A Musical Mood Trajectory Estimation Method Using
Lyrics and Acoustic Features
Naoki Nishikawa†nnishika@kuis.kyotou.ac.jp

Katsutoshi Itoyama†
iytoyama@kuis.kyotou.ac.jp

Hiromasa Fujihara‡ ∗h.fujihara@aist.go.jp

Masataka Goto‡
m.goto@aist.go.jp

Tetsuya Ogata†ogata@kuis.kyoto-u.ac.jp

Hiroshi G. Okuno†
okuno@kuis.kyoto-u.ac.jp† Dept. of Intelligence Science and Technology, Grad. School of Informatics, Kyoto University‡ National Institute of Advanced Industrial Science and Technology (AIST)∗ School of Electronic Engineering and Computer Science, The Queen Mary University of London

ABSTRACT

the acoustic features but also from the expression of theemotions. MIR systems based on the similarity of musical moods are expected to provide more intuitive retrieval
results with human sensibility than systems based on only
acoustic features [1, 2]. Various methods for musical moodestimation [4–12] have been reported, and these methods
are still being developed. This is because musical moods arehighly subjective and diﬃcult to quantify [3].
We believe that the following two aspects are importantfor musical mood representation:

In this paper, we present a new method that represents anoverall musical time-varying impression of a song by a pairof mood trajectories estimated from lyrics and audio signals.
The mood trajectory of the lyrics is obtained by using theprobabilistic latent semantic analysis (PLSA) to estimate
topics (representing impressions) from words in the lyrics.
The mood trajectory of the audio signals is estimated fromacoustic features by using the multiple linear regression analysis. In our experiments, the mood trajectories of 100 songsin Last.fm’s Best of 2010 were estimated. The detailed analysis of the 100 songs conﬁrms that acoustic features provide
more accurate mood trajectory and the 21% resulting moodtrajectories are matched to realistic musical mood available
at Last.fm.

1. musical moods depend on both lyrics and audio signals
2. musical moods have time-varying characteristics.
Regarding the former, lyrics have a large inﬂuence on musical moods because lyrics represent these moods linguistically. Some musical pieces have contradicting moods in theirlyrics and audio signals, e.g., a happy melody with melancholic lyrics. To represent these musical moods, we needboth lyrics and audio signals. In fact, the accuracy of musical mood detection is improved by using both lyrics andaudio signals [8–10]. Regarding the latter, humans receive
time-varying impressions from music [11,12]. Some pieces ofmusic have highly diﬀerent moods between sections such as
the verses and choruses. To represent these musical moods,
we need to model their time-varying aspect.
In previous MIR research [4–12], there was no researchdealing with these two points to the authors’ knowledge.
Research using only lyrics or audio signals [4–7] cannot reﬂect musical moods depend on both lyrics and audio signals.
Research using both lyrics and audio signals [8–10] focusedon static musical moods. Research focusing on time-varying
musical moods [11, 12] used only audio signals.
In this paper, a time-varying musical mood (a mood trajectory) estimation method using both lyrics and acoustic
features is proposed. We estimate the mood trajectories oflyrics and audio signals separately. In other words, we represent time-varying musical moods not as a mixture of lyrics
and audio trajectories but as a pair of these two trajectories.
This multilateral musical mood representation can describe
conﬂicts between the complex time-varying musical moodsof the lyrics and audio signals. We assume that humans
feel a constant mood in a certain musical section deﬁned
as a phrase. Under this assumption, the mood trajectories

Categories and Subject Descriptors
H.5.5 [Sound and Music Computing]: Modeling

General Terms
Algorithm, Design

Keywords
musical mood representation, musical mood estimation, timevarying impression, mood trajectory, lyrics and audio signals
music information retrieval

1. INTRODUCTION
Musical mood estimation is gaining increasing attention
in recent years in musical information retrieval (MIR) research [3]. Human listeners recognize music not only from

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51

Training
lyricsCan’ t buy me love...
All you need is love...

