Music Information Retrieval in P2P Networks - Intelligent Music Information Systems: Tools and Methodologies - page 208

phase's volume mainly depends on the existence
of answers and the number of false-positives,
while the forward phase depends on the size of R ,
the user defined coverage willingness as well as
the network reachability. In general, the volume
of information transferred during the backward
phase is larger than that of the forward phase.
Having outlined the searching procedure, the
following sections detail its parts, starting with
the features selected for the formation of R . Next,
a method for the acceleration of similarity search-
ing within each MH, using indexing, is presented.
Based on these, follow two searching algorithms,
which rely on different choices with respect to the
formation of R , while, finally, methods to improve
the backward phase are described.

Fu, & Yu, 2003) as well as for the incorporation
of the previously mentioned properties. However,
the approach can easily be extended to other types
of wavelet transforms.
Moving on to the indexing procedure within
peers to facilitate the searching, they propose the
following approach. In a peer, each original audio
sequence is transformed to a number of multidi-
mensional points. A sliding window of length
n is used over the sequence and apply Discrete
Wavelet Transform (DWT) to the contents of each
window, producing n coefficients per window. An
example is depicted in Figure 2a. Therefore, each
audio sequence produces a set of n -dimensional
points in the feature space. Since n depends on
the query length and, thus, takes relatively large
values (e.g., 64 K), in order to efficiently index
them in the feature space, only the first d dimen-
sions from each point (experiments with d = 64
are presented therein) are selected. This procedure
dramatically reduces both the size of the index
and the number of dimensions without affecting
much the quality of the index. The reason for the
latter is the merit of DWT to concentrate the en-
ergy of the sequence in the first few coefficients.
However, false-positives remain a possibility and
thus require resolution.
Most importantly, it has been proven by
Chan and Fu (1999) that no false dismissals are
introduced when using only the d first coef-
ficients (due to Parseval's theorem). Notice that
this property is proven in (Chan & Fu, 1999) for
the Euclidean distance. Although this distance
measure is simple, it is known to have several
advantages, as it has been illustrated by Keogh
and Kasetty (2002). Nevertheless, the methodol-
ogy proposed by Karydis et al. (2006) does not
decisively depend on the particular features and
distance measure.
To speed-up the retrieval, for each sequence the
collection of the resulting d -dimensional points
is organised in Minimum Bounding Rectangles
(MBRs), which are, then, stored in an R*-tree
(Beckmann, Kriegel, & Seeger, 1990). Answering

features and Indexing

The most typically encountered features for the
acoustic representation are produced by time
analysis (Papaodysseus, Roussopoulos, Fragoulis,
Panagopoulos, & Alexiou, 2001; Paraskevas &
Mourjopoulos, 1996), spectral analysis (Kostek &
Wieczorkowska, 1997; Papaodysseus et al., 2001;
Paraskevas & Mourjopoulos, 1996;), and wavelet
analysis (Wieczorkowska, 2001).
Karydis et al. (2006) do not concentrate on
devising new features, while their interest remains
in the searching procedure and their methodology
is able to embrace any high performance feature
extraction procedure. Accordingly, a feature ex-
traction process based on the wavelet transform
is utilised. Wavelet transforms provide a simple
but yet efficient representation of audio by taking
into consideration both nonuniform frequency
resolution and impulsive characteristics, as shown
by (Li, Li, Zhu, & Ogihara, 2002; Li, Ogihara, &
Li, 2003; Roads, Pope, Piccialli, & Poli, 1997).
More particularly, they consider the Haar
wavelet transformation for its simple incremental
computation, its capability concerning the capture
of time dependant properties of data and overall
multiresolution representation of signals (Chan,