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Don’t hide in the frames: Note- and pattern-based evaluation of automated melody extraction algorithms

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In this paper, we address how to evaluate and improve the performance of automatic dominant melody extraction systems from a pattern mining perspective with a focus on jazz improvisations. Traditionally, dominant melody extraction systems estimate the melody on the frame-level, but for real-world musicological applications note-level representations are needed. For the evaluation of estimated note tracks, the current frame-wise metrics are not fully suitable and provide at most a first approximation. Furthermore, mining melodic patterns (n-grams) poses another challenge because note-wise errors propagate geometrically with increasing length of the pattern. On the other hand, for certain derived metrics such as pattern commonalities between performers, extraction errors might be less critical if at least qualitative rankings can be reproduced. Finally, while searching for similar patterns in a melody database the number of irrelevant patterns in the result set increases with lower similarity thresholds. For reasons of usability, it would be interesting to know the behavior using imperfect automated melody extractions. We propose three novel evaluation strategies for estimated note-tracks based on three application scenarios: Pattern mining, pattern commonalities, and fuzzy pattern search. We apply the proposed metrics to one general state-of-the-art melody estimation method (Melodia) and to two variants of an algorithm that was optimized for the extraction of jazz solos melodies. A subset of the Weimar Jazz Database with 91 solos was used for evaluation. Results show that the optimized algorithm clearly outperforms the reference algorithm, which quickly degrades and eventually breaks down for longer n-grams. Frame-wise metrics provide indeed an estimate for note-wise metrics, but only for sufficiently good extractions, whereas F1 scores for longer n-grams cannot be predicted from frame-wise F1 scores at all. The ranking of pattern commonalities between performers can be reproduced with the * Corresponding optimized algorithms but not with the reference algorithm. Finally, the size of result sets of pattern similarity searches decreases for automated note extraction and for larger similarity thresholds but the difference levels out for smaller thresholds.
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Don’t hide in the frames: Note- and paern-based evaluation of
automated melody extraction algorithms
Klaus Frieler
University of Music “Franz Liszt”
Weimar, Germany
Doğaç Başaran
Audible Magic
London, United Kingdom
Frank Höger
University of Music “Franz Liszt”
Weimar, Germany
Hélène-Camille Crayencour
Centre National de la Recherche
Scientique
Paris, France
Georoy Peeters
Télécom ParisTech
Paris, France
Simon Dixon
Center for Digital Music, Queen Mary
University of London
London, United Kingdom
ABSTRACT
In this paper, we address how to evaluate and improve the perfor-
mance of automatic dominant melody extraction systems from a
pattern mining perspective with a focus on jazz improvisations.
Traditionally, dominant melody extraction systems estimate the
melody on the frame-level, but for real-world musicological appli-
cations note-level representations are needed. For the evaluation of
estimated note tracks, the current frame-wise metrics are not fully
suitable and provide at most a rst approximation. Furthermore,
mining melodic patterns (n-grams) poses another challenge because
note-wise errors propagate geometrically with increasing length of
the pattern. On the other hand, for certain derived metrics such as
pattern commonalities between performers, extraction errors might
be less critical if at least qualitative rankings can be reproduced.
Finally, while searching for similar patterns in a melody database
the number of irrelevant patterns in the result set increases with
lower similarity thresholds. For reasons of usability, it would be in-
teresting to know the behavior using imperfect automated melody
extractions. We propose three novel evaluation strategies for es-
timated note-tracks based on three application scenarios: Pattern
mining, pattern commonalities, and fuzzy pattern search. We apply
the proposed metrics to one general state-of-the-art melody esti-
mation method (Melodia) and to two variants of an algorithm that
was optimized for the extraction of jazz solos melodies. A subset of
the Weimar Jazz Database with 91 solos was used for evaluation.
Results show that the optimized algorithm clearly outperforms
the reference algorithm, which quickly degrades and eventually
breaks down for longer n-grams. Frame-wise metrics provide in-
deed an estimate for note-wise metrics, but only for suciently
good extractions, whereas F1 scores for longer n-grams cannot be
predicted from frame-wise F1 scores at all. The ranking of pattern
commonalities between performers can be reproduced with the
Corresponding author, klaus.frieler@hfm-weimar.de
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DLfM ’19, November 9, 2019, The Hague, Netherlands
©2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.
ACM ISBN 978-1-4503-7239-8/19/11. . . $15.00
https://doi.org/10.1145/3358664.3358672
optimized algorithms but not with the reference algorithm. Finally,
the size of result sets of pattern similarity searches decreases for
automated note extraction and for larger similarity thresholds but
the dierence levels out for smaller thresholds.
KEYWORDS
automatic melody extraction, evaluation, jazz, pattern mining
ACM Reference Format:
Klaus Frieler, Doğaç Başaran, Frank Höger, Hélène-Camille Crayencour,
Georoy Peeters, and Simon Dixon. 2019. Don’t hide in the frames: Note-
and pattern-based evaluation of automated melody extraction algorithms.
In 6th International Conference on Digital Libraries for Musicology (DLfM
’19), November 9, 2019, The Hague, Netherlands. ACM, New York, NY, USA,
8 pages. https://doi.org/10.1145/3358664.3358672
1 INTRODUCTION
In our ongoing research project “Dig That Lick” (DTL), we are
investigating pattern usage in jazz improvisations [
4
,
16
,
17
], such
as the transmission of patterns between performers over time. The
main idea is to create a large database of several thousands of
transcriptions of monophonic solos spanning the history of jazz.
