WEIGHTED TIME WARPING FOR TEMPORAL SEGMENTATION

OF MULTI-PARAMETER PHYSIOLOGICAL SIGNALS

Gartheeban Ganeshapillai and John Guttag

Massachusetts Institute of Technology, CSAIL, 77 Massachusetts Avenue, Cambridge, MA, U.S.A.

Keywords:

Temporal segmentation, Multi-parameter physiological signals, Time warping, Time series.

Abstract:

We present a novel approach to segmenting a quasiperiodic multi-parameter physiological signal in the pres-

ence of noise and transient corruption. We use Weighted Time Warping (WTW), to combine the partially

correlated signals. We then use the relationship between the channels and the repetitive morphology of the

time series to partition it into quasiperiodic units by matching it against a constantly evolving template. The

method can accurately segment a multi-parameter signal, even when all the individual channels are so cor-

rupted that they cannot be individually segmented.

Experiments carried out on MIMIC, a multi-parameter physiological dataset recorded on ICU patients, demon-

strate the effectiveness of the method. Our method performs as well as a widely used QRS detector on clean

raw data, and outperforms it on corrupted data. Under additive noise at SNR 0 dB the average errors were

5.81 ms for our method and 303.48 ms for the QRS detector. Under transient corruption they were 2.89 ms

and 387.32 ms respectively.

1 INTRODUCTION

In this paper, we address the problem of segmenting a

quasiperiodic multi-parameter physiological signal in

the presence of noise and transient corruption.

Early warning systems in an ICU require contin-

uous uninterrupted real-time monitoring of the phys-

iological signals (Tarassenko et al., 2006; Mark and

Shavdia, 2007; Cao et al., 2008; Henriques and

Rocha, 2009; Chen et al., 2009). Unfortunately, these

signals often suffer transient corruption. An algo-

rithm that estimates the correct values of the corrupted

signals can help automated systems produce more re-

liable results, and make them more amenable for vi-

sual inspection. An accurate segmentation makes the

estimation task easier.

We represent a multi-parameter signal by a ma-

trix S

n×m

, where each column represents an individ-

ual channel of the signal (e.g., an ECG channel, ABP

or PPG) and each row represents a point in time. For

simplicity, we assume that all the channels are sam-

pled at the same rate. If the matrix represents a quasi-

periodic multi-parameter signal (QPMS), it will have

a repetitive structure that is shared by all the channels

in the structure. This is common in situations where

the signal is generated by the same underlying system.

In the case of the cardiovascular system, the periodi-

1000 1200 1400 1600 1800 2000 2200

−5000

−4000

−3000

−2000

−1000

1000

2000

3000

4000

Sample number

Magnitdue

An excerpt from MIMIC dataset

ECG

ABP

Plethysmogram

Figure 1: The Electrocardiogram (ECG), Arterial Blood

Pressure (ABP) and the Photo Plethysmogram (PPG) ex-

tracted from MIMIC, record 039.

city of all the ECG channels, the blood pressure wave-

forms, and the plethysmogram are related to the heart

rate.

In practice, samples may be corrupted in an un-

known fashion. We would like to estimate the actual

values of the samples in row i of the matrix S that

represents a QPMS, using the corrupted values in that

row and the estimates of prior values up to row (i −1).

125

Ganeshapillai G. and Guttag J..

WEIGHTED TIME WARPING FOR TEMPORAL SEGMENTATION OF MULTI-PARAMETER PHYSIOLOGICAL SIGNALS.

DOI: 10.5220/0003128501250131

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 125-131

ISBN: 978-989-8425-35-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

However, many physiological signals (e.g., those

related to cardiovascular activity) are quasiperiodic.

For such signals, the estimation process starts by iden-

tifying the segment boundaries.

This paper presents a novel approach to identi-

fying segment boundaries in the presence of signiﬁ-

cant amounts of transient corruption spanning multi-

ple columns and rows of the matrix S. The key idea

is that by simultaneously considering all the channels

one can segment them more accurately than would be

possible by considering each channel independently.

