IEEE Signal Processing - March 2018 - 23
than 20 features including signal shape descriptors (e.g., rate
of attack and decay, temporal occurrence of the main peak),
statistical moments (e.g., mean, skewness, and kurtosis), and
signal power (e.g., peak power, average and power standard
deviation). In bioacoustics, similar features can be used; see,
e.g., [19] and [20] for such use to, respectively, distinguish boats
from whales and automatically identify bird species. In [21],
descriptors based on entropy were used for frog sounds classification. Similar features are also found to represent music for
genres classification, e.g., in [24], in which entropy, centroid,
centroid ratio, bandwidth, and silence ratio were considered.
Reference [23] also performed a classification of orchestral
instruments representing recordings in terms of their centroid,
skewness, kurtosis, or centroid velocity. Most of those features
are included in the feature set we propose in the section "Proposed Representation for Volcano-Seismic Signals."
Another issue related to signals representation is the feature selection process: How are the best features among a large
feature set selected for a given application? This question is of
great interest, and several approaches can be used. This topic,
however, is out of the scope of this article, and the reader is
welcome to consult the literature; see, e.g., some papers related
to the feature selection issue for the automatic processing of
volcano-seismic data [32], [39], [41], [44].
Proposed representation for volcano-seismic signals
As previously explained, the automatic classification of volcanoseismic signatures is still an open issue where reliable methods
still need to be tested. Real-time operational systems are especially lacking. In this scenario, automatic classification methods
take on a fundamental role since they allow
■ a supervised automatic discrimination of signals to be carried out when reference data (e.g., defined by the experts)
are available
■ large data sets to be analyzed without human prior knowledge and interpretation over the observed phenomena in an
unsupervised approach.
The role of features is critical in the automatic analysis (classification in this case) of the data, and we propose a feature
set appropriate for transient signals representation, particularly
for volcano-seismic signals. The main differences between the
state of the art and the feature set we propose is 1) the large set
of features we consider (102 features) that allow a thorough and
complete description of the signals and 2) the feature extraction process. In particular, we propose to compute the features
from three different representation domains of the observations. By doing so, we aim to better underline the complementary properties of signals and eventually give a more complete
characterization of the observations. The three representation
domains are as follows.
■ Temporal: The representation of the signal of interest in
this domain (x [t]) is useful to gain access to the waveform
properties in the original domain of acquisition [45].
■ Frequency: A Fourier transform ^ F {·}h of the discrete
temporal signal x [t] leads to X 6 f @ = F {x [t]}, which represents the spectral content of the observation.
Cepstral: The cepstral domain was originally used in
speech processing. By computing the Fourier transform
twice (i.e., the Fourier transform is computed on the frequency representation of a temporal signal), the cepstral
domain highlights harmonic properties of a given signal:
X [q] = F {X 6 f @}.
Keeping a physical sense associated with data descriptors
is a benefit of computing handcrafted features instead of blindly learning them from data. Such a physical interpretation of
features is extremely significant for volcanologists, since some
of these features can be directly related to specific characteristics of the physical phenomena in the volcano [47]. The set
of features used in this work is listed in Table 1. We organized
■
Table 1. Features computed on a signal s [i ] ni = 1 (in which i might
correspond to a temporal, frequency, or cepstral sample).
E = / ni = 1 s [i ] 2 and E i = s [i ] 2 , respectively, describe the signal energy
and the energy at sample i.
Statistic Features
Feature
Definition
Reference
Length
n = card ^sh
[22]
Mean
ns =
Standard deviation
vs =
1 / s [i ]
n i
1
^n - 1h
[22]
/ i ^s [i ] - n sh2
3
[46]
1 · / c s [i ] - n s m
i
vs
n
4
[46]
ir = 1 · / i E i ·i
E
[22]
Skewness
1 · / c s [i ] - n s m
i
vs
n
Kurtosis
i of central energy
Root mean square
bandwidth
[22]
Bi =
Mean skewness
1 / i 2 ·E - ir2
i
E i
[22]
/ i ^i - irh3 E i
[22]
/ i ^i - irh4 E i
[22]
E·B 3i
Mean kurtosis
E·B 4i
Entropy Features [with p ^s j h the probability of amplitude level s j ]
Feature
Definition
Reference
Shannon entropy
- / j p ^s j h log 2 ^p ^s j hh
[21], [24]
Rényi entropy
1 · log `/ p ^s ha j
2
j
j
1-a
[21]
Shape Descriptor Features
Feature
Definition
Reference
Rate of attack
s [i ] - s [i - 1]
m
n
s [i ] - s [i + 1 ]
m
min i c
n
Ratios, min, max, mean, etc.
[22]
max i c
Rate of decay
Specific values
IEEE Signal Processing Magazine
|
March 2018
|
[22]
[22], [46]
23
Table of Contents for the Digital Edition of IEEE Signal Processing - March 2018
Contents
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