Since manual transcription is very time-consuming, this goal is
attainable (with reasonable eort) only with the help of reliable
automatic melody extraction (AME) systems. The quality of the
transcriptions is of great importance because of the high standards
in the jazz research community and any downstream applications
and results derived therefrom might be strongly inuenced by it. In
order to produce reliable musicological results based on automated
transcription, the performance of the system has to be evaluated
carefully, optimally for all application scenarios separately, as it is
not a priori clear, how derived measurements and secondary tasks
are aected by transcription errors.
The present paper tries to address some of these issues in the
context of a specic research project. Hence, some of the met-
rics presented herein might not be of much use for other AME
applications, but we like to demonstrate by giving examples how
application-specic evaluation metrics can be constructed. We want
to stress the point that the usual approach in Music Information
Retrieval of using standardized evaluation measures for very gen-
eral algorithms might not suciently informative if it comes to
very specic applications such as musicological research with high
quality standards.
We thus ask the following questions:
DLfM ’19, November 9, 2019, The Hague, Netherlands Frieler et al.
How well does an AME system perform in extracting melodic
patterns from jazz solos?
How can an AME system be evaluated best in regard to
secondary applications?
How informative are standardized evaluation measures about
AME system performance in specic tasks?
AME systems are normally evaluated using a frame-wise com-
parison with the ground truth [
2
,
21
], but for most musicologi-
cal applications the note level is the relevant level, which calls
for a note-based evaluation [
22
]. Moving from frame-wise pitch
tracks to note tracks involves one more algorithmic step, e g., a
Hidden Markov Model used for smoothing with the Viterbi algo-
rithm [
8
,
22
], which might be a further source for errors, but also
an opportunity to compensate for lower-level errors.
However, note-level evaluation might still not be sucient, if,
as in our case, the objects of interest are patterns, i. e., sequences
of consecutive notes or n-grams. It is easy to see that note-level
errors propagate geometrically for consecutive sequences. If the
mean accuracy for transcribing a tone correctly is 0
α
1, then,
assuming independence of errors, the probability that in a sequence
of
N
tones (n-gram) all tones are correct is
αN
, which decreases
rapidly. For example, with an accuracy of
α=
0
.
8the probability
to get a 10-gram correct is just
(
0
.
8
)10 =
0
.
11. On the other hand,
to achieve an accuracy of 0
.
8for 10-grams the unigram accuracy
should be at least
α=
0
.
97. This demonstrates that a MIR system
which might be considered successful in regard to standard metrics
might in fact be insucient for evaluating secondary applications.
Note-level errors can give rough estimates of n-gram errors, but
only under idealized assumptions such as the independence of
errors, which might not be fullled in real-world scenarios, as
these depend, for instance, on audio quality, musical context, or
instrument specics. Furthermore, for research applications, rough
estimates are not enough. For more complex evaluation measures,
such as precision, recall, and F1 scores, this approximation might
fail. Since we want to make heavy use of patterns, we need more
precise numbers and propose an n-gram matching metrics where
the estimated n-grams are matched and compared to ground-truth
n-grams.
For a second metric, we use pattern commonalities which are a
way to assess the common share of patterns between solos, say, the
solos of two performers or two jazz styles. As such, it is a measure
for inuences between performers or jazz styles, and thus central
for many of our research questions. Pattern commonality is based
on the totality of all n-grams up to a certain maximal length
N
and is thus a statistical measure which might be tolerant to errors.
This is a rather specic measure which might be only of marginal
interest to others, but we need to know to what extent results based
on AME transcriptions can be trusted.
Finally, we propose two more metrics, that are based on mim-
icking real-world pattern similarity search. Using similarity search
could work as a counter-measure to transcription errors as the
correct pattern might still be in the result set even if some errors oc-
curred. Similarity search is also relevant for pattern mining in itself,
as patterns in jazz might be performed with slight variations [
11
].
However, using similarity search can blow up the result set quickly,
resulting in many uninteresting results, which might diminish the
usability. This problem might become even more prevalent when
using automatically derived estimates of the notes. The similarity
scenario will be used to construct an evaluation metrics based on ac-
tual retrieval results and by estimating the extent of the "by-catch"
in the search results depending on n-gram lengths and similarity
thresholds. In this work, we employ two AME methods for applying
the proposed evaluation metrics: convolutional-recurrent neural
networks (CRNN) [
3
], which was specialized for and trained on
monophonic jazz solos, and Melodia [
23
], a state-of-the-art but
generic AME algorithm, which will serve as baseline. Furthermore,
we introduce a novel Viterbi smoothing on top of the CRNN system
in the hope of improving the performance in pattern search tasks.
2 AUTOMATIC DOMINANT MELODY
ESTIMATION
Automatic melody estimation (AME) is dened as extracting the
main melodic line from polyphonic music. Most proposed AME
approaches are based on computing a time-frequency salience rep-
resentation where
F0
’s of the main (dominant) melody line are
emphasized [
3
,
5
,
7
,
23
]. To obtain salient features for main melody
F0
’s against a polyphonic background is not trivial and is still con-
sidered the main bottleneck in melody estimation algorithms [
3
,
5
].