The method is based on matching a sliding window

of the QPMS to a template. The template is a short

multi-parameter signal that is regularly updated based

upon recent estimates. The initial template is derived

from an archived QPMS.

Segmentation is done by ﬁnding the preﬁx of

the window that most closely matches the template.

The matching is done using a new method, Weighted

Time Warping (WTW) that minimizes the weighted

morphological dissimilarity between template and the

preﬁx of the window across all the channels. The

morphological dissimilarity is given by the warped

distance between a channel in the window and the

corresponding channel in the template. The weight

represents the estimated quality of the channel.

Experiments carried out on MIMIC (Goldberger

et al., 2000), a publicly available multi-parameter

physiological dataset recorded from ICU patients,

demonstrate the effectiveness of the method. We con-

sidered additive noise and the following types of cor-

ruptions: signal interruption, exponential damping,

overshooting, clipping, and superimposition of artiﬁ-

cial low frequency signals and high frequency signals.

Here, the corruptions across the channels are not per-

fectly correlated.

We compared our method to a widely used QRS

detection based segmentation method. Our method

performs as well as the QRS detector on the raw data

and signiﬁcantly outperforms it on the data syntheti-

cally altered with additive noise and transient corrup-

tion. When additive noise at SNR 0 dB was applied to

all m channels of the signal, the average errors were

5.81 ms for our method and 303.48 ms for the QRS

detector. The average errors were 2.89 ms and 387.32

ms respectively when transient corruption was added.

In the last two cases, the QRS detector was totally

unusable, whereas our method was able to do the seg-

mentation with reasonable accuracy.

The primary contributions of this work are

• Formulation of the problem of segmentation as a

dissimilarity minimization problem, and the use

of a new dissimilarity metric, weighted time warp-

ing.

• The use of a multi-parameter signal template that

eliminates the need of any prior knowledge of the

speciﬁc properties of the signal, and

• The dynamic adaptation of the template, which al-

lows us to accommodate the time evolution of the

signal.

2 BACKGROUND AND RELATED

WORK

Physiological signals in the ICU are often severely

corrupted; corruptions by noise, artifact and missing

data lead to serious errors in automated medical sys-

tems and early warning systems. (Li et al., 2008) pro-

vides a survey of strategies used to address this prob-

lem. Recent attempts to mitigate this problem focus

on using redundant measurements, and fusing data

from multiple sensors (Li et al., 2008; Aboukhalil

et al., 2008; Li and Clifford, 2008; Deshmane, 2009).

Typically they employ independent methods on dif-

ferent channels and combine the results only at the

ﬁnal stage. In contrast, we process all channels si-

multaneously.

Dynamic Time Warping (DTW) is increasingly

being used in temporal segmentation problems (Ko-

var and Gleicher, 2004; Zhou et al., 2008). (Park and

Glass, 2006) uses DTW to segment speakers in an au-

dio signal. DTW has also been used in locating mo-

tion clips (Gleicher and Kovar, 2004) and temporal

segmentation of human motions (Zhou et al., 2008).

(Vlachos et al., 2006) provides an overview on the

implementation of multidimensional Dynamic Time

Warping (DTW) over the L

norm. Based on this

work, we propose Weighted Time Warping (WTW), a

novel method that uses time warping to perform seg-

mentation.

WTW generalizes multidimensional DTW by

weighing the individual signals by the signal qual-

ity. In WTW, we also apply the local continuity and

global path constraints that reduce the inﬂuence of

outliers. The use of such constraints was proposed

in (Myers et al., 1980).

3 METHOD

First we present the overview of the algorithm, fol-

lowed by the discussion of a single iteration of the

loop. Additional details are provided later in this sec-

tion.

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

126

100

−0.2

0.2

0.4

0.6

0.8

1.2

−0.6

−0.4

−0.2

0.2

0.4

0.6

0.8

Time

Relative Amplitude

ABP

ECG

Figure 2: This template comprises of clean ECG and Ar-

terial Blood Pressure (ABP) waveforms. The positions of

the segment boundaries are denoted by `

, `

and `. The

template is little longer than two segments. It contains two

full segments of length `

− `

and ` − `

; the length of the

template is `.

