Distinction of Patterns within Time-Series Data Using

Constellation Graphs

Mayumi Oyama-Higa

, Michihiko Setogawa

and Teijun Miao

Department of Integrated Psychological Science, Kwansei Gakuin University

1-1-155, Ichibancho,Uegahara, Nishinomiya-City,662-8501, Japan

Research & Development Center, Hitachi Systems & Services, Ltd.

10-70, 2-Chome, Nanbanaka, Naniwa-ku, Osaka, 556-0011, Japan

Chaos Technical Research Laboratory and CCI Incorporation

3-1-2401, Ryodocho, Nishinomiya-City, 662-0841, Japan

Abstract. Constellation graphs for time-series data are very

effective tool for

displaying a physio-psychological index. In this study, we recorded fingertip

pulse waves of elderly subjects, carried out chaos analysis on the plethys-

mogram data thus obtained, and examined their relationship with dementia. We

discovered the Lyapunov exponent of the time series had a clear relationship

with the severity of dementia and the communication skill of the elderly sub-

jects. We could clearly demonstrate a relationship between dementia and the

Lyapunov exponents using constellation graphs of the time series data.

1 Introduction

Measuring fingertip pulse waves, which are biomedical signals, is easier than electro-

encephalography because it is less restrictive and more convenient. In this study, we

conducted experiments to examine whether senile and other types of dementia have

any relationship with the fingertip pulse waves. The study subjects were residents of

an elder care home and persons receiving day-care at the same facility. The fingertip

pulse waves of each subject were measured and chaos analysis was carried out to

obtain three minutes of time series data. The chaos attractor, entropy, and the largest

Lyapunov exponent were calculated as time series data. In order to obtain the criteria

for estimating the subjects’ quality of life and severity of dementia, we gathered data

on the activities of daily living (ADL) measured by the subjects’ caregivers and on

criteria of different levels of dementia severity. The relationship between the ADL

indices and the results of the chaos analysis and the severity of dementia was ana-

lyzed. We discovered that the mean value and standard deviation of the largest

Lyapunov exponent of the time series had a clear relationship with the severity of

dementia and the communication skill of the elderly subjects. We also examined the

relationship between dementia and communication skills and could clearly demon-

Oyama-Higa M., Setogawa M. and Miao T. (2005).

Distinction of Patterns within Time-Series Data Using Constellation Graphs.

In Proceedings of the 5th International Workshop on Pattern Recognition in Information Systems, pages 192-197

DOI: 10.5220/0002559301920197

 SciTePress

strate a relationship between dementia and the largest Lyapunov exponents using

constellation graphs of the time series data.

2 Data analyzed

Informed consent was obtained from both the subjects’ care home and their families.

There were 179 subjects (139 females and 40 males), who ranged in age from 65 to

100 years (mean 83.4). Measurements were made between August and November

2003. The temperature, systolic blood pressure, diastolic blood pressure, and pulse

rate were measured before recording the plethysmograms.

3 Measuring fingertip pulse waves and analyzing plethysmograms

3.1 Method of measurement

The pulse waves were measured using a photoplethysmography sensor (CCI

BC2000) using the following procedure. We gave the subjects at least 10 minutes

each, to become accustomed to the surroundings in a room maintained at 25°C. They

were allowed to sit comfortably in a chair with both hands placed in a relaxed manner

on a desk (at a height that was comfortable for writing). The subjects kept their eyes

open while the measurements were made on the left index finger for 180 seconds.

The signals were A/D converted. Digital data sampled at a frequency of 200 Hz and a

resolution of 12 bits were fed to a PC.

3.2 Method of chaos analysis

For the time series data x(i), with i=1,…, N obtained from the fingertip pulse waves,

the phase space was reconstructed using the method of delays. Assuming that we

create a d-dimensional phase space using a constant delay τ, the vectors in the space

are generated as d-tuples from the time series and are given by:

)}({)))1((),...,(()( ixdixixi

−

(1)

where x

(i) = x(i –(k – 1)τ), with k=1,...,d. In order to correctly reconstruct the phase

space, the parameters of delay, τ, and embedding dimensions d should be chosen

optimally [4]. In time series recorded from human finger photoplethysmograms, we

chose the parameters τ =50 ms and d=4, as in references [1] and [2].

In the reconstructed phase space, one of the important measures of complexity is the

largest Lyapunov exponent λ

. Considering X(t) is the evolution with time of some

initial trajectory X(0) in the phase space, it is given by

|)(|

limlim

→∞→

(2)

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where

)()()( ttt

εε

XXX −=

)0()0(

XX −=

for almost all initial difference vectors ε = X(0) – X

(0). We estimated λ

using the

algorithm of Sano and Sawada [3]. λ

describes the divergence and instability of the

orbits in the phase space.

