Information Technology Reference
In-Depth Information
Parametric and non-parametric methods have been applied to test the exis-
tence of a significant statistical dependence between complexity measures and
age. On the one hand, the Spearman's rank correlation coecient
ρ
was de-
termined. We will denote the resulting p-value as
ps
. On the other hand, the
coe
cient of determination
R
2
was computed by means of a simple first order
linear regression. In this case the p-value, denoted as
p
, is obtained by applying
an F-test. Values for
ρ
have to be compared with the correlation coecient
r
(
r
=
(
R
2
). The significance level for both cases was fixed as
α
=0
.
01.
A surrogate data methodology was applied to ensure reliable results. Surrogate
data hypothesis testing consist on generating an ensemble of artificial random
time series that preserve a given set of features of the original signal [16]. Con-
ventional surrogates may fail when there is a strong periodic component in the
original signal, as in our case. A few surrogate techniques for testing cyclic and
pseudoperiodic time series have been proposed [18,7,22].
We have applied the pseudoperiodic surrogate (PPS) algorithm [18], whose
surrogates do not suffer from stationarity and continuity problems. The PPS
algorithm first constructs a vector delay embedding from the scalar time series
in the phase space. Then, a random near neighbour of an initial point is selected
and the procedure is iterated until a random time series with the same length
as the original one has been generated. This method may be applied to test
against the null hypothesis of a quasiperiodic orbit with uncorrelated noise,
roughly preserving pseudoperiodic behavior. In our work, embedding dimension
has been selected according to the Cao's method [1] and the embedding lag has
been determined as the first minimum of the mutual information function [3],
as this value minimizes the dependence degree between delayed samples.
For each subject, a set of 99 PPS surrogates is generated. Then, a complexity
measure (see Section 3) is computed for each subject's surrogate and their mean
and standard deviation values are attributed to that particular subject. Finally,
the correlation between mean values and age is analyzed for surrogate means.
3 Complexity Measures
3.1 Approximate Entropy
The
ApEn
measure estimates the repeatability degree of short evolutive patterns
throughout the complete data series [11]. It provides a non-negative finite index,
where high values suggest high complexity, irregularity and unpredictability in
the recorded signal [19,2].
ApEn
can be applied to short time series, but it is
sensitive to noise. Equal length records are required for different subjects.
Given a time series
x
=
, its approximate entropy
ApEn
(
m, r
)
is obtained as follows. In the first place, the
n
{
x
1
,...x
n
}
m
+1 different
m
-dimension
vectors
y
(
i
)=[
x
i
,x
i
+1
...x
i
+
m−
1
] are extracted. Let the distance between two
vectors
y
(
i
)and
y
(
j
) be the greatest absolute value of the differences between
their components:
−
d
[
y
(
i
)
,y
(
j
)] =
max
1
(
|
x
i
+
k
−
x
j
+
k
|
)
(1)
0
≤k≤m−
Search WWH ::
Custom Search