3.1 Overview

Goal. Let S ∈ ℜ

n×m

be a multi-parameter time-

series consisting of set of m number of single param-

eter physiological, and Z

`×m

= {Z

∈ ℜ

}

an initial

template.

The goal is to segment S into a set of

quasiperiodic units Y = {Y

} where Y

de f

= S

i.+1

)

Here, S

)

denotes the window in the target se-

quence S from time t = p

to t = p

− 1.

We require the template (Figure 2) to be com-

prised of at least two segments. These segments are

used to ﬁnd the quasiperiodic unit Y

in Y. We also

assume that we know the locations of the segment

boundaries Z.`

, Z.`

and Z.` in the template. Here,

Z.k denotes the k

row in Z. It is a vector of samples

corresponding to time k. The prototypical template is

initially obtained from an archive.

Procedure. We start the process at some arbitrary

point in time p

start

on the signal that is to be seg-

mented. This need not be an actual segment boundary.

We then run the algorithm starting at p

start

, continu-

ously segment S, and add the segments to Y. We also

update Z to reﬂect the evolution of the time series.

This enables us to accommodate the gradual changes

in the morphology of the signal.

An Iteration. We start the iteration with the extrac-

tion of a window W = S

+v)

from the time series

Bold capital letters represent a matrix S, non-bold cap-

ital letters denote a column vector A, and lower-case letters

denote a scalar w.

data S at p

. Here, the window length is given by

v = ` + e, where e is the buffer length. In the follow-

ing discussion, we use j to index the single param-

eter signals. It is preprocessed, and the morpholog-

ical quality estimates {q

}

are computed, where q

represents the morphological similarity between the

channel W

from W and the corresponding channel

from the template Z

. For each channel j, a pairwise

Euclidean distance matrix pD

is calculated between

and W

(Equation 1-2). The ﬁnal distance matrix D

is obtained by weighting the pairwise distance matrix

with q

(Equation 3).

x,y

= W

x, j

− T

y, j

(1)







1,1

1,2

.. c

1,|Z

2,1

2,2

.. c

2,|Z

... .. .. ..

|,1

.. .. c

|,|Z







(2)

D =

∑

j=1

|pD

(3)

The accumulated distance matrix aD is then com-

puted from D using dynamic programming. For two

single parameter signals A ∈ ℜ

and B ∈ ℜ

, the ac-

cumulated distance can be calculated by the following

recursion

aD(A

) = D(A

) + min{D(A

i−1

aD(A

i−1

),aD(A

i−1

)}. (4)

We next check aD for such spurious matchings. When

a spurious matching is encountered, the buffer length

e is increased and the process is repeated. Otherwise

we trim W to obtain W∗ so that it contains only the

portion of the signal that matches the template.

We next use the accumulated distance matrix aD

to ﬁnd the optimal path alignment between Z and

W∗, as in DTW. From the alignment, we extract the

point W. f ∗ in W∗ that is matched with the segment

boundary Z.`

in Z. This corresponds to the segment

boundary we are interested in, because Z.`

marks the

end of the ﬁrst segment in the template. Then, the

corresponding length f ∗ is used to update p

i+1

with

+ f ∗. A second pass of the algorithm is used to ﬁne

tune the results. For ECG, a peak detector is used in

the second run. Finally S

i+1

)

is added to Y. Fol-

lowing the template update, the process is repeated to

ﬁnd the next segment boundary.

3.2 Weighted Time Warping

We introduce a weighted norm (Equation 3) over the

parameter signals to vary the inﬂuence exerted by

each parameter. The morphological quality metric q

WEIGHTED TIME WARPING FOR TEMPORAL SEGMENTATION OF MULTI-PARAMETER PHYSIOLOGICAL

SIGNALS

127

captures the morphological similarity between the pa-

rameter signal W

and the template Z

We hypothesize that the corrupted regions of the

signals are morphologically dissimilar to the clean

signals. We estimate the dissimilarity using the

warped distance cd

= min

(`,k) (5)

= argmin

(`,k) (6)

Here, aD

is the accumulated distance matrix ob-

tained from pD

using dynamic programming, k

the alignment length, and ` is the length of the tem-

plate.

