15th International Society for Music Information Retrieval Conference (ISMIR 2014)

SPOTTING A QUERY PHRASE FROM POLYPHONIC MUSIC AUDIOSIGNALS BASED ON SEMI-SUPERVISED NONNEGATIVE MATRIXFACTORIZATIONTaro Masuda1

Kazuyoshi Yoshii2 Masataka Goto3 Shigeo Morishima1
1
Waseda University 2 Kyoto University
3
National Institute of Advanced Industrial Science and Technology (AIST)
masutaro@suou.waseda.jp yoshii@i.kyoto-u.ac.jp m.goto@aist.go.jp shigeo@waseda.jp

ABSTRACTThis paper proposes a query-by-audio system that aims todetect temporal locations where a musical phrase given asa query is played in musical pieces. The “phrase” in thispaper means a short audio excerpt that is not limited toa main melody (singing part) and is usually played by asingle musical instrument. A main problem of this task
is that the query is often buried in mixture signals consisting of various instruments. To solve this problem, we
propose a method that can appropriately calculate the distance between a query and partial components of a musical piece. More specifically, gamma process nonnegative
matrix factorization (GaP-NMF) is used for decomposing
the spectrogram of the query into an appropriate number ofbasis spectra and their activation patterns. Semi-supervised
GaP-NMF is then used for estimating activation patterns of
the learned basis spectra in the musical piece by presuming
the piece to partially consist of those spectra. This enables
distance calculation based on activation patterns. The experimental results showed that our method outperformed
conventional matching methods.

Musical pieceQueryphraseSimilarity
Location of the query

Time

Figure 1. An overview of the proposed method.
eral information of musical scores [9, 16, 23, 31, 39] (suchas MIDI files) or some speech corpus [36] should be prepared for a music database in advance of QBH. To overcome this limitation, some studies tried to automaticallyextract main melodies from music audio signals included
in a database [25, 34, 35]. Other studies employ chroma
vectors to characterize a query and targeted pieces without
the need of symbolic representation or transcription [2].
We propose a task that aims to detect temporal locations at which phrases similar to the query phrase appear
in different polyphonic musical pieces. The term “phrase”
means a several-second musical performance (audio clip)
usually played by a single musical instrument. Unlike
QBH, our method needs no musical scores beforehand.
A key feature of our method is that we aim to find shortsegments within musical pieces, not musical pieces themselves. There are several possible application scenarios inwhich both non-experts and music professionals enjoy thebenefits of our system. For example, ordinary users could
intuitively find a musical piece by playing just a characteristic phrase used in the piece even if the title of the piece isunknown or forgotten. In addition, composers could learn
what kinds of arrangements are used in existing musicalpieces that include a phrase specified as a query.
The major problem of our task lies in distance calculation between a query and short segments of a musicalpiece. One approach would be to calculate the symbolic
distance between musical scores. However, this approachis impractical because even the state-of-the-art methods of

1. INTRODUCTION
Over a decade, a lot of effort has been devoted to developing music information retrieval (MIR) systems that aim
to find musical pieces of interest by using audio signals as
the query. For example, there are many similarity-based retrieval systems that can find musical pieces having similar
acoustic features to those of the query [5,13,21,22]. Audio
fingerprinting systems, on the other hand, try to find a musical piece that exactly matches the query by using acoustic
features robust to audio-format conversion and noise contamination [6,12,27]. Query-by-humming (QBH) systems
try to find a musical piece that includes the melody specified by users’ singing or humming [19]. Note that in genc Taro Masuda, Kazuyoshi Yoshii, Masataka Goto, Shigeo⃝
Morishima.
Licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). Attribution: Taro Masuda, Kazuyoshi Yoshii,
Masataka Goto, Shigeo Morishima. “Spotting a Query Phrase from Polyphonic Music Audio Signals Based on Semi-supervised Nonnegative Matrix Factorization”, 15th International Society for Music Information Retrieval Conference, 2014.

227

15th International Society for Music Information Retrieval Conference (ISMIR 2014)
automatic music transcription [4,11,17,29,38] work poorly
for standard popular music. Conventional distance calculation based on acoustic features [5] is also inappropriate because acoustic features of a phrase are drastically distorted
if other sounds are superimposed in a musical piece. In
addition, since it would be more useful to find locations inwhich the same phrase is played by different instruments,
we cannot heavily rely on acoustic features.
In this paper we propose a novel method that can perform phrase spotting by calculating the distance between aquery and partial components of a musical piece. Our conjecture is that we could judge whether a phrase is included
or not in a musical piece without perfect transcription, likethe human ear can. More specifically, gamma process nonnegative matrix factorization (GaP-NMF) [14] is used fordecomposing the spectrogram of a query into an appropriate number of basis spectra and their activation patterns.
Semi-supervised GaP-NMF is then used for estimating activation patterns of the fixed basis spectra in a target musical piece by presuming the piece to partially consist of
those spectra. This enables appropriate matching based on
activation patterns of the basis spectra forming the query.

phrase is included in the musical piece when decomposing
Y . This means that we need to make use of W (x) as muchas possible for representing Y . The Bayesian framework
is a natural choice for reflecting such a prior belief.