To tackle this problem, several methods have been proposed, in-
cluding hand-crafted features such as the harmonic sum spectrum
(HSS) [
23
], representation learning methods such as source-lter
non-negative matrix factorization (SF-NMF) [
7
,
9
], and, more re-
cently, deep learning based approaches [1, 3, 5, 24].
Due to the inherent temporal structure in music, a temporal
tracking or smoothing phase is usually involved in AME systems
[
3
,
6
,
8
,
23
]. It is necessary to model the correlations between the
frames. Popular choices for temporal tracking are HMMs [
9
,
22
],
contour tracking [7, 23], and recurrent neural networks [3, 19].
2.1 CRNN with SF-NMF pretraining
In [
3
], a convolutional-recurrent neural network was proposed
whose pretraining is based on the SF-NMF model by [
9
]. In SF-NMF,
the main melody is modeled by a source-lter model inspired by a
model of speech production. The source is further decomposed into
basis and activation matrices where the activations of the sources
are considered as the initial pitch salience. This initial estimation is
enhanced with a CNN and then a bi-directional RNN (Bi-GRU) is
employed for modeling the temporal information. The classication
layer outputs a frame-wise probability distribution over classes
(target
F0
’s and a non-melody class). A simple peak-picking strategy
is applied to the frame-wise probability distributions to obtain the
F0
estimates. The results show that when a good initial salience
input is provided to the CRNN system, it performs considerably
better without any augmentation or additional training data, hence,
keeping a lower model complexity. The block diagram of the CRNN
system is given in Fig. 1 (left).
2.2 Melodia
In Melodia [
23
], the salience representation is obtained by rst
detecting the sinusoidal peaks in the STFT and mapping each
peak’s energy to all harmonically related
F0
candidates in the STFT
frame, with exponentially decaying weights. Then the salience
Don’t hide in the frames: Note- and paern-based evaluation of automated melody extraction algorithms DLfM ’19, November 9, 2019, The Hague, Netherlands
Figure 1: AME architectures: CRNN with SF-NMF pretrain-
ing (left) and Melodia (right).
peaks, which are continuous in time and frequency, are sequentially
grouped to create contours which are treated as smooth melodic line
candidates and are characterised by a set of features such as pitch
and salience deviation. Finally, the melody contours are selected
using a set of heuristic rules based on the contour characterizations.
The block diagram of Melodia is given in Fig. 1 (right).
2.3 Viterbi smoothing with a time- and
note-dependent transition matrix
As stated in Sec. 2.1, the CRNN system exploits the temporal infor-
mation with an RNN layer (Bi-GRU) which is reported to increase
the overall accuracy signicantly. However, our initial experiments
with this system show that the output
F0
estimations are not smooth
enough, e. g., because of single frame estimation errors in a segment
of frames. Such errors have minimal eect on the overall frame-
level accuracy, but could negatively aect note-level and n-gram
accuracy. This suggests that a simple peak-picking on the CRNN
output probability distributions may not be suciently smooth for
the pattern extraction task. As a possible improvement, we propose
to replace peak picking with a novel frame-level Viterbi smoothing
algorithm. Details can be found in Appendix A.
3 EVALUATION METRICS
We devise three evaluation metrics, where one is based on precision,
recall and F1 scores, and the two other focus on performance in
actual applications needed for musicological research on patterns
in jazz, i. e., pattern search and pattern commonalities.
3.1 N-gram matching
This metrics is related to well-known note-based metrics in AME
[
21
]. We work on a set of target solos (the ground truth in the form
of acceptable transcriptions), that the AME algorithm is supposed to
reproduce as closely as possible. The problem lies in the denition of
closeness, which turns out to be a free parameter of the metric, and
which is constrained by musicological criteria. This parameter
δ
is
the width of a search window around the true onset of a note event.
From music psychological research [
10
,
13
], it is known that the
just noticeable dierence for onsets is in the order of 30–70 ms from
which we can obtain the order of magnitude for errors in human
annotation of onsets. This is also related to the speed of the fastest
human movements (trills), which is about 16 Hz–20 Hz, implying
an upper bound of about 50 ms–62.5ms for inter-onset intervals.
A grid search with
δ∈ {
30
,
50
,
70
,
90
}
showed that
δ=
50
ms
gave
the best results, so we used this value in the following. In many MIR
evaluation metrics, thresholds of similar magnitude are employed,
e. g. for beat tracking a threshold of 70 ms is customary [21].
To be more specic, let us dene some basic notions. A melody
µ
of length
N
is dened as a sequence of onset
ti
, pitch
pi
, and
duration
di
values,
µi=(ti,pi,di)
for
0i<N
. Duration values
are often of lesser importance, since for rhythm perception and
production the inter-onset intervals are the functional time struc-
ture, whereas duration governs articulation. In pattern analysis of
jazz, commonly only pitch or interval n-grams are considered. We
will neglect duration here, and timing (onset) information needs to
be “coarse-grained” in some way, which is achieved by using the
δ=50ms tolerance windows.