By simply inverting cd

we could obtain the mor-

phological quality metric q

. Because we use a sin-

gle metric across different channels such as ECG,

ABP and PPG, sometimes two morphologically simi-

lar but time warped sequences from one channel pro-

duce higher cost than two morphologically dissimilar

sequences from another channel. To address this, we

incorporate additional information such as the align-

ment length k

and the difference in the standard de-

viations of W

and T

to obtain q

. Shorter alignment

lengths indicate the partial matchings that usually re-

sult in lower costs. Also a signiﬁcant difference in

the standard deviation between W

and T

implies that

they represent two dissimilar processes. We also use

a non-linear transformation to amplify the dynamic

range of the values in the following equation that es-

timates the morphological quality.

= max











0,exp







1 −

λ × cd

×log(std

+1)

|std

−std







− 1











(7)

Here, std

and std

denote the standard deviation of

and W

respectively. Further, k

is the length of the

path alignment corresponding to cd

(Equation 5). λ

is a normalization coefﬁcient which was empirically

chosen to be 0.05.

3.3 Path Constraint

In a typical formulation of DTW, the distance func-

tion that is used to solve DTW (Equation 4), allows

any path to be taken from (A

) to (A

). This

makes DTW susceptible to degenerate matchings, es-

pecially in the presence of noise. For example, a long

subsequence of a signal might be matched with a sig-

niﬁcantly shorter subsequence of another signal.

Therefore, we use local continuity and global path

constraints (proposed as Type III and Type IV local

continuity constraints in (Myers et al., 1980)) to pre-

vent such physiologically implausible alignments by

updating Equation 4 with

aD(A

) = D(A

) + min{D(A

i−1

aD(A

i−1

i−2

) + D(A

i−1

aD(A

i−1

i−3

) + D(A

i−1

) + D(A

i−2

aD(A

i−2

i−1

) + D(A

i−1

aD(A

i−3

i−1

) + D(A

i−1

) + D(A

i−2

)}.

(8)

This ensures that there are no long horizontal or

vertical paths in the matrix aD along the alignment.

It also results in global path constraints, by excluding

excluding certain parts on the accumulated distance

matrix in which optimal warping paths could lie.

3.4 Templates

The templates (Figure 2) are initially derived from

an archive of the prototypical multi-parameter signal.

They are then updated using the recent signal esti-

mates.

3.4.1 Template Length

When searching for the segment boundaries we only

assume the approximate location of the starting point

). This allows us to start the algorithm at an arbi-

trary location (p

start

). It also makes the detection of

the segment boundary p

i+1

less sensitive to an inac-

curacy in determining the previous segment boundary

). To accommodate this we use templates that are

more than two segments long.

3.4.2 Template Update

To follow the gradual changes that are common in the

physiological signals, we update the template regu-

larly. However, we do this only when the behavior

is consistent, i.e., the recent estimates of the segment

lengths have gradual variation. In that case, if all the

channels are also clean enough, i.e., q

> β; ∀ j, we

update the template by averaging the excerpt of the

last two segments with the time warped version of the

current template (Equation 10). Here, the time warp-

ing is necessary, since the current template Z∗ and the

excerpt of the last two segments Z

can be of different

lengths. Finally we normalize the template.

= S

[(p

(i−1)

−ε),p

(i+1)

]

;ε ≥ 1 (9)

= warp(Z) + ηZ

;η ≥ 0 (10)

Z∗ = normalize(Z

) (11)

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

128

Here, ε ensures that the template consists of at

least two segments. We vary the inﬂuence of the re-

cent segments on the template through the constant

η, where η = 0 implies a static template. We chose

η = 0.6 empirically.

3.5 Long Segments

Spurious matchings occur when the segments in the

window W are signiﬁcantly longer than the segments

in the template Z; therefore the current buffer length

e is not long enough to span at least two segments in

the window. In such cases, the window W = S

+v)

would not contain two full segments and does not give

the expected matching. In such situations, we have

to repeat the matching with a longer window. We in-

crease v through e and repeat the process with a longer

window. Otherwise we trim the window and obtain

W∗, the portion of the window that matches the tem-

plate.