2. PHRASE SPOTTING METHOD

We then perform semi-supervised NMF for decomposing
the spectrogram of the musical piece Y by fixing a partof basis spectra with W (x) . The idea of giving W as adictionary during inference has been widely adopted [3, 7,
15, 18, 24, 26, 28, 30, 33, 38].
We formulate Bayesian NMF for representing the spectrogram of the musical piece Y by extensively using the
fixed bases W (x) . To do this, we put different gamma priors on H (y) and H (f ) . The shape parameter of the gamma
prior on H (y) is much larger than that of the gamma prioron H (f ) . Note that the expectation of the gamma distribution is proportional to its shape parameter.

2.2 NMF for Decomposing a Query
We use the gamma process NMF (GaP-NMF) [14] forapproximating X as the product of a nonnegative vectorθ ∈ RKx and two nonnegative matrices W (x) ∈ RM ×Kx
and H (x) ∈ RKx ×Nx . More specifically, the original matrix X is factorized as follows:
Xmn ≈

Kx
∑

(x)

(x)

θk Wmk Hkn ,

(1)

k=1
(x)

where θk is the overall gain of basis k, Wmk is the power(x)of basis k at frequency m, and Hkn is the activation ofbasis k at time n. Each column of W (x) represents a basis
spectrum and each row of H (x) represents an activation
pattern of the basis over time.
2.3 Semi-supervised NMF for Decomposing a Musical
Piece

This section describes the proposed phrase-spotting
method based on nonparametric Bayesian NMF.
2.1 Overview
Our goal is to detect the start times of a phrase in the polyphonic audio signal of a musical piece. An overview of the
proposed method is shown in Figure 1. Let X ∈ RM ×Nx
and Y ∈ RM ×Ny be the nonnegative power spectrogramof a query and that of a target musical piece, respectively.
Our method consists of three steps. First, we perform NMF
for decomposing the query X into a set of basis spectra
W (x) and a set of their corresponding activations H (x) .
Second, in order to obtain temporal activations of W (x)in the musical piece Y , we perform another NMF whose
basis spectra consist of a set of fixed basis spectra W (x)and a set of unconstrained basis spectra W (f ) that are required for representing musical instrument sounds except
for the phrase. Let H (y) and H (f ) be sets of activations of
Y corresponding to W (x) and W (f ) , respectively. Third,
the similarity between the activation patterns H (x) in thequery and the activation patterns H (y) in the musical pieceis calculated. Finally, we detect locations of a phrase where
the similarity takes large values.
There are two important reasons that “nonparametric”“Bayesian” NMF is needed. 1) It is better to automaticallydetermine the optimal number of basis spectra according
to the complexity of the query X and that of the musicalpiece Y . 2) We need to put different prior distributions
on H (y) and H (f ) to put more emphasis on fixed basis
spectra W (x) than unconstrained basis spectra W (f ) . If
no priors are placed, the musical piece Y is often represented by using only unconstrained basis spectra W (f ) .
A key feature of our method is that we presume that the

2.4 Correlation Calculation between Activation
Patterns
After the semi-supervised NMF is performed, we calculate
the similarity between the activation patterns H (x) in thequery and the activation patterns H (y) in a musical piece tofind locations of the phrase. We expect that similar patterns
appear in H (y) when almost the same phrases are played in
the musical piece even if those phrases are played by different instruments. More specifically, we calculate the sum of
the correlation coefficients r at time n between H (x) andH (y) as follows:
(
) (
)
(x) T
(y)
(y)
(x)
Kx
h
−
h
h
−
h
∑
k1
kn
k1
kn
1
r(n) =
, (2)
(x)
(y)
(x)
(y)
Kx Nx
h −h
h −h
k=1

k1

k1

kn

kn

where
(·)

hki

(·)

hkn

228

=

[
]T
(·)
(·)
Hki · · · Hk(i+Nx −1) ,
x
1 ∑
(·)
H
× [1 · · · 1]T .
Nx j=1 k(n+j−1)

(3)

N

=

(4)