Given a ground truth reference solo in reduced representation,
i. e.,
µT
i=(tT
i,pT
i)
of length
N
, and an automatically extracted
melody
µQ
i=(tQ
i,pQ
i)
of length
M
, we will now dene recall, pre-
cision and F1 scores using a time window
δ
applying the following
procedure.
For each tone event
µT
k
in the reference melody, we nd all tone
events in the estimated melody with onsets in a window of
±δ
around the onset tT
kof the ground truth event, i. e., the set
Mk={Qi| |tQ
itT
k| ≤ δ}.(1)
If the set is empty,
Mk=
, then we have a false negative and set
FNk=
1, else
FNk=
0
.
If the set contains exactly one element with
the same pitch, we have a true positive
TPk
. All other cases are
counted as one false positive
FPk
, even if there are more events,
which in practice rarely happens due to the small time window and
the smoothing step of the AME algorithms. This allows to get a
unique triplet
(TPk,FPk,FNk)
with
TPk+FPk+FNk=
1for each
reference event. This procedure is not yet complete as it ignores
extra events in the estimated melody outside of all time windows
around the reference onsets. These events should be taken into
account as extra false positives. To calculate these, we use the same
procedure as before but with the roles of reference and estimated
events interchanged while ignoring all but the false negative (un-
matched) events which are added to the false positives in the nal
summation over a melody. Setting
ξ=Íkξk
for
ξ∈ {TP,FP,FN}
,
precision, recall and F1 scores can then be dened in the usual way.
As we are not only interested in single tone events but also in
patterns, the approach will be generalized to arbitrary n-grams. To
DLfM ’19, November 9, 2019, The Hague, Netherlands Frieler et al.
this end, we dene an n-gram event for a melody as
µn
i=(tn
i,pn
i)
with
tn
i=1
nÕ
ik<i+n
tk,(2)
where tn
iis the mean onset, and pn
i
pn
i=(pi,pi+1, . . . , pi+n1),(3)
the corresponding multi-pitch event (pitch n-gram). The choice
of the mean onset for the onset of a multi-pitch event seems to
be most principled, as it evens out small temporal variations of
the onsets of the constituting pitches. Using the rst onset of the
n-gram would make the matching too strongly dependent on the
error of a single event. Theoretically, this procedure allows n-grams
with grossly mismatching onsets of the single pitches to match
a ground truth n-gram, if only the mean onset matches. This is,
however, not a problem, because it is very unlikely to happen and it
would mean that preceding and succeeding n-grams will not match,
which would have a strong negative impact on the metric.
From these denitions, we get a surrogate n-gram event sequence
of
Nn+
1elements, where
N
is the length of the melody and
n
the length of the n-grams. The metrics from above can then simply
be carried over for any value of
n
. This n-gram based approach
has some similarity with the BLEU method [
18
] used for automatic
translation, where also n-grams are matched but without regard to
position.
3.2 Pattern search
In the "Dig That Lick" project, we developed two pattern search
tools [
12
], the DTL Pattern Search
1
, featuring regular expressions
and two-staged searches, and the DTL Similarity Search
2
, based
on similarity of symbol sequences, derived from abstractions of
the musical surface (e. g., pitches and intervals). The main idea
of our second metrics is to compare the retrieval results for the
ground truth with the retrieval results for the automatically ex-
tracted melodies using the similarity search.
For two symbol sequences
t=tn
i
and
q=qm
j
of lengths
n
and
m, we dene the edit distance similarity as
σ(t,q)=1η(t,q)
max(n,m),(4)
where
η(t,q)
is the edit distance, the minimum number of substitu-
tions, insertions, and deletions to transform one sequence into the
other. Edit distances are a well-known family of sequence metrics
which have been shown to provide good approximations for human
similarity judgements, even using only single dimensions such as
pitch, interval, and rhythm alone [
14
,
15
], and are often used in
pattern mining of melodies (e. g., [
25
,
26
]). Hence, the good approx-
imation property and the ease of implementation suits the needs
of our pattern similarity search over a range of dierent melodic
representations that can be chosen by the user. It should be noted
that the evaluation procedure proposed below does not depend on
the details of the employed similarity measure, it would work with
any similarity measure.
The proposed metrics tries to mimic similarity searches over a
range of query patterns with a range of similarity thresholds and
1https://dig-that- lick.hfm-weimar.de/pattern_search/
2https://dig-that- lick.hfm-weimar.de/similarity_search/
maximum length dierences as parameters. For each query and pa-
rameter setting, the search will retrieve all n-grams in the database
that have a similarity to the query greater or equal to the specied
threshold and with a length dierence of at most the specied value.
The result set also contains information on the containing solos for
any retrieved instance. All searches are performed on the ground
truth database as well as the corresponding database of estimated
solos. For a similarity threshold of
τ=
1, the search is exact, which
allows to dene retrieval scores in the following way.
For each query, the result set is compared with the ground truth
in terms of the set of solos in which the matches are found. For each
solo in the result set from the ground truth database, containing the
query n-gram, we compare the number of instances found in the
ground truth (
nR
) and in the corresponding solo in the estimated
database (
nE
). We set
ni
E=
0, if document
i
is not contained in the
query result from the estimated database. We use the following
partition of
nR
as dening equation for true and false positives and
false negative counts:
nR=T P F P +F N
=min(nE,nR) − θ(nEnR)+θ(nRnE),
with
θ(x)=max(x,
0
)
the ramp function. If
nEnR
then we have
T P =nE
,
F N =nRnE
, and
FP =
0; if
nE>nR
, then we have
T P =nR
,
FP =nEnR
, and
F N =
0. These values are summed up
across all solos in the ground truth result set, from which precision,
recall and F1 scores can be calculated for a query.