4 EXPERIMENTAL RESULTS

We applied our method to multi-parameter physiolog-

ical signal data from MIMIC at Physionet.org (Gold-

berger et al., 2000). The database has 72 waveform

records with several annotation sets including ECG

beat labels. It includes recordings from multiple ECG

channels, Arterial Blood Pressure (ABP) and Photo

Plethysmogram (PPG). The signals are sampled at

125 Hz. From this database, we selected 70 records

that contained one continuous hour of at least one

ECG channel, and ABP, PPG or both.

Figure 3: Record 213 contains a) ECG channel I, b) ECG

channel II, c) ECG channel V, d) ABP and e) PPG. The

plethysmogram is completely absent over the 12 hour pe-

riod. A severe corruption spans across all the channels for

signiﬁcant amount of time also.

We compared our method to a widely used QRS de-

tection based segmentation method (Pan and Tomp-

kins, 1985; Urrusti and Tompkins, 1993). This

method provides high speciﬁcity and sensitivity with

low computational load (Kohler et al., 2002). Further

it is publicly available as open source software.

We conducted the following experiments : 1) on

the raw MIMIC data we compared our algorithm to

the QRS detector, and 2) we selected clean excerpts

from the raw data, artiﬁcially corrupted them, and

compared our algorithm to the QRS detector on this

corrupted data.

We evaluate the performance using the number

of errors and the average error in milliseconds. The

number of errors is deﬁned as the total number of the

estimated segment boundaries that are different from

actual boundaries by more than one sample. This

also includes the cases where a segment boundary

is completely missed and an erroneous boundary is

found. The average error is the mean distance be-

tween an actual segment boundary and the closest

segment boundary found by the method.

4.1 Raw MIMIC Data

We performed two tests on the raw data. In the ﬁrst

test, we randomly selected 10 records and ran the tests

for the minimum of 12 hours and till the end of the

record. We compared the results of our method and

the QRS detector to the segment boundaries marked

in the data.

The results are presented in Table.1. The results

exhibit signiﬁcant inter-record deviations. This is

mainly due to the presence of sporadic corruptions in

certain records, which results in a burst of errors in

these records. For example, in record 213 (Figure 3),

the corruption is severe, and it spans all the channels.

It causes signiﬁcantly large number of errors for both

our method and the QRS detector. The median num-

ber of errors for our algorithm was 65, whereas it was

330 for the QRS detector.

In the second test, we ran the test across 70 records

for an hour. WTW was able to segment 4.121 × 10

segments accurately while the QRS detector was able

to segment 4.111 × 10

segments correctly. Although

our method made fewer mistakes compared to that

made by the QRS detector, the difference in the accu-

racies of both the methods is not signiﬁcant because

of the sparsity of the occurrence of corruption in the

raw data.

http://www.eplimited.com/

WEIGHTED TIME WARPING FOR TEMPORAL SEGMENTATION OF MULTI-PARAMETER PHYSIOLOGICAL

SIGNALS

129

Table 1: Comparison of WTW against the QRS detector on

selected records.

WTW QRS

Rec avg Sgmt Err avg Err Err avg Err

ID len (ms) # (ms) # (ms)

39 506.25 6 0.01 30 0.25

41 737.91 2 0.00 31 0.47

55 671.13 19 0.05 385 28.27

208 642.67 215 20.63 699 135.39

216 771.33 293 1.10 330 1.64

220 632.88 5 1.65 4 1.20

253 864.40 35 0.15 346 35.13

262 824.93 65 0.30 249 3.55

284 651.70 119 0.23 191 0.96

226 532.17 311 0.55 675 6.25

213 660.31 1921 3.19 2927 42.22

Median number of beats in one record is 56007

4.2 Artiﬁcially Corrupted MIMIC Data

4.2.1 Additive Noise

In this experiment we evaluated our algorithm’s per-

formance on noisy data. We obtained clean excerpts

from the raw MIMIC data and corrupted it with artiﬁ-

cial noise. We randomly extracted 1000 high quality

5 minute excerpts for which both our method and the

QRS detector were 100% accurate. We added AWGN

noise at different Signal/Noise (SNR) levels to these

excerpts and tested both the methods on them.

