ISMIR 2008 – Session 2b – Music Recognition and Visualization

MUSIC THUMBNAILER: VISUALIZING MUSICAL PIECES
IN THUMBNAIL IMAGES BASED ON ACOUSTIC FEATURES
Kazuyoshi Yoshii
Masataka Goto
National Institute of Advanced Industrial Science and Technology (AIST){k.yoshii,m.goto}@aist.go.jp
ABSTRACT

Thumbnails the user has ever seen before

This paper presents a principled method called MusicThumbnailer to transform musical pieces into visual thumbnail images based on acoustic features extracted from their audio
signals. These thumbnails can help users immediately guessthe musical contents of audio signals without trial listening.
This method is consistent in ways that optimize thumbnails
according to the characteristics of a target music collection.
This means the appropriateness of transformation should bedeﬁned to eliminate ad hoc transformation rules. In this paper, we introduce three top-down criteria to improve memorability of thumbnails (generate gradations), deliver information more completely, and distinguish thumbnails moreclearly. These criteria are mathematically implemented asminimization of brightness differences of adjacent pixels
and maximization of brightness variances within and between thumbnails. The optimized parameters of a modiﬁed
linear mapping model we assumed are obtained by minimizing a uniﬁed cost function based on the three criteria with asteepest descent method. Experimental results indicate thatgenerated thumbnails can provide users with useful hints as
to the musical contents of musical pieces.
1 INTRODUCTION
Music recommender systems are increasingly important inonline music-distribution services to help users discover theirfavorite pieces among a huge music collection. For instance,
recommender systems based on collaborative ﬁltering [1, 2]
recommend musical pieces to the user by taking into account someone else’s ratings of those pieces. Content-based
ﬁltering systems [3, 4] select musical pieces that are similar
to the user’s favorites in terms of musical content (acoustic features). Recently, several hybrid systems that integratethese two techniques have been proposed to enable more accurate recommendations [5, 6].
An important problem that has not been resolved is thatusers cannot immediately grasp the musical contents of recommended pieces after these pieces are listed. Users haveto listen to all listed pieces, including those they do not like,to ﬁnd which pieces are worth listening to. This often prevents users from seamlessly listening to their favorite pieces.
Worse still, trial listening is time-consuming because the information of audio signals (temporal media) is not simultaneously delivered to users whereas visual images (spatial

211

M. Carey J. Jackson

W. Houston

Beethoven

Haydn

Mozart

The generated thumbnailof an unknown pieceThis piece would have pops features

Figure 1. Expected scenario: A user can roughly guess themusical contents of unknown pieces by seeing only thumbnails and without time-consuming trial listening.
media) can be easily skimmed through.
To solve this problem, we propose an audio-visual transformation method called MusicThumbnailer that generates
compact images corresponding to the audio signals of individual pieces. This helps users guess the musical contentsof audio signals without trial listening. For example, thismethod will work well in recommender systems, as shownin Fig. 1. Initially, users only glance at compact thumbnails
attached to recommended pieces when they actually listen
to these pieces. While accumulating this experience, users
will unconsciously associate particular types of thumbnailwith their preferred music. Users thus learn to understandthe musical meanings of the thumbnails’ features. Finally,users will be able to efﬁciently select audio signals of their
desired pieces by using their eyes rather than their ears.
One advantage of our method is that the visual features(colors and patterns) of thumbnails are automatically optimized for a given collection. To achieve this, it is necessary
to eliminate ad hoc rules that arbitrarily associate acoustic
features with visual features, because these rules lack a principled justiﬁcation that is consistent for different collections.
In this paper, we deﬁne some top-down criteria on generated
thumbnails from the viewpoint of usability, independentlyof the characteristics of music collections. We then mathematically represent these criteria in a uniﬁed cost function.
Audio-visual associations are obtained in a self-organized
way so that the cost function is minimized.

