MODELLING STABILOMETRIC TIME SERIES

Juan A. Lara, Aurora Pérez, Juan P. Valente

Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo, 28660, Boadilla del Monte, Spain

África López-Illescas

Centro Nacional de Medicina del Deporte, Consejo Superior de Deportes, C/ El Greco s/n, 28040, Madrid, Spain

Keywords: Data Mining, Time Series, Event Detection, Stabilometry.

Abstract: Stabilometry is a branch of medicine that studies balance-related human functions. Stabilometric systems

generate time series. The analysis of these time series using data mining techniques can be very useful for

domain experts. In the field of stabilometry, as in many other domains, the key nuggets of information in a

time series are concentrated within definite time periods known as events. In this paper, we propose a

technique for creating reference models for stabilometric time series based on event analysis. After testing

the technique on time series recorded by top-competition sportspeople, we conclude that stabilometric

models can be used to classify individuals by their balance-related abilities.

1 INTRODUCTION

Stabilometry is responsible for examining balance in

human beings. For this purpose, a device, called

posturograph, is used to measure the balance-related

functionalities. The patient stands on a platform and

completes a series of tests (Figure 1). We have used

a static Balance Master posturograph. In a static

posturograph, the platform on which the patient

stands does not move. The platform has four

sensors, one at each of the four corners: right-front

(RF), left-front (LF), right-rear (RR) and left-rear

(LR). Each sensor records a datum every 10

milliseconds during the test. This datum is the

intensity of the pressure that the patient is exerting

on that sensor. At the end of the test, we have a

multidimensional time series.

In the time series generated by the posturograph,

the key information happens to be confined to

definite regions of the time series, known as events.

This is not unique to stabilometry, and applies to

many other domains.

Figure 1: Patient completing a test on a posturograph.

Regarding the analysis of time series there are

proposals based on the identification of events

(Povinelli, 2000) (Chen et al., 2008), but they do not

address the creation of models. Other techniques

build models from a set of time series

(Papadimitriou et al., 2005) (Chan and Mahoney,

2005), but they do not identify events that contain

the key information of interest to the expert in each

domain. In this article we propose a method for

modelling time series based on event analysis,

taking into account the expert knowledge by means

of criteria for defining such events.

This work was funded by the Spanish Ministry of Education

and Science as part of the 2004-2007 National R&D&I Plan

through the VIIP Project (DEP2005-00232-C03).

485

Lara J., Pérez A., Valente J. and López-Illescas Á. (2010).

MODELLING STABILOMETRIC TIME SERIES.

In Proceedings of the Third International Conference on Health Informatics, pages 485-488

DOI: 10.5220/0002768904850488

 SciTePress

We will explain the stabilometric domain in

more detail in Section 2, whereas Section 3 will

describe the generation of models from stabilometric

time series. The results and conclusions of applying

this technique to the stabilometric domain will be

discussed in Section 4.

2 STABILOMETRIC DOMAIN

In this research, we worked on time series generated

by a stabilometric device known as a posturograph.

This device can be used to run a wide range of tests

according to a predefined protocol. We have worked

with the three tests that output most information for

domain experts. These are called Limits of Stability,

Unilateral Stance and Rhythmic Weight Shift tests.

In the following sections we will describe the

possible events appearing in the time series of each

test and the attributes used to describe these events.

Both the events and their attributes were determined

by the domain experts.

2.1 Limits of Stability (LOS)

This test is composed of eight parts. Each part lasts

10 seconds during which patients have to try to

move his or her centre of gravity to a particular

position in space (called target) and keep it there.

The different targets are: front, rear, left, right, front-

left, front-right, rear-left, rear-right. Patients do not

do one part of the test immediately after another, but

are given time to recover in-between the different

parts of the test. Figure 2 is an example of the paths

of a patient moving his or her centre of gravity

towards the different targets.

The point of the test, then, is to measure patients’

ability to voluntarily move, with both feet on the

platform, their centre of gravity towards a specific

position in space and hold this position for a while

without losing balance.

In this case, preferably, there should only be

movements towards the target (positive movements)

and, once the target has been reached, the subject’s

centre of gravity should not move. In actual fact,

though, the patient wobbles and makes movements

away from the target (negative movements). These

positive and negative movements are the events in

which the expert is interested.