PLSA


`

audio signals`

MLR

Estimation
Hold me tight...

I love you...

PLSA

MLR

Figure 2: Russell’s circumplex model

Figure 1: Overview of mood trajectory estimation
methodthe mood trajectories of lyrics and an audio signal are estimated as sequences of coordinates on V-A space from lyrics
and an audio signal divided into phrases. The musical moodof an input song is represented by combining the mood trajectories of lyrics and an audio signal.
The mood trajectory of lyrics is estimated by using a
PLSA [14] constrained by aﬀective words as prior knowledge. The PLSA is a probabilistic generative model basedon the co-occurrence data of documents (lyrics) and words.
This model is used to estimate semantic relations between
words and semantic topics of documents. As the PLSA isbased only on the co-occurrence data of documents (lyrics)
and words, a lot of training data can be used without labeling. Because of this, the PLSA is widely used in natural
language processing [15, 16].
As the normal PLSA focuses on the co-occurrence data of
documents and words, the estimated semantic relations andlatent topics are not certain to represent moods. By usingaﬀective words as prior knowledge and estimating parameters of the PLSA by maximum a posterior (MAP) estimation, the estimated semantic relations and latent topics are
mapped on V-A space.
The mood trajectory of an audio signal is estimated by using a multiple linear regression (MLR). The input variables
are the phrases’ acoustic features, and the output variables
are the phrases’ V-A coordinates. By using a MLR, acoustic
features can be mapped on V-A space. In a training phase,combination of phrases and V-A coordinates of phrases are
made manually as training data, and the MLR regressor istrained to relations between acoustic features and V-A coordinates of phrases. In an estimating phase, the V-A coordinates of phrases are calculated from the acoustic featuresof phrases by a trained MLR regressor, and the estimated
V-A coordinates construct a mood trajectory.

are estimated as sequences of coordinates on V-A space [13]from lyrics and audio signals divided into phrases. The VA space has two axes: valence (positive-to-negative) andarousal (high-to-low energy).
A mood trajectory of lyrics is estimated by the probabilistic latent semantic analysis (PLSA) [14]. As the normal
PLSA focuses on the co-occurrence data of documents andwords, estimated latent topics are not certain to represent
moods. To obtain emotional representation from a PLSA,
topics are mapped to V-A space by using prior knowledge. A
mood trajectory of an audio signal is estimated by multiple
linear regression (MLR) [11,12]. Multi-dimensional acoustic
features for each musical phrase are mapped to V-A space.
The rest of this paper is organized as follows. In Section 2, we take a general view of our method. Section 3 andSection 4 explain a mood trajectory estimation method for
lyrics and audio signals. In Section 5, we analyze resultsof an experimental evaluation and conﬁrm eﬀectiveness of
our method. Finally, Section 6 conclude and summarize themain ﬁndings.

2. OVERVIEW OF A MOOD TRAJECTORY
ESTIMATION
The goal of this paper is to estimate a musical mood trajectory, i.e. the time-varying musical moods of lyrics andaudio. The input are lyrics and an audio signal of a song,and the output are the mood trajectories of lyrics and anaudio signal. Though our method can be applied to songs
from arbitrary musical genres with lyrics, we used popularsongs for our experimental evaluation. Figure 1 shows an
overview of our method.
We deﬁne “a phrase” as a certain section in which humans
feel a constant mood. Note that boundaries between phrases
and those between structural sections (e.g., verses, choruses)
are not always the same though they tend to be similar toeach other. In addition, the numbers of phrases in audio
signals do not necessarily coincide with those in lyrics. In
this paper, we assume that the input lyrics and audio signals
were manually divided into phrases in advance.
The musical mood of each phrase is deﬁned as the coordinates on V-A space [13]. V-A space is a psychologicalmodel that represents an emotional state as coordinates on
two-dimensional space (see Figure 2). The horizontal axis
(valence) ranges from positive to negative, and the verticalaxis (arousal) ranges from high to low energy. Therefore,

3.