15th International Society for Music Information Retrieval Conference (ISMIR 2014)
Finally, we detect a start frame n of the phrase by finding
peaks of the correlation coefficients over time. This peak
picking is performed based on the following thresholding
process:

After obtaining ϕkmn and ωmn , we update the parametersof the GIG distributions as follows:(W )γmk = a(W ) ,(W )ρmk = b(W ) + Eq [θk ]∑ Eq [Hkn ]

,
ωmn
[ ]∑
[
]
1
1
(W )
τmk = EqVmn ϕ2kmn Eq, (11)
θk n
Hkn∑ Eq [Wmk ](H)(H)
γkn = a(H) , ρkn = b(H) + Eq [θk ]
,
ωmn
m
[ ]∑
[
]
1
1
(H)
2
τkn = EqVmn ϕkmn Eq, (12)
θk m
Wmk∑ ∑ Eq [Wmk Hkn ]
α
(θ)
(θ)
γk = , ρk = αc +
,
K
ωmn
m n
[
]
∑∑
1
(θ)
Vmn ϕ2kmn Eqτk =. (13)
Wmk Hknm nnr(n) > µ + 4σ,(5)where µ and σ denote the overall mean and standard deviation of r(n), respectively, which were derived from all
the musical pieces.

2.5 Variational Inference of GaP-NMF
This section briefly explains how to infer nonparametric
Bayesian NMF [14], given a spectrogram V ∈ RM ×N .
We assume that θ ∈ RK , W ∈ RM ×K , and H ∈ RK×N
are stochastically sampled according to a generative process. We choose a gamma distribution as a prior distribution on each parameter as follows:p(Wmk )
p(Hkn )p(θk )()
Gamma a(W ) , b(W ) ,()= Gamma a(H) , b(H) ,)(α= Gamma, αc ,K

The expectations of W , H and θ are required in Eqs. (9)and (10). We randomly initialize the expectations of W ,H, and θ and iteratively update each parameter by using
those formula. As the number of iterations increases, thevalue of Eq [θk ] over a certain level K +∑decreases. Therefore, if the value is 60 dB lower than k Eq [θk ], we remove the related parameters from consideration, whichmakes the calculation faster. Eventually, the number ofeffective bases, K + , gradually reduces during iterations,suggesting that the appropriate number is automatically determined.

=(6)

where α is a concentration parameter, K is a sufficiently
large integer (ideally an infinite number) compared with
the number of components in the mixed sound, and c is theinverse of the mean value of V :
(
c=

1 ∑∑
Vmn
MN m n3. CONVENTIONAL MATCHING METHODSWe describe three kinds of conventional matching methods used for evaluation. The first and the second methods
calculate the Euclidean distance between acoustic features(Section 3.1) and that between chroma vectors (Section3.2), respectively. The third method calculates the ItakuraSaito (IS) divergence between spectrograms (Section 3.3).

)−1
.

(7)

3.1 MFCC Matching Based on Euclidean DistanceWe then use the generalized inverse-Gaussian (GIG) distribution as a posterior distribution as follows:()(W ) (W ) (W )GIG γmk , ρmk , τmk ,()(H) (H) (H)q(Hkn ) = GIG γkn , ρkn , τkn ,)((θ) (θ) (θ).
q(θk ) = GIG γk , ρk , τkq(Wmk )

Temporal locations in which a phrase appears are detectedby focusing on the acoustic distance between the queryand a short segment extracted from a musical piece. In
this study we use Mel-frequency cepstrum coefficients(MFCCs) as an acoustic feature, which have commonly
been used in various research fields [1, 5]. More specifically, we calculate a 12-dimensional feature vector fromeach frame by using the Auditory Toolbox Version 2 [32].
The distance between two sequences of the feature vector
extracted from the query and the short segment is obtainedby accumulating the frame-wise Euclidean distance overthe length of the query.
The above-mentioned distance is iteratively calculatedby shifting the query frame by frame. Using a simple peakpicking method, we detect locations of the phrase in which
the obtained distance is lower than m − s, where m ands denote the mean and standard deviation of the distanceover all frames, respectively.

=(8)

To estimate the parameters of these distributions, we first
update other parameters, ϕkmn , ωmn , using the following
equations.

ϕkmn

=

ωmn

=

[
]−1
1
Eq
,
θk Wmk Hkn∑
Eq [θk Wmk Hkn ] .

(9)
(10)

k

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15th International Society for Music Information Retrieval Conference (ISMIR 2014)
an extremely large value (outlier). The mean of the distance tends to be excessively biased by such an outlier. In
addition, we ignore values of the distance which are morethan 106 when calculating S for practical reasons (almost
x ,j)
3
4
all values of E(NC(Nx ,j) range from 10 to 10 ). Once the end
point is detected, we can also obtain the start point of thephrase by simply tracing back along the path from the end
point.