Furthermore, we are interested in comparing the total sizes of
result sets for a query in the ground truth and the AME databases,
because for similarity search, results sets can grow quickly, and
it is interesting to see if more or less results are generated for the
AME databases. We use the relative dierence of result set sizes
with respect to the ground truth result set size as a metrics:
R(qk;τ,δ)=#R(qk,DR;τ,δ) − #R(qk,DE;τ,δ)
#R(DR;τ,δl),(5)
where #
R(DI
;
τ,δ)
is the size of the result set from database
I
for the
query
qk
with similarity threshold
τ
and maximal length dierence
δ
. Since these are relative dierences, the values can be averaged
across all queries to give overall evaluation values.
3.3 Pattern commonalities
Another application of interest in jazz pattern research is the as-
sessment of similarity of subsets of solos with regard to pattern
commonalities, e. g., comparing performer
X
with performer
Y
to
investigate musical inuence and stylistic closeness via shared pat-
terns. We denote the set of all dierent n-gram values of length
n
for a set
S
as
n(S)
. The pattern commonality of
S
and
R
for a xed
length
n
is then dened as the total variation distance of the relative
frequency distributions:
σn(S,R)=1
2Õ
qn(SR)
|fS(q) − fR(q)|,(6)
where
fX(q)
is the relative frequency of n-gram
q
in
X=S,R
,
and we set
fX(q)=
0for
q<n(X)
. This can be interpreted as the
half of the
L1
-norm of the dierence vector of n-gram frequencies
over the joint n-gram set. There are many dierent possibilities to
measure commonalities of two sets, e. g., the Jaccard similarity and
Don’t hide in the frames: Note- and paern-based evaluation of automated melody extraction algorithms DLfM ’19, November 9, 2019, The Hague, Netherlands
its many variants. However, informal experiments showed that all
these options are strongly correlated with each other, so we decided
to use total variation distance as it has a better numerical solution
and is somewhat easier to compute.
To compare the ground truth and the extracted melodies, one
can calculate the pattern commonalities over a range of subsets
(solos) and n-gram lengths, and use the mean of absolute relative
dierence (compared to the ground truth) as a metrics for how well
the estimated values approximate the true pattern commonalities.
Formally, for two corresponding sets
SR,SE
with
K
elements
µi,µ
i
,
σn(SR,SE)=2
K(K1)Õ
i<j
|σn(µi,µj) − σn(µ
i,µ
j)|
σn(µi,µj)(7)
In practice, one will not compute all pairings but use a random sam-
ple. Moreover, for large
n
, the frequency distributions are more and
more degenerated, with very few common n-grams in any pair of
solos. Hence, it will be reasonable to restrict the evaluation to lower
values of
n
. Additionally, true and estimated pattern commonalities
can be correlated to yield another metrics.
4 RESULTS
In this section, we demonstrate the proposed evaluation metrics by
comparing the melody estimation performances of CRNN, CRNN
with Viterbi smoothing (CRNN-V) and Melodia algorithms on the
jazz solo recordings from the Weimar Jazz Database [
20
]. The WJD
contains 456 transcribed and annotated solo recordings (~13 hours)
from 78 artists with 13 dierent types of instruments, spanning a
time range from 1925 to 2009. The pitches are transcribed with MIDI
numbers, hence, we use a semitone resolution for both methods.
4.1 Training and Initialization
We trained the CRNN from scratch using only jazz solo tracks from
the WJD in order to have a system specialized for jazz music. For
this reason, we created train, validation, and test sets following
an artist-conditional random partitioning as described in [
7
]. This
resulted in 290, 75, and 91 tracks in train, validation, and test sets,
respectively. All tracks were initially downsampled to 22050 Hz
sampling rate and the time resolution was set to 11.6 ms for all
algorithms. The conguration of CRNN as well as the parameters
of SF-NMF were chosen following [
3
] where the target
F0
range
is between A1 = 55 Hz and A6 = 1760 Hz. For Melodia, we tried
dierent sets of parameters for optimizing the accuracy, but the
highest accuracy was obtained with the default parameters.
For the Viterbi smoothing algorithm, we calculated the frame-
level and note-level state transition probabilities from the train and
validation sets by simply counting the occurrences of each tran-
sition with subsequent normalization. To convert the frame-level
pitch track into a note track, we rst converted
F0
from Hertz to
MIDI values and then formed notes by simply grouping consecutive
frames with the same MIDI values. For all evaluations, we used the
test set with 51,825 note events in 91 solos from 14 artists playing
four dierent instruments, covering a time range from 1938 to 2009.
We calculated all pitch n-grams up to length 10, which resulted in
511,725 n-grams in total.
Figure 2: Frame-wise evaluations of CRNN, CRNN-V and
Melodia.