MOOD TRAJECTORY ESTIMATION FOR
LYRICSWe estimate a mood trajectory of lyrics by estimating theV-A coordinates of each word in the lyrics, calculating theV-A coordinates of phrases, and plotting the V-A coordinates of phrases. We estimate the V-A coordinates of eachword in the lyrics by using a PLSA [14] based on a MAP estimation using prior knowledge. Our method assumes thatthe lyrics were manually segmented to phrases before usinga PLSA since it requires certain amount of lyrics to estimate an appropriate mood stably. It is one of our future
works to preclude this presumption. PLSA estimates moodof each word of lyrics and moods of phrases are calculated
by summing up moods of words of segmented phrases.

52

1. By searching the synsets of each word of ANEW andextending ANEW with synonyms, ANEW is extended
from 1034 to 9757 words.
2. αw,z of words of ANEW on any quadrant of V-A space
is set. If a word of ANEW is on the origin of V-A space,
αw,z is set to 1. According to the distance between
each word of ANEW and origin of V-A space, αw,z is
set ranging from 1 to 1.01. We compare the estimated
V-A coordinates of words of ANEW in the training
data and original coordinates of ANEW, and decide
the max of αw,z for accurate estimation.

Figure 3: Graphical model of a probabilistic latentsemantic analysis (PLSA)

Each musical phrase’s coordinates on V-A space are calculated by:

3.1 Probabilistic Latent Semantic Analysis
We estimate a mood trajectory of lyrics by using a PLSA.
The PLSA is a probabilistic generative model used to estimate the semantic relations between words and semantic
topics of documents. The co-occurrent probabilities of documents and words are associated with latent variables (Figure 3). A latent variable z is assumed to be observed froma document d, and a word w is assumed to be generated
from z. A latent variable z can be understood as a topic of
documents. Using d, w, and z, a co-occurrence probability
P (d, w) is deﬁned as:∑
P (d, w) = P (d)P (z|d)P (w|z)
=

∑

1 ∑
((P (V+A+|wk ) + P (V+A−|wk ))
K
K

V =

k=1

−(P (V−A+|wk ) + P (V−A−|wk )))1 ∑((P (V+A+|wk ) + P (V−A+|wk ))
K
K

A=

k=1

−(P (V+A−|wk ) + P (V−A−|wk ))).
Here, K is the number of words of musical phrases, andP (z|w) can be calculated from P (w|z), P (z), and P (w).
Calculated V-A coordinates are plotted on V-A space, anda mood trajectory of lyrics are described.

z

P (z)P (d|z)P (w|z).

z

P (w|z) is the observed probability of words from topics, andwords having a high P (w|z) represent topics of z.

4.

3.2 MAP Estimation of Parameters of PLSA

We estimate a mood trajectory of an audio signal by using a multiple linear regression (MLR). We train a MLR
regressor based on acoustic features and V-A coordinates ofeach phrase by using a prepared training data set. The V-A
coordinates of phrases are estimated from acoustic featuresby a trained regressor, and mood trajectories are describedby plotting estimated V-A coordinates. As with the case ofmood trajectory for the lyrics, it is necessary to segment theaudio signals to phrases beforehand. We input acoustic features of each phrase to a trained regressor to estimate each
V-A coordinates of each phrase.

For a mood trajectory estimation for lyrics, it is necessary
for z to represent the moods of the lyrics. However, z does
not always represent a mood because normal PLSA focuseson the co-occurrent data of documents and words, and estimates the semantic relations between words and semantic
topics of documents. We condition on z representations by
maximum a posterior (MAP) estimation of PLSA parameters by using aﬀective words such as happy and sad of which
the V-A coordinates are already known.
Here, z is deﬁned as:

4.1

z ∈ {V+A+, V+A−, V−A+, V−A−}.