3.2 Chromagram Matching Based on Euclidean
Distance
In this section, temporal locations in which a phrase appears are detected in the same manner as explained in Section 3.1. A difference is that we extracted a 12-dimentional
chroma vector from each frame by using the MIRtoolbox [20]. In addition, we empirically defined the thresholdof the peak-picking method as m − 3s.
3.3 DP Matching Based on Itakura-Saito Divergence

4. EXPERIMENTS

In this section, temporal locations in which a phrase appears are detected by directly calculating the Itakura-Saito(IS) divergence [8, 37] between the query X and the musical piece Y . The use of the IS divergence is theoreticallyjustified because the IS divergence poses a smaller penalty
than standard distance measures such as the Euclidean distance and the Kullback-Leibler (KL) divergence when the
power spectrogram of the query is included in that of themusical piece.
To efficiently find phrase locations, we use a dynamic
programming (DP) matching method based on the IS divergence. First, we make a distance matrix D ∈ RNx ×Ny
in which each cell D(i, j) is the IS divergence between thei-th frame of X and the j-th frame of Y (1 ≤ i ≤ Nx and1 ≤ j ≤ Ny ). D(i, j) is given by
)
∑(
Xmi
Xmi
D(i, j) = DIS (Xi |Yj ) =
− log
+
−1 ,
Ymj
Ymj
m
(14)
where m indicates a frequency-bin index. We then let
E ∈ RNx ×Ny be a cumulative distance matrix. First, E
is initialized as E(1, j) = 0 for any j and E(i, 1) = ∞ for
any i. E(i, j) can be sequentially calculated as follows: 1) E(i−1, j −2) + 2D(i, j −1) E(i, j) = min 2) E(i−1, j −1) + D(i, j)3) E(i−2, j −1) + 2D(i−1, j)

This section reports comparative experiments that wereconducted for evaluating the phrase-spotting performancesof the proposed method described in Section 2 and thethree conventional methods described in Section 3.

+D(i, j).

(15)

Finally, we can obtain E(Nx , j) that represents the distance between the query and a phrase ending at the j-thframe in the musical piece. We let C ∈ RNx ×Ny be a cumulative cost matrix. According to the three cases 1), 2),
and 3), C(i, j) is obtained as follows: 1) C(i − 1, j − 2) + 3
2) C(i − 1, j − 1) + 2(16)
C(i, j) =3) C(i − 2, j − 1) + 3.
This means that the length of a phrase is allowed to range
from one half to two times of the query length.
Phrase locations are determined by finding the local
x ,j)minima of the regularized distance given by E(NC(Nx ,j) . Morespecifically, we detect locations in which values of the obtained distance are lower than M − S/10, where M and S
denote the median and standard deviation of the distanceover all frames, respectively. A reason that we use the median for thresholding is that the distance sometimes takes

230

4.1 Experimental Conditions
The proposed method and the three conventional methods
were tested under three different conditions: 1) Exactly thesame phrase specified as a query was included in a musicalpiece (exact match). 2) A query was played by a different
kind of musical instruments (timbre change). 3) A query
was played in a faster tempo (tempo change).
We chose four musical pieces (RWC-MDB-P-2001
No.1, 19, 42, and 77) from the RWC Music Database:
Popular Music [10]. We then prepared 50 queries: 1) 10
were short segments excerpted from original multi-trackrecordings of the four pieces. 2) 30 queries were playedby three kinds of musical instruments (nylon guitar, classic piano, and strings) that were different from those originally used in the four pieces. 3) The remaining 10 queries
were played by the same instruments as original ones, but
their tempi were 20% faster. Each query was a short performance played by a single instrument and had a duration
ranging from 4 s to 9 s. Note that those phrases were notnecessarily salient (not limited to main melodies) in musical pieces. We dealt with monaural audio signals sampled
at 16 kHz and applied the wavelet transform by shifting
short-time frames with an interval of 10 ms. The reason
that we did not use short-time Fourier transform (STFT)
was to attain a high resolution in a low frequency band.
We determined the standard deviation of a Gabor wavelet
function to 3.75 ms (60 samples). The frequency interval
was 10 cents and the frequency ranged from 27.5 (A1) to8000 (much higher than C8) Hz.
When a query was decomposed by NMF, the hyperparameters were set as α = 1, K = 100, a(W ) = b(W ) =(x)a(H) = 0.1, and b(H ) = c. When a musical piece
was decomposed by semi-supervised NMF, the hyperpa(y)rameters were set as a(W ) = b(W ) = 0.1, a(H ) = 10,(f )a(H ) = 0.01, and b(H) = c. The inverse-scale parameterb(H) was adjusted to the empirical scale of the spectrogramof a target audio signal. Also note that using smaller valuesof a(·) makes parameters sparser in an infinite space.
To evaluate the performance of each method, we calculated the average F-measure, which has widely been usedin the field of information retrieval. The precision rate wasdefined as a proportion of the number of correctly-found15th International Society for Music Information Retrieval Conference (ISMIR 2014)

