Journal of Robotics, Networking and Artificial Life, Vol. 1, No. 4 (March 2015), 303-311

Experimental Investigation of Feature Quantity in Sound Signal
and Feeling Impression Using PCA
Yusuke Kawakami, Tetsuo Hattori *Graduate School of Engineering, Kagawa University, 2217-20, Hayashi-Cho
Takamatsu, Kagawa 761-0396, Japan
E-mail: hattori@eng.kagawa-u.ac.jp
Hiromichi Kawano

NTT Advanced Technology Corporation, 19-18, Nakamachi
Musashino, Tokyo 180-0006, Japan
E-mail: hiromichi.kawano@ntt-at.co.jp
Tetsuya Izumi

Micro-Technica Co., ltd., 3-12-2, Higashi-Ikebukuro
Toshima, Tokyo 170-0013, Japan
E-mail: t-izumi@microtechnica.co.jp

Abstract
This paper describes experimental investigation of the relationship between feature quantity of sound signal andfeeling impression using PCA (Principal Component Analysis). As the feature quantity, we use Fluctuation value
and sum of squared errors (Residual) which is calculated by regression analysis of sound signal, in the same way as
our previous paper. In order to investigate the feeling impression and effect from sound signal, we use aquestionnaire survey method, that is, we ask some examinees to evaluate their feeling impression about sound(music) that we provide. As a result, we have found that the feeling response of examinees can be classified into
three groups by a clustering analysis. And we have verified the feeling impression effects depending on each groupof examinees and four kinds of frequency zone of sound signal from the results of PCA. In this paper, we also
discuss the analysis results on the Kansei (or feeling) effect.
Keywords: Signal processing, Fluctuation, Intercept, Sum of squared errors, Feeling impression, PCA

1. Introduction
Recently, 1/f fluctuation in various fields of signal has
been actively researched, and it brings about an effect ofsuch healing as a human being psychologically feels atease, if there is a 1 /f relation between the power

spectrum of the signal and the frequency f 1-7. However,
we focused that the power spectrum have same
fluctuation but the distribution are different. And we
doubted the strong influence of the emotional
impression factors other than fluctuation value.8*

Graduate School of Engineering, Kagawa University, 2217-20, Hayashi-Cho, Takamatsu, Kagawa 761-0396, Japan
E-mail: hattori@eng.kagawa-u.ac.jp

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303

Therefore, in the previous research, we have defined
three kinds of parameters such as fluctuation value (orFluctuation), intercept (or Intercept), and sum ofsquared errors (or Residual) as feature quantity in soundsignal obtained from the calculation of the signals’
fluctuation degree. And we have investigated therelation between feeling impression and thoseparameters, by using multiple regression analysis8. And
we eliminate “Intercept” from the analysis, because thisquantity (or parameter) is substantially equal to thevolume of sound8.
Moreover we had considered possibility of the effect offeeling impression from frequency domains. So we
divided into three frequency domains (Low Frequency(LF); 0~300Hz, Middle Frequency (MF); 300~1000Hz,
High Frequency (HF); 1000~22050Hz) and analyzed
each domain10, 11, 16.
As the results, we have understood that feeling
impression have an impact on Residual more thanFluctuation, especially high frequency. In the regression
analysis, we can be seen the impact of the soundfeatures for the evaluation value of individual sensibility
adjective items (for example, lightness, quickness, etc.).
Although, it is difficult to capture the main factors on
the relation between feature quantity of sound which
presented to examinees, and feeling impression of
examinees.
In this paper we analyze the affect of the feeling
impression, from the music's Fluctuation and Residual,
by use of principal component analysis. At first, weinvestigate the feeling impression of the music by using
questionnaire survey. Then, from result we separate theexaminees into the groups using clustering analysis.
After that, we perform the PCA by the feeling
impression or feature quantity of sound signal eachfrequency domains.
Furthermore we analyze relationship between feeling
impression, and Fluctuation or Residual through thecorrespondence relationship of principal component
axis.

proportional to the 1/f of frequency. Moreover, it ispointed out that there is an effect that a h uman being
feels pleasantness1-6.
Fig. 1 is shown the conceptual image of PS. Let Y(f) andε(f) be the power of PS and its error, respectively. And
we define the PS which is shown in Fig. 1 as Eq. (1).

Y( f )=k+ε(f )
fa(1)

Taking the logarithm of both sides,
 k

 k

log Y ( f ) = log a + ε ( f ) = log a (1 + ε~ ( f ))
 f

 f





 k 
= log a  + log(1 + ε~ ( f ))
 f 


log Y ( f ) = −a log f + log k + log(1 + ε~ ( f ))(2)

Let y ( f ) = log Y ( f ) and εˆ ( f ) = log(1 + ε~ ( f )) , respectively.
And let b = log k , then we have the following Eq. (3).

y ( f ) = − a log f + log k + εˆ ( f )= −a log f + b + εˆ ( f )(3)Fig. 2 shows the regression line of Eq. (3). In Fig. 2, thevertical axis and the horizontal axis are logarithm of PS
and logarithm of frequency f, respectively. In this paper,
we define the absolute-degree of the regression line a“Fluctuation”. Then, we define the intercept of theregression line (“Intercept”) as b, and we also define theerror from the line as e.8
Furthermore, we define the sum of squared errors(“Residual”) as Eq. (4). In this equation, y and Y mean
the actual measurement value and the theoretical value,
respectively8.
s=∑e = ∑(y − Y )
i

i

2

i

i

2

(4)

i

Y

Y( f )=

2. Investigation between 3 Parameters
Accompanying on the Calculation Fluctuation
value (3PACF) and Feeling Impressionk+ε(f )
fa

2.1. Fluctuation and 3PACF
Among fluctuations, the well-known 1/f fluctuationmeans that the power spectrum (PS) of a s ignal isfFig. 1. Conceptual image of PS curve.