Training data collection

As a training data set, V-A coordinates and phrase switching times are needed. We developed the graphical interface
seen in Figure 4 for data collection. We referred to the interactive game developed by Kim et.al. [19] to develop thisinterface. The horizontal axis represents valence (positive
vs. negative), and the vertical axis represents arousal (highvs. low energy). Users listen to music and click on this interface when they recognize that moods are switching. The
collected data are saved as matrices, and the V-A coordinates and phrase switching time are stored in each row.

Each z represents a distinct quadrant of V-A space. Prior
distribution of P (w|z) is deﬁned as:∏∏
P (w, z|αw,z ) ∝P (w|z)αw,z −1 .
w

MOOD TRAJECTORY ESTIMATION FOR
AUDIO SIGNALSz

By setting αw,z for aﬀective words and increasing P (w|z) foraﬀective words, each z can represent each quadrant of V-Aspace. For example, if z1 = V+A+, we set αw,z of words on
the V+A+ quadrant such as happy and glad.
As prior knowledge, ANEW [17] and WordNet [18] areused. ANEW is constructed during psycholinguistic experiments and contains 1,034 words that have coordinates on
V-A space. WordNet is a lexical database for English. This
links English words to sets of synonyms called synsets, andsynsets are linked to each other through semantic relations.
By using ANEW and WordNet, αw,z is set according to thefollowing procedure:

4.2

Acoustic Features

The accuracy of musical mood detection is increased byusing multiple acoustic features [3]. With this knowledge, we
select signiﬁcant acoustic features from the multiple featuresby using a principal component analysis (PCA).
First, we extract some acoustic features from each of themusical phrases according to the previous mood detection

53

arousal

acoustic features by a multiple linear regression (MLR) usinga polynomial basis function. The input variables are theacoustic features of phrases, and the output variables are
the V-A coordinates of phrases. The regression function isdeﬁnes as:

valence

V =

M
−1 ∑
22
∑
i=0 j=1

Table 1: Extracted 71 acoustic features

Mel-frequency
cepstralcoeﬃcients (MFCCs)
Chroma vector

Line spectral pair
(LSP)
Zero crossing

Description
Includes spectral centroid, ﬂux, roll-oﬀ,
and ﬂatness. They represent spectrum
shape and reﬂect timbral features (27 dimensions).
Short-term and low-dimensional features
based on spectrum. These features areused in the modeling of audio signals etc.
[21] (13 dimensions).
The sum of the magnitude at some octaves
divided into 12 divisions corresponding to
12 pitch classes [22] (12 dimensions).
The feature used to represent linear prediction coeﬃcients (18 dimensions).
The number of times of crossing zero
points of a waveform (1 dimension).

5.

3. conﬁrming that mood trajectories can be matched tomood tags selected from social tags.
We classiﬁed songs based on the forms and positions of moodtrajectories by clustering based on the similarity of the trajectories. The variance of acoustic features in each class wascompared to validate the time-varying mood expressivenessof the mood trajectories. Moreover, the mood trajectories
and mood tags of each class were compared to conﬁrm theaccuracy of the mood trajectories.
As a dataset, we used 100 songs taken from the top 20
albums of “Last.fm’s Best of 2010” (http://www.last.fm/
bestof/2010/about). We ﬁrst segmented the lyrics and audio signals of these songs into phrases. For audio signals,
three university students listened to the songs and labeled
the VA coordinates of each of the phrases and phrase switching times by using GUI. Lyrics were segmented into phrases
based on line feed positions of the lyrics sheets. Note thatthese manually-annotated phrase boundaries were used not
only for training but also for testing. The V-A labels of thephrases of the audio signals were used for training a MLR
regressor.
We then collected the social tags of the songs before theexperiment. Social tags are frequently used in some pieces
of research [23, 24] as they are tagged to songs by an unspeciﬁed large number of people based on the metadataof songs (for example mood, composer, genre) and tend
to contain mood tags. We selected 106 tags from last.fm(http://www.last.fm/) that were tagged more than threetimes and found in the extended ANEW. Tags representing genre (e.g., rock, jazz) and musical instruments (e.g.,guitar, piano) were excluded because they were consideredirrelevant to moods. The average number of mood tags in asong was 5 and the maximum number of mood tags was 18.