4.2 Frame-wise performance analysis
AME systems are usually evaluated with a frame-wise comparison
to the ground-truth using overall accuracy (OA), raw pitch accuracy
(RPA), raw chroma accuracy (RCA), voicing recall (VR), and voicing
false alarm rate (VFA) metrics as dened in [
21
]. Here, we compare
the performances of CRNN, CRNN-V and Melodia systems on a
test set with 91 solos from the Weimar Jazz Database [
20
]. The
evaluation results, given in Figure 2, show that, unsurprisingly, the
CRNN and CRNN-V are signicantly better than Melodia for all
metrics. This is due to training CRNN directly on jazz tracks whilst
Melodia performs a more generic melody estimation. CRNN and
CRNN-V have similar performances on RPA and RCA. CRNN has
a better OA and VR but worse VFA (higher). This is actually not
unexpected due to the nature of Viterbi smoothing. As the aim is to
obtain more precise estimations for the pattern mining task, Viterbi
smoothing results in a much higher rate of non-melody frames
than simple peak picking, that eventually decreases VFA but also
VR. It can be concluded that CRNN performs slightly better than
CRNN-V, however, this does not indicate how well these systems
perform for pattern extraction.
4.3 N-gram-based evaluations
4.3.1 N-gram matching evaluation. N-gram matching evaluation
was carried out according to the algorithm in Sec. 3.1 for each AME
system. The resulting precision, recall, and F1 scores are depicted
in Fig. 3. The CRNN models attain very high values for small
N
(cf.
Tab. 1) and keep a rather good performance for large
N
. Melodia
on the other hand has
F1=.
59 for unigrams and eectively no
correct recall at
N=
10. The curves also show that for CRNN
systems the decrease in performance with increasing
N
is much
slower than geometrical, whereas Melodia comes quite close to this
behaviour. This indicates that the errors for the CRNN systems are
not independent from each other, which is further corroborated
by the correlation coecients of the n-gram matching and the
frame-wise overall accuracy, which rapidly decreases for larger
N
. As stated earlier, the frame-wise evaluation can be used as an
approximation for note-wise evaluation scores, but it works better
for recall and F1 scores than for precision. However, from Tab. 1, it
seems that these correlations are themselves correlated with the
n-gram-based scores, so frame-wise accuracy might be only a good
approximation if overall accuracy is already very high. This justies
DLfM ’19, November 9, 2019, The Hague, Netherlands Frieler et al.
Recall
Precision
F1
12345678910
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
N−gram Length
CRNN CRNN−V MELODIA
Figure 3: F1, precision, and recall values for the n-gram
matching metrics for CRNN, CRNN-V and Melodia.
F1
Precision
Recall
5 6 7 8 9 10 5 6 7 8 9 10 5 6 7 8 9 10
0.0
0.1
0.2
0.3
0.4
0.5
Query length
Mean
CRNN CRNN−V MELODIA
Figure 4: CRNN, CRNN-V and Melodia retrieval results (F1,
precision, and recall) for exact pattern search (τ=
1
) and a
set of 25 search queries for each length value.
that our approach to generalize the matching evaluation to n-grams
of arbitrary length is necessary for good estimation of pattern
retrieval performances based on AME systems. One thing to note is
that precision for the CRNN-V system is systematically higher than
for the non-Viterbi version, which shows that the optimization for
precision was successful, even though this happens at the expense
of slightly lower recall and F1 scores.
4.3.2 Similarity search retrieval values. For the similarity search
evaluation, we used a randomly selected set of 150 queries with
n-gram lengths in the range of 5 to 10 in order to simulate realistic
application scenarios where one rarely searches for very short
patterns. For each length condition, we randomly picked 25 queries
from the ground truth test set without further constraints. For each
query, we ran a similarity search for each possible combination
of similarity thresholds
τ∈ {
0
.
5
,
0
.
6
, . . . ,
1
}
and three maximum
N AME F1 rF1 prec rprec rec rrec
1 CRNN 0.84 0.73 0.79 0.69 0.90 0.66
1 CRNN-V 0.85 0.68 0.85 0.65 0.86 0.60
1 MEL 0.59 0.40 0.52 0.36 0.71 0.39
5 CRNN 0.59 0.64 0.54 0.67 0.66 0.51
5 CRNN-V 0.58 0.59 0.57 0.67 0.60 0.41
5 MEL 0.17 0.44 0.13 0.40 0.25 0.39
10 CRNN 0.35 0.58 0.31 0.63 0.41 0.46
10 CRNN-V 0.34 0.55 0.33 0.64 0.36 0.37
10 MEL 0.03 0.40 0.02 0.38 0.06 0.36
Table 1: F1, precision (prec), and recall (rec) scores from the
n-gram matching evaluation along with correlation coe-
cients with overall frame-wise accuracy (OA) for a selection
of n-gram lengths N.
0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9
−50%
0%
50%
100%
Similarity Threshold
Percentage (%)
CRNN CRNN−V MELODIA
Figure 5: Relative result set sizes for similarity search with
τ<
1
. All values averaged across queries of length 7 and max.
length dierences. Left: Averaged absolute relative changes
in result sizes of AME compared to the ground truth. Right:
Averaged relative changes.
length dierences
δ∈ {
0
,
1
,
2
}
. Separate searches were run over
the n-gram databases derived from the ground truth and the AME
systems, and evaluation scores given in Sec. 3.2 were calculated.