The attributes characterizing the events for this

test are as follows: a) duration, b) timestamp at

which the events occur, and c) movement of the

subject’s centre of gravity in space.

Figure 2: Example of the patient paths towards the

different points in space.

2.2 Unilateral Stance (UNI)

This test aims to measure the patient’s ability to

keep his or her balance when standing on one leg

with both eyes either open or closed (see Figure 1).

The ideal thing for this test would be for the

patient not to wobble at all but to keep a steady

stance throughout the test. The interesting events of

this test occur when the patient loses balance and

puts the lifted foot down on the platform. This type

of event is known in the domain as a fall. The

attributes characterizing the falls are as follows: a)

duration, b) intensity, c) timestamp at which the

events occur, and d) region towards which the

patient is moving when he or she loses balance and

falls.

2.3 Rhythmic Weight Shift (RWS)

The aim of this test is to measure patients’ ability to

rhythmically move their centre of gravity

horizontally (from left to right and from right to left)

and vertically (from front to back and back to front)

at different speeds.

Because the patient continually moves from left

to right and right to left in the case of horizontal

movement, the four time series (LF, LR, RR and

RF) are grouped by pairs (the two left leg and the

two right leg time series pair up, respectively). Also,

as the movement is repetitive, the resulting time

series has a sinusoidal appearance. Figure 3 clearly

illustrates these two issues.

In this case, the events that are of interest to the

expert are each of the transitions the patient makes

from one side to the other. Preferably these

transitions should be as smooth as possible and the

time series plots should closely resemble a

sinusoidal curve. The attributes characterizing each

HEALTHINF 2010 - International Conference on Health Informatics

486

Figure 3: RWS time series with one highlighted event.

event are as follows: a) duration, b) amplitude, c)

smoothness, and d) sinusoidal curve fit.

3 EVENT- BASED MODEL

GENERATION METHOD

The model generation method proposed in this

article receives a set of stabilometric time series A =

, A

, …, A

}, each containing a particular number

of events, and generates a model M that represents

this set of time series. The model M is build on the

basis of the most characteristic events.

To find out whether a particular event in a time

series A

also appears in the other time series, the

event has to be characterized by means of an

attribute vector and compared with the other events

of the other series. To speed up this process, all the

events present in the time series are clustered, so

similar events belong to the same cluster. The

objective is to find those clusters containing events

from as many time series as possible. Having located

those groups with similar events, we extract the

representatives of each of these groups. These

extracted representatives will be part of the final

model.

Let A = {A

, A

,…, A

} be a set of n stabilometric

time series such that m is the mode of the number of

events that appear in the time series of A. In this

case, the algorithm for generating a model M

representing the set A is as detailed below:

1. Initialize the Model (M = ∅).

2. Identify Events. Extract all the events E

from

the series of A and use an attribute vector to

characterize each event.

3. Determine m, the mode of the number of

events in time series of A.

4. Cluster Events extracted in step 2. We have

used bottom-up hierarchical clustering

techniques.

Repeat steps 5 to 9 m times

5. Get the Most Significant Cluster. Determine

which cluster C

of all the clusters output in step

4 is the most significant. Cluster significance is

measured using Equation (1).

#()

()

TS C

SIGNF C

(1)

That is, cluster significance is given by the

number of time series that have events in that

cluster over the total number of time series n.

Events that have already been examined (step 8)

are not taken into account to calculate the

numerator.

6. Extract the Event that Best Represents the

Cluster. Extract the event that is most

representative of the cluster C

, that is, the event

that minimizes the distance to the other

events in the cluster. Let A

be the time series in

which the event E

was found.

7. Add Event E

to the Model. M = M ∪ {E

8. Mark Event E

as Examined.

9. Mark Similar events as Examined. From the

cluster C

obtain for each time series A

≠ A

the event E

from A

that is the most similar

to the representative event (E

) output in step

6. Mark event E

as examined. The overall

conception of the method is based on searching

for events that are very similar to others that

appear in as many time series as possible.

Consequently, if we include event E

in the

model and discard it for later iterations, we

should also discard similar events in other time

series present in that cluster.