Table 2: Three major principal components, theircontribution ratios of three components, and theircontributing acoustic features
Principal components
Second
Third
10.6%
8.06%
Chroma vector
LSP

EXPERIMENTAL EVALUATION

2. validating that mood trajectories can represent timevarying musical moods, and

The V-A coordinates of each phrase are estimated fromCentroid
MFCC

i=0 j=1

1. investigating how songs are classiﬁed by mood trajectories,

4.3 Multiple Linear Regression

Contribution
ratio
Contributing
featuresaij (xj )i .

We conducted an experimental evaluation to conﬁrm thevalidity of our method bymethods [8–12]. The extracted features and descriptions
are in Table 1. These features are extracted using a 32-ms
frame (no overlap), and the means and variances of thesefeatures are calculated as a 142 dimensional feature vector.
We extract acoustic features from stereo audio signals at
a sampling rate of 44.1 kHz using MARSYAS [20]. The
142 dimensional vectors are normalized (mean = 0, variance= 1) and compressed to 18 dimensions by PCA (cumulative
contribution ratio = 90%). We use these 18 dimensional
vectors as acoustic features.
First, second and third principal components and the contributing acoustic features are in Table 2. The acoustic features of which the absolute value of the principal component
axis is in the top 5 are selected as contributing features. According to Table 2, MFCC, LSP, chroma vector, and spectral
centroid contribute principal components that have a highcontribution ratio.

First
48.5%

M
−1 ∑
22
∑

Here, xj is the jth element of a 22 dimensional feature vector, vij and aij are parameters of MLR, and M is the numberof parameters. According to preliminary experiments, M is
set to four for the smallest prediction error. By using training data, we estimate vij and aij and train an MLR regressor. With the trained MLR regressor, we estimate the V-A
coordinates of the phrases of input songs from the acoustic
features. The estimated V-A coordinates are plotted on V-A
space, and the audio’s mood trajectories are described.

Figure 4: Graphical interface for manual annotation

Acoustic features
specStatisticaltrum descriptorsvij (xj )i , A =Chroma vector
LSP

54

two

Trajectory’s varianceTrajectory’s mean
Trajectory’s transition variancedistance

Table 3: Mood trajectory features
Features
Distance oftrajectories

Description
Summation of Euclidean distance between each musical phrase of lyrics andan audio signal’s mood trajectory.
Variance of a mood trajectory.
Mean of a mood trajectory.
Variance of transition of a mood trajectory.

13 songs
25 songs

class 1

26 songs

18
songs

class 2class 3class 4100 songs
Figure 6: A dendrogram of hierarchical clustering
according to the two mood trajectories

trajectory mean

Table 4: Means of the acoustic feature variance inthe songs of each classtrajectoryvariance: audio’s mood trajectoryClass 1
Class 2
Class 3
Class 4: lyric’s mood trajectorytransitions of coordinates

First
15.87
15.96
15.79
15.91

Principal components
Second
Third
8.20
4.88
8.28
4.96
8.13
4.77
8.19
4.83

Euclidean distance of phrases

Figure 5: Mood trajectory featuresconcluded that four classes were obtained by hierarchicalclustering.

5.1 Hierarchical Clustering
By performing hierarchical clustering using Ward’s method[25], we clustered all of the songs. To conﬁrm whether thesongs were classiﬁed based on the complexity of time-varying
musical mood, we compared variance of the acoustic featuresof the songs in each class. We used the mood trajectory features deﬁned in Table 3 and Figure 5 for hierarchical clustering by using Ward’s method.