The similarity search retrieval values for the exact search with
similarity thresholds
τ=
1(implying also a maximum length dif-
ference of 0) for the three dierent systems can be seen in Fig. 4.
As expected, the CRNNs outperform the Melodia estimation by a
large margin. Retrieval scores for the CRNN systems start with
values between 0.4 and 0.5, as could be expected from the n-gram
matching evaluation scores, and decrease rather steeply with query
length. The zigzag pattern for the CRNN version is rather puzzling,
and also the increase from query lengths 9 to 10. But this is probably
due to the specic set of queries or a result of the Viterbi smoothing.
The relative dierence of result set sizes for all other cases with
τ<
1is depicted in Fig. 5 for queries of length 7, graphs for the
other lengths are qualitatively similar. The relative dierences of
result set sizes increase with the similarity threshold, being on
average about 55 %–60% smaller for
τ=.
90, but nearly of the same
size for
τ=.
50. Since the averaged absolute change is larger than
the averaged signed dierence, this is pattern dependent. However,
on average less by-catch is retrieved by the AME systems. This is
Don’t hide in the frames: Note- and paern-based evaluation of automated melody extraction algorithms DLfM ’19, November 9, 2019, The Hague, Netherlands
1 2 3 4 5 6 1 2 3 4 5 6
−1.0
−0.5
0.0
0.5
1.0
N−gram Length
CRNN CRNN−V MELODIA
Figure 6: Results of comparing pattern commonalities for
n-gram lengths 1–6. Left: Spearman correlation coecients
between estimated and ground-truth commonalities. Right:
Relative dierences of estimated and ground-truth values
with regard to ground-truth values. Positive/negative values
mean that pattern commonalities are over/underestimated.
probably due to the fact that the transcription errors introduced
by the AME systems are of a dierent nature than the pattern
variations used by the performers.
4.3.3 Paern commonalities evaluation. For 10 batches with 10
randomly selected performers each, we calculated pattern common-
alities between all possible pairs for n-gram lengths 1 to 6. This was
done separately for the ground truth and the three AME systems.
From this, we calculated Spearman correlations between similarity
values obtained from the ground truth and the AME estimations.
Furthermore, we calculated relative dierences of the AME values
with respect to the ground truth values. Results can be seen in Fig.
6. For the CRNN models correlations are very high and stay rather
high with increasing n-gram length (
rN=6=.
80 for CRNN and
rN=6=.
76 for CRNN-V). For Melodia, correlations are also rather
high for small
N
but drop quickly (
rN=6=.
32). Consequently, the
mean relative dierences are close to zero for the CRNN systems
and short n-grams, but for larger
N
they are overestimating pat-
tern commonalities, whereas Melodia grossly underestimates the
pattern similarity values already for N=3.
5 DISCUSSION
In this paper, we proposed several new evaluation methods for
AME systems driven by the needs of musicological applications
in jazz research. We demonstrated that a specialization of AME
systems for specic data sets and purposes is an inevitable step
for high-quality research applications. General algorithms trained
on publicly and readily available datasets from a dierent musical
domain are unlikely to work out of the box for a genre like jazz. We
also showed that evaluations should be tailored for secondary tasks
and derived features beyond the primary goal of estimating the
main melody. Whereas the retrieval values for note tracks are rather
satisfying for small to moderate n-gram lengths, it is very hard to
retain this good measure for longer n-gram lengths, which is, of
course, a function of quality of the primary note estimation, which
has to be very high ab initio. Furthermore, frame-wise evaluation
metrics only provide a good estimate for note-based evaluation, if
the quality of extraction is high, but not for n-gram-based measures.
On the other hand, for certain derived tasks of a more statistical
nature which average across many events, such as pattern com-
monalities, even sub-par performances of AME systems might still
give reasonable and usable results, but again only, if a certain level
of quality is reached. The Melodia note estimations, for example,
are not sucient in this application scenario at all.
For pattern research, even a single frame error can be destructive
depending on when it occurs, e. g., inside a note event. As a result,
the precision of an AME system according to the n-gram matching
metrics is one of the most relevant indicators about how it will
behave on pattern search tasks. The CRNN system already has a
temporal modelling via RNN stage but the results show that CRNN-
V has a higher precision for all n-grams. Hence, the proposed Viterbi
smoothing, even not better than the CRNN for F1 and recall, might
be useful if precision is the main goal.
Even though the CRNN systems show a highly improved perfor-
mance, there is still room for further improvements. As an example,
current AME systems are devised to nd the ’dominant’ melody.
However, in jazz solo tracks, the dominant melody may not be
necessarily the soloist all the time, i. e., accompanying instruments
such as piano and bass can become dominant for small time inter-
vals. Such notes from the background, although being dominant,
have to be correctly estimated as non-melody from a pattern search
point of view. One solution for this problem is to integrate instru-
ment information into AME systems to be able to extract only notes
from particular instruments. Especially for jazz tracks, meta-data is
available through jazz discographies such as Tom Lord
3
or Linked
Jazz
4
and solo instrument information can also be retrieved from
such sources. First experiments showed that using (frame-based) in-
strument information was able to boost note-wise accuracy beyond
the 90 % sonic wall. Furthermore, all evaluation results reported
here are average values, but there is in fact considerable variation
in the AME results, as can be seen in the boxplots in Fig 3. It would
be desirable to be able to predict the AME quality for a solo from
available metadata or from audio features. We assume that record-
ing quality (e. g., the prominence of the solo instrument in the mix)
as well as instrument timbre qualities of certain performers (e. g.,
strong vibrato) have strong inuences on AME performance.