10. Return M as a model of the set A.

4 RESULTS AND CONCLUSIONS

We have developed a method to generate a model

from a set of stabilometric time series by matching

up the events that they contain. Apart from

stabilometry, the method described here can be

applied to other domains where the key information

is concentrated in specific regions of the series,

called events, and where the remaining regions are

irrelevant. The proposed method enables the expert

in each domain to define the regions of interest,

which is a plus compared with other methods

addressing the time series as a whole without taking

into account that certain regions can be irrelevant in

the domain in question.

To evaluate the proposed method we used

stabilometric time series taken from a total of 30

top-competition sportspeople, divided into two

groups. The first group was composed of 15

professional basketball players, whereas the second

MODELLING STABILOMETRIC TIME SERIES

487

was made up of 15 young elite skaters. Thirty is a

reasonable number of patients, taking into account

that the tests are quite complex (a single patient

check-up, including the above three tests, occupies

2-3 Mb).

The ultimate aim of the evaluation is to measure

how good the model generation method is. To do

this, we have created two models from each of the

above groups of sportspeople. These two models are

actually composed of three submodels, one for each

individual test (UNI, RWS and LOS). The first

model (M

basketball

) was created from a training set

composed of 10 of the 15 basketball players. The

other 5 players constituted the test set. The second

model (M

skating

) was generated from a training set

composed of 10 of the 15 skaters. The other 5

skaters were used as test set. The sportspeople in the

test set were chosen at random from all the

sportspeople in each group. Table 1 summarizes the

above.

Table 1: Model data distribution.

Model #Training Set #Test Set

basketbal

10 5

skatin

10 5

To evaluate both models, they were used to

classify patients in the test sets. The aim is to check

whether the M

basketball

model properly represents the

group of professional basketball players and whether

the M

skating

model is representative of the group of

elite skaters. Note that the method proposed here is a

modelling not a classification method. To test how

good the method is at creating models, we are going

to evaluate whether the created models are useful for

classification. However, time series modelling has

many other applications like, for example, feature

identification across a group of time series or model

comparison measuring the likeness among groups of

time series or the evolution of one and the same

group over time. In actual fact, in many domains,

like medicine, the mere observation of the model by

the expert can turn out to be very useful in the

decision-making process.

To enact the classification process, we have

compared each of the ten individuals in the test

group against each of the two created models,

making use of the stabilometric time series

comparison method described in (Lara et al., 2008).

All sportspeople have been classified taking into

account how similar they are to the two created

models, selecting the model most like the patient in

question as the class. As regards the five skaters in

the test set, four were correctly classified as skaters.

The fifth could not be successfully classified

because it was very similar to both models. On the

other hand, the five basketball players were correctly

classified as basketball players.

Table 2 summarizes the results. It shows that, of

the ten elite sportspeople that were used to test the

created models, nine were classified correctly within

the respective model of their sports speciality.

Table 2: Sportspeople classification results.

Sport

#Successfully

Classified

#Wrongly

Classified

Basketball 5 0

Skatin

Considering the results, we conclude that the models

generated by our method represent reliably

population groups according to their balance-related

abilities. These results were considered very

satisfactory by both the research team and the expert

physicians. This has encouraged the physicians to

continue cooperating in this field.

REFERENCES

Chan, P. K., Mahoney, M. V., 2005. Modeling Multiple

Time Series for Anomaly Detection, Fifth IEEE

International Conference on Data Mining, ICDM.

Chen, Z., Yang, B. R., Zhou, F. G., Li, L. N., Zhao, Y. F.,

2008. A New Model for Multiple Time Series Based

on Data Mining, International Symposium on

Knowledge Acquisition and Modeling, KAM.

Lara, J. A., Moreno, G., Pérez, A., Valente, J. P., López-

Illescas, A., 2008. Comparing Posturographic Time

Series through Event Detection, 21st IEEE

International Symposium on Computer-Based Medical

Systems, CBMS.

Papadimitriou, S., Sun, J., Faloutsos, C., 2005. Streaming

Pattern Discovery in Multiple Time-Series, 31st VLDB

Conference, Trondheim, Norway.

Povinelli, R., 2000. Using Genetic Algorithms to find

Temporal Patterns indicative of Time Series Events,

GECCO Workshop: Data Mining with Evolutionary

Algorithms.

HEALTHINF 2010 - International Conference on Health Informatics

488