Biomedical Engineering Reference
In-Depth Information
Because of diculty of collecting the measurements, especially from
individuals with AMD, the original datasets were cut into equal length
pieces to exploit their usage. Another reason of the segmentation is that the
original measurements are not equally long. The segmentation is conducted
after the 'Six Law' ltering, as mentioned above. The dataset contains the
sum of 351 segments of measurements after segmentation and necessary
outlier detection and each have the length of 2048. The distribution of the
number of the segments among the four groups (Control, #1, #2 and #3)
is reported in Table 1.
3. Multifractality Features
In this section, we discuss the concept of multifractality and the denition
of the multifractal spectrum and analyze the features of the multifractal
spectrum from the perspective of discrimination.
3.1. Scaling and multifractal spectrum
Many measurements encountered in nature, industry, and science
are characterized by complex scaling behavior, namely multifractality.
Multifractals are processes that possess a continuous range of irregu-
larity indices, rather than a single irregularity index H (usually the worst
overall index of irregularity) typical of monofractality. Prime examples of
multifractals are turbulence measurements where the deviation from the
constant scaling, characterized by a Hurst exponent of 1/3 and called the
Kolmogorov K41 law, is explained by multifractality of such measurements
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.
The wavelet-based energy spectrum is a commonly used tool to check the
scaling behavior of the process. This spectrum describes the second order
statistics (i.e., variance) of the process at dierent scales (frequency points).
The linearity (or curvature) of this spectrum reects the fractality of the
process and this connection could be utilized to the estimation of the Hurst
exponent of the process. The exact denition of the wavelet-based energy
spectrum and its estimation could be found in the monograph of Vidakovic
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. Figure 2 shows the wavelet-based energy spectrum of typical PRB
measurement. This spectrum suggests that fractal behavior exists in PRB
and that the multifractal model can be used to identify the inherent features
within the PRB signals of dierent individuals.
The measure of multifractality is given by the multifractal spectrum,
which describes the \richness" of the process in terms of various regular-
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