ISMIR 2008 – Session 2b – Music Recognition and Visualization

The rest of this paper is organized as follows. Section 2
introduces related work. Section 3 explains the principles of
our audio-visual transformation method and its implementation. Section 4 reports on our experiment using the RWCMusic Database [7]. Section 5 summarizes the key ﬁndingsof this paper.
2 RELATED WORK
Many visualization methods have been proposed for spatial
representation, organization, and browsing of music collections [8–16]. These methods typically locate musical pieces
in a two- or three-dimensional space so that musical pieces
that have similar musical contents (acoustic features) are arranged close to each other. This enables users to easily understand relationships between musical pieces because similarity in acoustic features can be observed as spatial distance. From a mathematical viewpoint, this kind of visualization can be interpreted as information compression ofhigh-dimensional feature vectors according to some criteria. The self-organizing map (SOM) is often used for thispurpose (e.g., Islands of Music [8]).
In a music-playback interface called Musicream [17], individual musical pieces are visualized as colored discs using
an ad hoc rule. The disc color (hue and saturation) is determined from the color circle whose circumference and radiuscorrespond to hue and saturation, respectively. Each piece ismapped into the circle according to its feature vector. Principal component analysis (PCA) is used to reduce the dimensionality of acoustic feature vectors to a two-dimensional
vector on a plane. Musicovery [18] uses arbitrary rules for
associating genres with colors speciﬁed in advance.
In the work described in this paper, we aimed to visualize
individual pieces, rather than a collection, as compact images (thumbnails) without using ad hoc rules. In general, visual images are represented as super-high-dimensional vectors that contain the color values of numerous pixels. Therefore, our objective was to ﬁnd an appropriate mapping froma low-dimensional acoustic space (several-tens dim.) to ahigh-dimensional visual space (several-thousands dim.). A
unique feature of this problem lies in this drastic increase indegrees of freedom. To solve such an ill-posed problem byusing an optimization method, it is necessary to incorporate
some criteria on the appropriateness of the mapping.
3 MUSIC THUMBNAILERThis section describes our method of generating thumbnailsof musical pieces based on acoustic features.
3.1 Problem Speciﬁcation
Given a collection of musical pieces (audio signals) as input data, our objective is to output appropriate thumbnails

212(visual images) that reﬂect acoustic features extracted fromthese pieces. We ﬁrst prepare some criteria to evaluate theappropriateness of the generated thumbnails as discussed
later. In this paper, we focus on generating gray-scale thumbnails as the ﬁrst step towards obtaining full-color thumbnails
in the future. This means we have only to deal with thebrightness of pixels contained in each thumbnail.
We ﬁrst deﬁne constant values in advance. Let N be thenumber of musical pieces. Let S be the number of acoustic
features taken into account. Let T be the number of pixels contained in each thumbnail, where T is the product ofwidth, W , and height, H; i.e., T = W H.
The input data is given by X = [x1 x2 · · · xN ], which
is a collection of feature vectors extracted from all musicalpieces. Here, xn = (xn,1 , · · · , xn,S )T is an S-dimensionalfeature vector of piece n (1 ≤ n ≤ N ), where xn,s (1 ≤s ≤ S) represents the value of feature s in piece n.
The output data is represented as Y = [y 1 y 2 · · · y N ],which is a set of brightness vectors of generated thumbnails.
y n = (yn,1,1 , · · · , yn,1,H , yn,2,1 , · · · , yn,2,H , · · · , yn,W,1 ,· · · , yn,W,H )T is a T -dimensional brightness vector of piecen, where yn,w,h (1 ≤ w ≤ W, 1 ≤ h ≤ H) is the brightnessof pixel (w, h) in thumbnail n. The range of yn,w,h is given
by 0 < yn,w,h < 1.
3.2 Top-down Criteria for Principled Transformation
To evaluate the appropriateness of the generated thumbnails,
we introduce three top-down criteria from the viewpoint ofuser friendliness (usability) as follows:
1. Memorability: Each thumbnail should be easily remembered by users. The visual pattern is an important factor that affects the ease of remembering thumbnails, as shown in Fig. 2. This is related to how easily
users can understand the musical meanings of visual
patterns based on their memories. We assume that
gradation images are suitable to our purpose.
2. Informational delivery: Each thumbnail should provide a large amount of information to users. This isachieved if thumbnail’s pixels have a wide variety ofbrightness, as shown in Fig. 3. This enables users to
associate a thumbnail with detailed information about
the music content.
3. Distinguishability: Users should be able to easily distinguish thumbnail images of different pieces. To enable this, each thumbnail should have a distinctive visual pattern that explicitly reﬂects the content of music, as shown in Fig. 4. This enables users to efﬁciently ﬁnd their favorite pieces based on thumbnails
they recognize.
Note that these criteria mention neither speciﬁc genres ofmusic nor speciﬁc colors of thumbnails.

