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Figure 7. Constructing the mel-frequency cepstral coefficients method from elementary extraction opera-
tors. Solid arrows show the data flow; dashed lines define the tree structure.
flatness measure or the spectral crest factor can be
expressed as an arithmetic combination of simple
functions (Jayant & Noll, 1984).
line. In the next chapter, we will describe the
concept of method trees like the one depicted in
Figure 7 and we will also see how these method
trees can automatically constructed for a given
learning task.
Similar to the tree for mel-frequency cepstral
coefficients more complex trees for high-level
features could be constructed. For example, other
trees exist calculating the used chroma vector in
a time window of a song. The set of high-level
features is only limited by the set of basic ex-
traction methods. If a basic feature is absolutely
necessary for the high-level feature method tree,
but it is not part of the method repository than
the corresponding high-level feature cannot be
constructed. This can usually be fixed easily by
adding the necessary basic extraction method to
the used method repository.
from low-level to high-level
features
In this chapter, we discussed most of the current
methods to work on series data and grouped them
into transformations (basic transformations and
filters) and functionals. In the next chapter, we
will see how this systematization will help to
constraint the search space for automatic feature
extraction methods. Before we describe this au-
tomatic process we would like to point out that
these basic feature extraction methods can be
combined to form more complex features. As an
example we describe how the mel-frequency ceps-
tral coefficients can be constructed as a general
windowing, where the frequency spectrum of the
window is calculated, its logarithm is determined
and a psychoacoustic filtering is performed, and
the inverse Fourier transformation is applied to
the result. Figure 7 shows how the methods for
feature extraction are put together to compute
the cepstral coefficients. From these coefficients
additional features can be extracted. It is easy to
see how variants of this series can be generated,
for example, replacing the frequency spectrum
and its logarithm by the gradient of a regression
automatIc constructIon of
feature extractIon methods
The elementary methods described earlier can be
manually combined in order to construct more
complex features for classification tasks. Figure
7 already showed how elementary methods could
be used for the reconstruction of known complex
feature extraction methods. There are many more
complex feature extraction methods which can
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