The largest Lyapunov exponents, λ

, were calculated for a basic window of 8,000

points (40 sec). The 180 sec (36,000 points) were covered by sequentially sliding,

200 points (1 sec) at a time and λ

was determined for each window.

4 Activities of daily living (ADL) and dementia level data of the

elderly subjects

Data recorded by the persons caring for the subjects in the care home was used as the

ADL data. The dementia data used were those recorded by healthcare professionals.

For the ADL, each activity of daily living, such as walking, eating, toileting, bathing,

dressing, and grooming was assigned to one of three care dependence categories: a)

can do independently although it takes a long time; b) needs some assistance; and c)

totally dependent on assistance. Each subject’s communication skill was also as-

signed to one of the three levels: a) can communicate normally; b) can communicate

to some extent; and c) can hardly communicate.

Data on dementia obtained from the healthcare professionals were categorized into

the five grades of dementia: 0: none, 1: mild, 2: moderate, 3: severe, and 4: very se-

vere.

5 Pulse wave parameters and analysis of ADL indices and severity

of dementia

We examined whether the values of the largest Lyapunov exponent (group means and

standard deviations) had any significant correlation with each of the factors—sex,

age, body temperature, systolic blood pressure, diastolic blood pressure, pulse rate,

walking, eating, toileting, bathing, dressing, grooming, communication skill, and

severity of dementia—in order to examine the relationship between the ADL indices

and dementia with the pulse wave data.

We found that only communication skill and the severity of dementia were signifi-

cantly correlated with the mean and standard deviation of the Lyapunov exponent.

Figs. 1 and 2 show the relationship of these factors with mean and standard deviation

of the Lyapunov exponent, respectively.

The Lyapunov exponent is a measure of the divergence of the attractor trajectory. It

became clear from the above results that communication skill and dementia were

related to the deviation of the Lyapunov exponent and that elderly persons who could

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not communicate well had less deviation of the exponent compared with those who

could communicate well. We observed similar relationships with dementia.

Fig. 1. Relationship of the mean Lyapunov exponent with communication skill and dementia

Fig. 2. Relationship between the standard deviation of the Lyapunov exponent with communi-

cation skill and dementia

6 Representation of dementia in a constellation graph

If we could represent the changes in the Lyapunov exponent obtained by sliding

within the 180-second time interval visually, it would be possible to measure the

changes in the severity of dementia easily.

We realized such a visual representation by preparing constellation graphs[5]. In

these constellation graphs, the numerical data of a time series were converted into

angles between 0 and 180°, and the vectors of the same length were joined and de-

picted on a semicircular graph. The maximum and minimum values were set auto-

matically from the values of the Lyapunov exponent. Each line represents the data for

one subject. The smaller the Lyapunov exponent, the closer the vector is to the bot-

tom right of the constellation graph. As the value of the Lyapunov exponent in-

creases, the line moves to the left in the graph. The line is straighter when the stan-

dard deviation is small, and is bent more when it is large.

Figure 3 shows the relationship between dementia and the Lyapunov exponents ob-

tained from the analysis. The five levels of dementia are shown in different colors.

Subjects with more severe dementia have their lines more to the right side of the

graph. The subjects in the five different dementia categories were sorted according to

severity and five subjects around the median value were selected from each category

195

to prepare this graph. Fig. 4 is similar to Fig. 3, but shows the relationship between

communication skill and the Lyapunov exponent.

Fig. 3. The relationship between the severity of dementia and the Lyapunov exponents of the

time series (each line represents one subject)

Fig. 4. The relationship between communication skill and the Lyapunov exponents of the time

series

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7 Conclusion

The traditional view of homeostasis has been that when certain factors disturb vital

signs, such as the pulse rate, respiration rate, blood pressure, and temperature, that are

directly related to the maintenance of life, and push them outside the normal range,

corrective feedback is activated to stabilize them, and stable values of these signs

indicate the proper functioning of the control mechanisms of the living body. How-

ever, even when a healthy subject is placed at bed rest, the heart beat interval fluctu-

ates irregularly. Respiration rate, blood pressure, and body temperature act similarly.

In fact, the fluctuations of the heart rate are less prominent in elderly persons and sick

persons.

In this study, changes in vital signs caused by aging were measured through finger-

tip pulse waves, represented as constellation graphs, and verified. We demonstrated

that the Lyapunov exponent was related to dementia in elderly persons. Our research

showed that the decrease in the divergence of the Lyapunov exponent in subjects with

advanced senile dementia was similar to that observed in persons with depressive

psychosis. We plan to advance this study further by obtaining detailed data on the

changes in divergence during the time when a newborn infant becomes a young child

and in patients with mental diseases, like depressive psychosis.

Acknowledgments

We thank the staff of the elder care home, Associate Professor Hirohashi of Seisen

University, and Dr. Junko Tsujino and the students of the Oyama Laboratory of

Kwansai Gakuin University for their help and cooperation in collecting data and

taking measurements from our elderly subjects.

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