ACKNOWLEDGMENTS
The “Dig That Lick” project was funded by the “Diggin’ into Data
Challenge” as DFG project PF 669/9-1 (Germany), ESRC project
ES/R004005/1 (UK), ANR project ANR-16-DATA-0005 (France), and
NEH project NEH-HJ-253587-17 (USA).
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A VITERBI SMOOTHING WITH A TIME- AND
NOTE-DEPENDENT TRANSITION MATRIX
In a simple Viterbi algorithm, the current frame-level state at frame
t
is conditioned only on the previous frame-level state at frame
t
1. Our novel contribution here is that we model the note-level
state transitions as well and condition the current frame-level state
also on the previous note-level state. The rationale behind this
comes from the inherent structure in music, where the consecutive
notes in a piece are correlated. One can utilize this information
in computing the next frame-level state. In addition, we account
for the phenomenon that the dependency between notes decreases
with increasing time dierence (oset-onset interval) in modelling
note-level state transitions.
Formally, we denote output note classes of the CRNN by
Um=
{u1:U}
, the non-melody class by
u0
and the list of all classes by
U
. We also denote the frame-level hidden state at frame
t
by
sf
t
U={u0:U}
and the note-level state by
sn
t1,t2Um
where
t1
and
t2
represent the onset and oset frames respectively. We dene the
note-level state transition probability as
p(sn
t3,t4|sn
t1,t2,t3t2)where t2<t3.(8)
Then, we dene the time- and note-dependent transition probability
distributions as
p(sf
t|sf
t1,sn
t1,t2,tt2)where t2<t.(9)
Note that the dependency on the previous note state
sn
t1,t2
and time
dierence drops for
sf
t=u0
, since (8) does not model transitions to
the non-melody state. On the other hand, for
sf
t,u0
, we choose
the expressions in (9) and (8) to be equal at
t=t3
, so that
sn
t3,t4=
sf
t=ui, where uiUm.
Both note-level state transitions and frame-level state transitions
can be computed from the available data by simply counting the
occurrences. Analysis of the frame-level transitions in the Weimar
Jazz Database (WJD) [
20
] shows that a direct transition from a
note to another note happens in less than 0.05% of the transitions.
As a result, we may further simplify the model by keeping the
dependency on the previous note-level state only for the case where
sf
t,u0and sf
t1=u0.
... Common practical applications of AMT systems include transcribing music to traditional score notation [97,112,18,38,31,50,33], extracting melodies from a signal with various sound sources [55,100,8,39,45,63], extracting chords from audio [46,54,22,30,65,61,53] and generating sheet music from pitch representations [62,69]. These tasks are difficult and time-consuming for human annotators to perform, require significant expertise and are prone to error [102]. ...
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This work explores the use of source-filter models for pitch salience estimation and their combination with different pitch tracking and voicing estimation methods for automatic melody extraction. Source-filter models are used to create a mid-level representation of pitch that implicitly incorporates timbre information. The spectrogram of a musical audio signal is modelled as the sum of the leading voice (produced by human voice or pitched musical instruments) and accompaniment. The leading voice is then modelled with a Smoothed Instantaneous Mixture Model (SIMM) based on a source-filter model. The main advantage of such a pitch salience function is that it enhances the leading voice even without explicitly separating it from the rest of the signal. We show that this is beneficial for melody extraction, increasing pitch estimation accuracy and reducing octave errors in comparison with simpler pitch salience functions. The adequate combination with voicing detection techniques based on pitch contour characterisation leads to significant improvements over state-of-the-art methods, for both vocal and instrumental music.
Conference Paper
Full-text available
Due to the scarcity of labeled data, most melody extraction algorithms do not rely on fully data-driven processing blocks but rather on careful engineering. For example, the Melodia melody extraction algorithm employs a pitch contour selection stage that relies on a number of heuristics for selecting the melodic output. In this paper we explore the use of a discriminative model to perform purely data-driven melodic contour selection. Specifically, a discriminative binary classifier is trained to distinguish melodic from non-melodic contours. This classifier is then used to predict likelihoods for a track's extracted contours, and these scores are decoded to generate a single melody output. The results are compared with the Melodia algorithm and with a generative model used in a previous study. We show that the discriminative model outperforms the generative model in terms of contour classification accuracy, and the melody output from our proposed system performs comparatively to Melodia. The results are complemented with error analysis and avenues for future improvements.
Conference Paper
In this paper, we focus on transcribing walking bass lines, which provide clues for revealing the actual played chords in jazz recordings. Our transcription method is based on a deep neural network (DNN) that learns a mapping from a mixture spectrogram to a salience representation that emphasizes the bass line. Furthermore, using beat positions, we apply a late-fusion approach to obtain beat-wise pitch estimates of the bass line. First, our results show that this DNN-based transcription approach outperforms state-of-the-art transcription methods for the given task. Second, we found that an augmentation of the training set using pitch shifting improves the model performance. Finally, we present a semi-supervised learning approach where additional training data is generated from predictions on unlabeled datasets.