ISMIR 2008 – Session 2b – Music Recognition and Visualization

1

2

1

W

1

1

2

2

H

H

Easy to remember

2W

3.3 Mathematical Formulation

Hard to remember

Figure 2. Difference in ease of remembering thumbnails.
Both thumbnails have the same histogram of brightness.
1

2

1

W

1

1

2

2

2

W

From a mathematical point of view, the objective is to obtain optimal parameters of a mapping model that transforms
a S-dimensional space to a T -dimensional space so that acost function deﬁned according to the three criteria is minimized. This transformation has a high degree of freedom; ahigher-dimensional space can always preserve the complete
information of an original space. We thus incorporate linear
mapping into a mapping model. This is reasonable because
linear mapping can strongly limit the degree of freedom intransformation. In addition, musical pieces which are close
to each other in an acoustic space are expected to be mapped
still close to each other in a visual space. This effect is suitable to achieve the expected scenario shown in Fig. 1. We
deﬁne the mapping model as
Y = Sig(AX),H

H

Large amount of info. Small amount of info.
Figure 3. Difference of the amount of information obtained
from thumbnails.

(1)where A is a T -by-S transformation matrix to be optimized,
which is given by
⎤ ⎡
⎡
⎤
AT1,1
A1,1,1A1,1,2 · · · A1,1,S
⎥ ⎢
⎢
..
⎥
..
..
⎥ ⎢
⎢
⎥
.
.
.
⎥ ⎢
⎢
⎥
⎥ ⎢
⎢ AT
A1,H,1 A1,H,2 · · · A1,H,S ⎥
⎢
1,H ⎥
⎢
⎥
⎥ ⎢
⎢
⎥
..
..
..
⎢
⎥=⎢
⎥ (2)
.
.
.
⎢
⎥ ⎢
⎥
⎥ ⎢
⎢
T
⎢ AW,1 ⎥ ⎢ AW,1,1 AW,1,2 · · · AW,1,S ⎥
⎥
⎥ ⎢
⎢
⎥
..
..
..
⎥ ⎣
⎢
⎦
.
.
⎦
⎣
.
T
AW,H,1 AW,H,2 · · · AW,H,S
AW,Hand Sig is the sigmoid function given by

Sig(x) =Easy to distinguishHard to distinguish

Figure 4. Difference in ease of distinguishing thumbnails
of different pieces.
These top-down criteria enable us to design thumbnails
in a non-ad-hoc way. In general, system designers tend todeﬁne ad hoc rules that directly associate musical contentsof musical audio signals with speciﬁc colors of visual images (e.g., rock-red, jazz-green, and classic-blue). However,
the appropriateness of these arbitrary rules cannot be guaranteed. In contrast, the criteria we proposed only regulate
the appropriateness of transformation. The actual colors andpatterns of thumbnails are optimized for a given collection
in a self-organized way so that the criteria are best satisﬁed.
Therefore, our approach is methodologically and mathematically sound.
A remaining problem here is how to mathematically implement these criteria. In this paper, we will present a simple
implementation of the three criteria below.

213

1(−∞ < x < ∞).
1 + e−x(3)

In Eq. (1), we applied the sigmoid function to each cell of
matrix AX so that the value of each cell of matrix Y ranges
from 0 to 1. Note that the differential of the sigmoid function is given by Sig’(x) = Sig(x) (1 − Sig(x)) .
To evaluate the appropriateness of the mapping model,
we deﬁne a cost function, C, as
C = Cs + αw Cw + αb Cb ,(4)

where Cs , Cw , and Cb are the costs corresponding to thethree criteria described in Section 3.2, and αw and αb are
the weighting parameters. We mathematically deﬁne thesethree costs below.
3.3.1 Minimization of adjacent-pixel distances
To generate gradation images, we focus on a necessary condition that the brightness values of adjacent pixels should beclose to each other. One way to mathematically implement
this condition is to minimize the differences of the brightness values of adjacent pixels included in each thumbnail.

