Biomedical Engineering Reference
In-Depth Information
We have discussed the features of multifractal spectra in section 3. The
most important feature of the spectrum is the spectral Mode, which cor-
responds to the Hurst exponent if the process is monofractal. The Hurst
exponent is a measure of \roughness" of the self-similar process. The Hurst
exponent coincides with the Holder regularity index, and processes with H
close to 0 look quite irregular and intermittent, while for H close to 1 the
processes look smooth. Such an important property of the spectral Mode
enables us to explain the dynamics of PRB.
Informally speaking, large values of spectral Mode correspond to less
dynamic changes in pupil size (\frozen eye") while low values of the expo-
nent indicate bursty and frequent changes. Therefore, the spectral Mode
could discriminate the measurements. The boxplots of spectral modes for
the four groups are shown in Figure 5. According to this gure, the group
#1 have spectral Modes much lower than the Control group, which reects
that the individuals from this group have more irregular PRB than those
from the Control group.
As can be seen in Figure 5, the spectral Mode could not completely
discriminate the groups. This motivates us to introduce other discrimina-
tory quantities. Another measure we just dened is the Broadness, which is
able to quantify the level of deviations from mono-fractality. The Broadness
measure describes the richness in the distribution of local singularity in-
dices.
PRB measurements with narrow multifractal spectra are close to
monofractals (i.e., the scaling is quite uniform over all scales). The box-
plot of Broadness measures are given in Figure 6. It is very hard to tell
the dierence among the four groups. However, the last group #3 signif-
icantly diers in terms of the Broadness from other experimental groups
(#1, #2). Group #3 has relatively high large Broadness measures, which
indicates that the PRB of the individuals from this group deviates from
mono-fractal much more than groups #1 and #2. Physiologically speak-
ing, more change patterns of the PRB dynamics exist in group #3.
Neither the spectral Mode nor the Broadness measure is able to achieve
the complete discrimination by itself, but each of them distinguish the PRB
from dierent perspectives.
Thus, we need to combined these two measures, characterizing the data
with both measures. Figure 7 presents the centroid points for the four
groups. These four points look nearly evenly distributed on the plane. From
this gure, we can see that the spectral Mode from the Control group is
relatively large although it is not the largest. Only group #2 has a larger
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