MFCC
ChromaDP
Proposed

Precision (%)
24.8
33.4
1.9
53.6

Recall (%)
35.0
61.0
55.0
63.0

F-measure (%)
29.0
43.1
3.6
57.9

(a)

Table 1. Experimental results in a case that exactly thesame phrase specified as a query was included in a musicalpiece.

MFCC
ChromaDP
Proposed

Precision (%)
0
18.1
1.1
26.9

Recall (%)
0
31.7
66.3
56.7

(b)
(b)

F-measure (%)
0
23.0
6.2
36.5

(c)

Table 2. Experimental results in a case that a query wasplayed by a different kind of instruments.

MFCC
ChromaDP
Proposed

Precision (%)
0
12.0
0.5
15.8

Recall (%)
0
19.0
20.0
45.0

F-measure (%)
0
14.7
2.7
23.4

Table 3. Experimental results in a case that the queryphrases was played in a faster tempo.

Figure 2. Sum of the correlation coefficients r(n). The
target piece was RWC-MDB-P-2001 No.42. (a) The query
was exactly the same as the target saxophone phrase. (b)The query was played by strings. (c) The query was played
20% faster than the target.
based method often detected false locations including asimilar chord progression.
Although our method worked best of the four, the accuracy of the proposed method should be improved for practical use. A major problem is that the precision rate wasrelatively lower than the recall rate. Wrong locations weredetected when queries were played in staccato manner because many false peaks appeared at the onset of staccato
notes.
As for computational cost, it took 29746 seconds tocomplete the retrieval of a single query by using our
method. This was implemented in C++ on a 2.93 GHzIntel Xeon Windows 7 with 12 GB RAM.

phrases to that of all the retrieved phrases. The recall rate
was defined as a proportion of the number of correctlyfound phrases to that of all phrases included in the database(each query phrase was included only in one piece of music). Subsequently, we calculated the F-measure F by
R
F = P2P+R, where P and R denote the precision and recall rates, respectively. We regarded a detected point as acorrect one when its error is within 50 frames (500 ms).
4.2 Experimental Results
Tables 1–3 show the accuracies obtained by the four methods under each condition. We confirmed that our method
performed much better than the conventional methods interms of accuracy. Figure 2 shows the value of r(n) obtained from a musical piece in which a query phrase (originally played by the saxophone) is included. We found thatthe points at which the query phrase starts were correctly
spotted by using our method. Although the MFCC-based
method could retrieve some of the query phrases in theexact-match condition, it was not robust to timbre change
and tempo change. The DP matching method, on the other
hand, could retrieve very few correct points because the IS
divergence was more sensitive to volume change than thesimilarity based on spectrograms. Although local minimaof the cost function often existed at correct points, thoseminima were not sufficiently clear because it was difficult
to detect the end point of the query from the spectrogram ofa mixture audio signal. The chroma-based method worked
better than the other conventional methods. However, it
did not outperform the proposed method since the chroma-

5. CONCLUSION AND FUTURE WORKThis paper presented a novel query-by-audio method thatcan detect temporal locations where a phrase given asa query appears in musical pieces. Instead of pursuing
perfect transcription of music audio signals, our method
used nonnegative matrix factorization (NMF) for calculating the distance between the query and partial componentsof each musical piece. The experimental results showedthat our method performed better than conventional matching methods. We found that our method has a potential tofind correct locations in which a query phrase is played bydifferent instruments (timbre change) or in a faster tempo(tempo change).
Future work includes improvement of our method, especially under the timbre-change and tempo-change conditions. One promising solution would be to classify basis
spectra of a query into instrument-dependent bases (e.g.,231

15th International Society for Music Information Retrieval Conference (ISMIR 2014)
noise from the guitar) and common ones (e.g., harmonic
spectra corresponding to musical notes) or to create an universal set of basis spectra. In addition, we plan to reducethe computational cost of our method based on nonparametric Bayesian NMF.
Acknowledgment: This study was supported in part by the JST
OngaCREST project.

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