5.4.2

5.2 Comparing Acoustic Features of Each Class
We compared the variance of the acoustic features of thesongs in each class. Songs with complex time-varying moods(i.e., songs expected to have complex mood trajectories)
were considered to have variable audio signals. Thereby,
we were able to conﬁrm the time-varying mood expressiveness of the mood trajectories by comparing the variance of
the acoustic features of the songs in each class.

Comparing Acoustic Features of Each Class

Table 4 is the means of the acoustic feature variance in thesongs of each class. We compared the ﬁrst, second, and thirdprincipal components. In Table 4, the principal component
variances of class 2 were the largest. In contrast, the principal component variances of class 3 were the smallest. These
results suggest that the songs of class 2 were classiﬁed ascomplex time-varying musical mood songs, and the songs ofclass 3 were classiﬁed as simple time-varying musical moodsongs.

5.4.3

Comparing Mood Tags and Mood Trajectories

We calculated Euclidean distance on V-A space between

class 1class 2class 3class 4

5.3 Comparing Social Tags and Mood Trajectories
We compared the mood tags selected from social tags andmood trajectories of the songs in each class. Since social
tags are tagged by an unspeciﬁed large number of people as
described above, mood tags taken from them can be considered as a ground-truth for mood recognition. Thus, we wereable to conﬁrm the accuracy of mood trajectories by comparing the V-A coordinates of the social tags and estimatedmood trajectories.

5.4 Results and Discussion
5.4.1 Clustering Results: trajectory distributionof lyrics: trajectory distributionof audio signals

Figure 6 contains the result of hierarchical clustering. The
horizontal line describes all songs, and the vertical line describes the distance of each cluster. Figure 6 is colored bya threshold set at 25% of the maximum distance. The ﬁgure is colored with six colors. Since songs colored with blue
are less than half of the songs colored with other colors, we: social tags

Figure 7: Distribution of mood trajectories in eachclass and V-A coordinates of mood tags

55

Table 5: Comparing results of mood tags and moodtrajectories
Matched songs

Class 1
10%Class 2
13%

Class 327%

Class 419%

All songs
21%

each phrase of mood trajectories and mood tags of a song.
The V-A coordinates of mood tags were calculated using theextended ANEW. If more than half of mood tags have thedistance of 0.25 or less, we regarded that the song’s moodtrajectories matched the mood tags and, thus, the song’s
mood was correctly estimated. Table 5 shows percentagesof songs that moods were correctly estimated. We can seethat 21% of the songs are correctly estimated. This results,
though there is still much room for improvement in it, ispromising given the diﬃculty of the task we are tackling.
Figure 7 shows the distributions of mood trajectories ineach class and the V-A coordinates of the mood tags. According to Table 5, it can be seen that class 3 yielded thebest result among the four classes. This result is in line with
Figure 7 where the distributions of mood tags and estimatedmood trajectory of class 3 are the most similar to each otherthan those of the other classes.

6. CONCLUSION AND FUTURE WORK
We proposed a mood trajectory estimation method for
lyrics and audios signals. Mood trajectories can represent
relationship between lyrics’ and audio signal’s moods andtime-varying musical moods. In an experimental evaluation,
we clustered songs based on mood trajectories, compared
the acoustic features of each class, and compared social tags
and mood trajectories. Comparing acoustic features of eachclass showed that songs could be classiﬁed according to thecomplexity of time-varying moods. Moreover, comparing
social tags and mood trajectories showed that our method
could correctly estimate the mood trajectories for 21% of
the songs. We should implement MIR systems based onmood trajectories and subjective experiments to conﬁrm thevalidity of systems for future work.

7. ACKNOWLEDGEMENTS
This work is partially supported by Kakenhi (S) 19100003
and JST PRESTO.

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