Principal Components in Contemporary Dance Movements

sharpfartsAI and Robotics

Nov 8, 2013 (3 years and 9 months ago)

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Principal Components in Contemporary Dance Movements

Kristen Hollands*
1
, Alan Wing
2

& Andreas Daffertshofer
3


1
Health Maintenance & Rehabilitation, School of Health Sciences, University of Birmingham, UK

Email: k.hollands@bham.ac.uk

2
Sensory Motor Neuroscience, School of Psychology, University of Birmingham, UK

3
Faculty of Human Movement Sciences, Vrije Universiteit, NL


306.16

Introduction

Highly

skilled

movers,

such

as

dancers,

may

employ

kinematic

synergies

(coupled

movements

of

several

segments)

in

order

to

simplify

the

control

of

complex

movement

execution
.

Recently,

Principal

Component

analysis

(PCA)

has

been

used,

with

good

effect,

in

studies

of

human

locomotion

[
1
-
4
]

to

reduce

high

dimensional

data

sets

and

to

identify

interrelationships

of

temporal,

kinematic

and

kinetic

variables
.

The

goal

of

this

research

is

to

investigate

the

utility

of

PCA

to

identify

invariant

or

common

features

within

contemporary

dance

movement

patterns
.

Methods


A

15
s

movement

phrase

of

contemporary

dance

choreography

was

created

and

performed

in

silence

by

two

dancers

(S
1
,

female

&

S
2
,

male)

from

a

professional

dance

company
.
The

movement

phrase

was

created

by

defining

3

self
-
selected

reference

points

in

space

around

the

body

and

then

weaving

a

series

of

movements

in

and

around

these

points

in

such

a

way

that

both

hands

passed

repeatedly

through

the

reference

points
.

The

paths

of

the

hands

between

points

varied

from

curved

to

straight

trajectories

resulting

in

a

movement

phrase

incorporating

whole

body

translations

and

rotations
.

The

phrase

was

performed

5

times

under

each

of

three

different

conditions

(arms

only,

legs

only

&

full

body)
.



The

kinematics

of

the

movements

were

measured

using

a

6

camera,

Vicon

3
D

motion

analysis

system

(Oxford,

Metrics)

with

a

32

marker

whole

body

set
-
up

sampled

at

120

Hz
.




Data Analysis

Principal Component Analysis (PCA)





PCA

was

applied

separately

for

each

dancer

to

the

raw

kinematics

of

all

markers

then

to

a

subset

of

5

markers
.

Results

of

these

analyses

(Figure

2
)

indicate

that

only

9

components

are

required

to

account

for

90
%

of

the

total

variance

using

either

marker

set
.

As

a

result,

PCA

was

applied

to

the

subset

of

5

markers

(R&L

toes,

R&L

forearms

&

sternum)

using

a

covariance

matrix

of

225

time
-
series,

per

dancer,

as

input

for

the

analysis
.






References

1)
A
.
Daffertshofer,

C
.
J
.
C
.

Lamoth,

O
.
G
.

Meijer,

P
.
J
.

Beek

(
2004
)

PCA

in

studying

coordination

and

variability
:

a

tutorial
.

Clinical

Biomechanics
;

19
(
4
)
:
415
-
428
.

2)
C
.
J
.
C
.

Lamoth,

A
.

Daffertshofer,

O
.
G
.

Meijer,

G
.
L
.

Moseley,

P
.
i
.
J
.
M
.

Wuisman

&

P
.

Beek

(
2004
)
.

Effects

of

experimentally

induced

pain

and

fear

of

pain

on

trunk

coordination

and

back

muscle

activity

during

walking
.

Clinical

Biomechanics
;

19
(
6
)
:
551
-
563
.

3)
Olney,

S
.
J
.
,

Griffin,

M
.
P
.

&

McBride,

I
.
D
.

(
1998
)

Multivariate

examination

of

data

from

gait

analysis

of

persons

with

stroke
.

Physical

Therapy
;

78
(
8
)
:

814
-
828
.

4)
Troje,

N
.

F
.

(
2002
)
.

Decomposing

biological

motion
:

A

framework

for

analysis

and

synthesis

of

human

gait

patterns
.

Journal

of

Vision
,

2
:
371
-
387

























Discussion

1) PCA allows for data clustering and extraction of movement
features which are commonly present in different performers and
conditions. Here we use it primarily for data reduction.



2) Since PCA modes combine different physical features,
functional interpretation of identified modes is difficult and the
value of this technique in rapidly facilitating insight into
movement control strategies remains to be seen. It seems that
one has to accept that complicated movements require more
complicated analyses and that classification/quantification in
terms of single scalar values is invalid.



3) The combination of eigenvector coefficients and its time series
helps to identify synergies.

Summary

A.
225 time series were reduced to 9 components accounting for
85
-
90% of the total variance (log
-
eigenvalue spectra in Figs. 3&4
upper left panels).


B.
Subdividing the principal axes (lengths of the eigenvectors in
Figs. 3&4

upper right panels) indicate the first mode is common
only to legs
-
only and full
-
body performance conditions.


This
mode represents whole body translations/rotation in space.


C.
Time series (Fig. 3&4

lower left panels) of component 1 are very
similar between dancers. Indicating that movement execution is
achieved using similar synergies between performers.

D.
Eigenvector coefficients for component 1 (Fig. 3&4

lower right
panels) show that discrimination between conditions can be seen
in the forearm and toe markers in the
x
and
z directions
.





Acknowledgements

Figure 1:

Whole body marker
Placement (32 markers)



Figure 2:

Log
-
Eigenvalue Spectra A)
full marker set, B) 5 marker subset



Results



A

B

Figures 3&4:

PCA of kinematic data for 15 performances (5 repetitions
in each of 3 conditions) of the movement phrase by S1 (Fig 3) & S2 (Fig
4).

A

B

D

A

B

D

Figure 4: S2

Figure 3: S1

C

C