ISMIR 2008 – Session 2b – Music Recognition and Visualization

However, this calculation is not efﬁcient because it would
have to be repeated for all thumbnails. To solve this problem, we directly deﬁne the cost function, Cs , for the transformation matrix, A, as follows:
1
Dw,h,s ,
(5)
Cs =
W HS

3.4 Parameter Optimization
To minimize the total cost function, C, as an optimization
method, we use a steepest descent method that iteratively
updates the parameters until the cost reduction is converged.
The updating formula is given by

w,h,s

where Dw,h,s is the average of the following eight distances:
1 
2Dw,h,s =(Aw,h,s − Aw+i,h+j,s )(6)
8 i,j=±1
1 
2+(Aw,h,s − Aw+i,h,s )(7)8 i=±1
1 
2+(Aw,h,s − Aw,h+j,s ) .
(8)
8 j=±1
3.3.2 Maximization of within-thumbnail variances
To increase the amount of information delivered by a thumbnail, the brightness variance within the thumbnail should be
maximized. We formulate this condition for each thumbnail
and deﬁne the cost function, Cw , based on the average ofbrightness variances over all thumbnails:
1  1 2
Cw = −(yn,w,h − ȳn ) ,(9)
N n WHw,hwhere ȳn is an average of the brightness values of wh pixels
within a thumbnail of piece n, given by
1 
ȳn =
yn,w,h .
(10)
WH
w,h

Note that maximization of within-thumbnail variances is equivalent to minimization of the cost function Cw .
3.3.3 Maximization of between-thumbnail variances
To enable users to clearly distinguish generated thumbnails,
the brightness vectors of these thumbnails should be far fromeach other. A simple way to satisfy this condition is to maximize the brightness variance between all thumbnails, where
the between-thumbnail variance is calculated in each position, (w, h). We deﬁne the cost function, Cb , based on the
average of brightness variances over all positions as1  1 2
Cb = −(yn,w,h − ȳw,h ) ,
(11)
WH
N n
w,h

where ȳw,h is an average of the brightness values of n pixels
in the same position (w, h), given by
1 
yn,w,h .
(12)ȳw,h =
N n
Note that maximization of between-thumbnail variances is
equivalent to minimization of the cost function Cb .

214

Aw,h,s ← Aw,h,s − η∂C,∂Aw,h,s(13)

where η is a learning parameter (0 < η < 1) and ∂A∂C
isw,h,s
decomposed into three terms:
∂Cs
∂C
∂Cw
∂Cb
=
+ αw
+ αb
. (14)∂Aw,h,s∂Aw,h,s∂Aw,h,s∂Aw,h,s3.4.1 Derivation of updating formula
We now explain how to derive the updating formula. The
ﬁrst term in Eq. (14) is obtained by∂Cs
2
Aw,h,s − Āw,h,s ,=∂Aw,h,sW HS(15)where Āw,h,s is an average of the values in the vicinity of
Aw,h,s , given by
Aw,h±1,s + Aw±1,h,s + Aw±1,h±1,s.
8The second and third terms are calculated as∂Cw∂Cw∂yn,w,h=·,∂Aw,h,s∂yn,w,h ∂Aw,h,s∂Cb∂Cb∂yn,w,h=·,∂Aw,h,s∂yn,w,h ∂Aw,h,sĀw,h,s =

where
∂Cw
∂yn,w,h∂Cb∂yn,w,h∂yn,w,h∂Aw,h,s2(yn,w,h − ȳn ) ,
NW H
2
= −
(yn,w,h − ȳw,h ) ,
NW H
= −

(16)

(17)
(18)

(19)
(20)

= Sig’(ATh,w xn )xn,s(21)
= Sig(ATh,w xn ) 1 − Sig(ATh,w xn ) xn,s .
(22)

3.4.2 Visual effects of updating formula
Next, we will discuss the visual effects of the three termsof Eq. (14) in the mathematically derived updating formula.
Eq. (15) means the ﬁrst term tries to make transformation
coefﬁcients close to their smoothed versions. Eq. (16) corresponds to a visual processing algorithm that is used forsmoothing images by using a convolution matrix. Eq. (19)and Eq. (20) mean the second and third terms try to makethe brightness value of each pixel far from the within- andbetween-thumbnail averages. This enhances the dynamic
range of each thumbnail and the variety of generated thumbnails. These effects intuitively match our expectation.

