accuracy.
Competing interests
The authors have
no competing interests.
Authors' contributions
YCH, HL and JLL
conceived the study. YCH and HL participated in the acquisition of data,
designed the experiment, wrote the program, and drafted the manuscript. YLH
revised and restructured the study and the manuscript. All of authors read and
approved the final manuscript.
Acknowledgements
We thank for
Doctor Albert C.C. Yang. He offered the samples of the AF group and provided a
detailed explanation.
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