We carried out two tests. In the ﬁrst test, we added

noise to all m channels, whereas in the second test, we

added noise to only m − 1 channels.

The results of these tests are presented in Table 2.

Our method was able to identify the segment bound-

aries with reasonable accuracy even in the presence

of signiﬁcant additive noise; further, if any one of the

channel is free of noise, the performance is compara-

ble to the performance on the clean raw data.

4.2.2 Transient Corruption

In this experiment we evaluated our algorithm’s per-

formance on data altered, by transient corruption. We

randomly extracted 1000 high quality 5 minute ex-

cerpts and artiﬁcially corrupted them. On each of

these excerpts, we corrupt m − 1 single parameter sig-

nals. For each of these single parameter signals, we

randomly selected 5 non-overlapping 1 minute long

regions and applied one of the following types of cor-

ruptions: signal interruption, exponential damping,

overshooting and clipping, or superimposition of ar-

tiﬁcial low frequency signals and high frequency sig-

Table 2: Summary of the experimental results on the artiﬁ-

cially corrupted data.

Average error (ms) on artiﬁcially corrupted data

Type QRS WTW

all m any m − 1

AWGN 20 dB 12.87 0.87 0.0097

(SNR) 10 dB 188.11 3.27 0.0011

0 dB 303.48 5.81 0.008

Transient Corruption 387.32 - 2.89

Average segment length is 521 ms.

nals. The ECG channels and either ABP or PPG were

corrupted.

The results are presented in Table 2. Under tran-

sient corruption, the average error was 2.89 ms for

WTW. This is comparable to that of the data with

AWGN at SNR 10 dB on all m parameters. Under

severe transient corruption the QRS detector becomes

totally unusable.

5 CONCLUSIONS

We presented a novel online method for temporal seg-

mentation of quasiperiodic multi-parameter physio-

logical signals in the presence of noise and transient

corruption. Our method uses Weighted Time Warping

to exploit the relationship between the partially corre-

lated channels and the repetitive morphology of the

time series.

Our method has a greater constant overhead in

computational complexity relative to QRS detection

based segmentation algorithm. For a window of

length `, our method uses dynamic time warping

which runs in O(`

) time and space. A QRS detection

based segmentation runs in O(`) time. In the exam-

ples used in this paper ` is less than 500.

Our method is particularly useful when the sys-

tem suffers noise and transient corruption. For cor-

ruptions, we tested our method on few artiﬁcial cor-

ruptions; but the real world corruptions could be dif-

ferent, and perhaps adversarial. We haven’t tested our

method on these speciﬁc types of corruptions. In the

case of additive noise, AWGN is the most difﬁcult to

handle because it spans the entire frequency spectrum

and has the highest uncertainty. Our method performs

well against AWGN.

We chose ABP, PPG and ECG for testing, because

they are commonly available in the recordings of ICU

patients. However, our method should be applicable

to any set of correlated physiological signals such as

Central Venous Pressure (CVP), Pulmonary Arterial

Pressure (PAP) and respiratory signal.

BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing

130

We showed that our method performs as well as

an excellent QRS detector on relatively clean ECG

data. On 1 hour long test data across 70 records, our

method achieved 99.56% accuracy, whereas the QRS

detector achieved 99.41% accuracy. When AWGN is

synthetically added, the difference in the performance

between our method and the QRS detector becomes

signiﬁcant. Our method was able to limit the aver-

age error to 5.81 ms when all m parameters were cor-

rupted with AWGN at SNR: 0dB, and to 0.008 ms

when m − 1 parameters were corrupted at the same

SNR. The average error for the QRS detector rose to

303.48 ms when the ECG channel is corrupted with

the same AWGN. Similar results were observed on

transient corruption.

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