ISMIR 2008 – Session 2b – Music Recognition and Visualization

4 EXPERIMENTThis section reports on a thumbnail-generation experiment
done to evaluate the usefulness of MusicThumbnailer.
4.1 Experimental Conditions
As a music collection, we used the “RWC Music Database:Music Genre” (RWC-MDB-G-2001) [7], which consists of
100 pieces (N = 100) in total with three pieces prepared foreach of 33 genres and one for a cappella. This database isdivided into 10 main genre categories (popular, rock, dance,
jazz, Latin, classical, march, world, vocal, and traditional
Japanese music) and 33 subcategories (pops, ballad, rock,heavy metal, rap/hip-hop, house, techno, funk, soul/R&B,
big band, modern jazz, fusion, bossa nova, samba, reggae,tango, baroque, classic, romantic, modern, brass band, blues,
folk, country, gospel, African, Indian, ﬂamenco, chanson,
canzone, traditional-style Japanese popular music, Japanesefolk music, and ancient Japanese court music).
To extract acoustic features, we used the MARSYAS [19].
We obtained a 42-dimensional feature vector for each piece,
which consists of the average and variance of local spectral features (centroid, rolloff, and ﬂux) and zero-crossings
across the entire piece (8 dimensions), average and varianceof Mel-frequency cepstral coefﬁcients (MFCC) across theentire piece (26 dimensions), and rhythmic content features
reﬂecting periodicity in beat (8 dimensions). We then used
PCA to reduce the dimensionality; the 42-dimensional space
was transformed into a 20-dimensional space still accounting for 95% of the variance of the original data (S = 20).
The size of thumbnails was 50 × 50 (W = H = 50, T =2500). In this experiment, gray-scale thumbnails were converted to full-color ones according to a lookup table shownin Table 1 (called “Jet” color scheme in MATLAB) from anaesthetic point of view. Note that this is just for convenience
because we should essentially eliminate such an ad hoc rule.
The values of parameters, αw , αb , and η were empirically
set to 0.4, 0.4, and 0.1.
4.2 Experimental Results
The experimental results indicate that the generated thumbnails are useful for guessing the musical contents, as shownin Fig. 5. At the main-category level, thumbnails of popular/rock pieces, those of classical (orchestra) pieces, andthose of marches seem to be close to each other, respectively. In the dance category, similar thumbnails were obtained in each subcategory, where we can ﬁnd the similarity between rap/hip-hop and funk. The thumbnails offunk pieces somewhat resemble those of reggae and African
pieces across the main category. This corresponds with thefact that funk music has been developed while absorbing
the characteristics of African music and reggae. In the categories of Latin, world, and traditional Japanese, we can215

Table 1. Lookup table for converting brightness to RGB.
Brightness
0.00
0.33
0.66
1.00
(0,0,1) (0,1,1) (1,1,0) (1,0,0)
RGBroughly say that similar thumbnails were obtained in eachsubcategory. In the vocal category, each subcategory yielded
the similar thumbnails, which have especially unique patterns among the database. In the jazz category, however,there were comparatively wide variations in thumbnails ofeach category. Moreover, fusion pieces tend to reﬂect andmix the styles of other pieces.
5 CONCLUSION
We presented an audio-visual transformation method called
MusicThumbnailer that generates thumbnail images reﬂecting acoustic features of audio signals. To achieve principled
transformation free from ad hoc rules, we designed three
top-down criteria regarding memorability, informational delivery, and distinguishability. These criteria are used to evaluate the appropriateness of generated thumbnails from theviewpoint of usability rather than to associate speciﬁc acoustic features with actual colors and patterns of thumbnails.
From a mathematical viewpoint, we formulated this problem as a constrained minimization of a cost function basedon the three criteria. The experiment showed promising results as to the usefulness of MusicThumbnailer.
Many issues still remain regarding the reﬁnement of our
method through subjective experiments. First, we plan to introduce a new criterion to preserve the topological relationsof feature vectors in audio-visual transformation. Then, we
will improve the mathematical implementation of each criterion and attempt to use a more sophisticated optimization
algorithm that can achieve fast convergence while avoiding
the local-minimum problem. Several experiments using different features and collections would be important. An interesting application of our method would be to generate avisual effect (a temporal sequence of visual images) that dynamically represents the local musical contents in a musicalpiece. This can be done by interpreting feature vectors extracted from individual time frames in a musical piece in thesame way as for those extracted from individual pieces in amusic collection. Such a visualizer will give users a practical overview of structures within a musical piece.
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ISMIR 2008 – Session 2b – Music Recognition and Visualization

BalladPopular
#1~#6

Rock

Heavy metalRock#7~#12

Rap/Hip-hop

House

TechnoFunkSoul/R&B

Big band

Pops

Modern jazz

FusionBossa nova

Samba

ReggaeTango

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Brass band

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Romantic

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Country

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A Cappella

A Cappella#100

Figure 5. Experimental results of generating thumbnail images of 100 pieces included in RWC-MDB-G-2001 [7].
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