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14, 15, 17

y( f )
= −a log f + b + εˆ( f )

y

log f

Fig. 2. Example of regression line.14, 15, 17

2.2. Evaluation of feeling impression
Next, we have used questionnaire survey in order toinvestigate the relation between 3PACF and feeling
impression of music. The examinees are 34 students inthe age of early twenties. The list of music used in thissurvey is shown in Table 1.
These sampling frequency and file format are 44.1 kHz
and 16 bit wav, respectively. The files are ripped fromCD using “Exact Audio Copy V1.0 Beta 3" with
Pioneer BDR-S03J BD-drive.
For every piece of the music, we have taken 20 seconds
to play it. The examinees evaluated the 4 items asshown in Table 2, by scoring from one to four. Also
they have judged the preference for each of music byscoring from one to ten.
Table 1. Music list of wave files.

14, 17

impression, by using the results of questionnaire survey.
As preprocessing, we convert the evaluation (Item1~Item4) and Preference as follows;• {Item1 ~ Item4} ≥ 3 → 1• {Item1 ~ Item4} ≤ 2 → 0• Preference≥6→1• Preference≤5→0
Therefore, the data of whole examinees are consist from34 set of 50 dimensional ((Item1 ~ Item4, andPreference) × 1 0songs) data. That is, this clustering
analysis is performed in the 50-dimensional space. And
we adopt Ward method9 as the analysis.
Ward method is the method which uses often in theclustering analysis. As its characteristics, it i s known
that it hardly occur the Chain Effect9. In this method,
the distance of clusters between C i and C j is defined by
Eq. (5), and it is fused from small cluster of distance.
In Eq. (5), d(x, y) and µ ij are Euclidean distance and themean vector of the cluster that fused the cluster C i andCj.

D (Ci , C j ) =∑ d (x, μ ) −  ∑ d ( x, μ ) + ∑ d (x, μ )  (5)2x∈Ci , C jij

2 x∈Ci

i

2

j

x∈C j



Fig. 3 shows the concept of cluster fusion process byusing Ward method. In the figure, cluster C i , C j , and C khave mean vectors µ i , µ j , and µ k , respectively. Because
the distance between C j and C k is the smallest in Fig. 3,
they will be fused.

Ci

µi
µik

Table 2. Evaluation items of the questionnaire survey.17
Item1
Slow
Quick
1⇔4
1⇔4
Light
Item2
Heavy
Item3
Natural1 ⇔ 4 Artificial
Item4
Negative 1 ⇔ 4
Positive
Preference Dislike
1 ⇔10
Like

µj
µjk

Cj

µk

Ck
Fig. 3. Conceptual image of cluster fusion process by using
Ward method.

2.3. Clustering analysis
Subsequently, we have conducted clustering analysis todivide into examinees groups who was similar feeling

And then, we perform Wilk’s Lambda test as thestatistical test9. It is a test of the difference between the

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mean values of the vector comprising a plurality ofvariables. The null hypothesis H 0 and alternative
hypothesis H 1 are as follows;
H 0 : Difference of all mean vectors are equal.
H 1 : Difference of all mean vectors are not equal.
Whenever each time of clustering has finished, weapply Wilk’s Lambda Test repeatedly. In this test, we
set significance to 1%. And then, if it will not come into
effect significance of 1% on next-time test, theclustering is quit10, 15, 16.
2.4. Principal Component Analysis (PCA)
In this section, we describe the PCA12, 13 performing
space and the set of vectors. However, we decide toeliminate Intercept because it substantially equal to thevolume of sound.
First, we define Physical Quantity Space (PQS) that is
two-dimensional space which axis is the fluctuation
value and Residual. The subject of PCA is a set of 10
pieces of music vectors (Table 3), and also we perform
PCA in each frequency domain (AF, LF, MF, and HF).
The other hand, we define Feeling Adjective Space(FAS) that is five-dimensional space which axis is the
feeling impression of the examinees. The subject of
PCA is a set of 10 pieces of music’s Feeling Impression
Vectors (FIVs).

Title (*.wav)

1 Another_Sky
2 Londonderry_Air
3 Blieve_you
4 Drafting
5 Down_by_the_Riverside
6 Space_Odessey3_Revelation
7 Tomorrow
8 Old_French_Song
9 Freedom
10 Red_River_Valley (brass)

AF
Fl.
Re.
1.715
0.414
1.627
0.399
2.111
0.466
1.593
0.431
1.724
0.448
0.990
0.323
2.268
0.555
1.398
0.433
2.173
0.589
1.520
0.526

LF
Fl.
Re.
0.454
0.487
1.023
0.489
0.457
0.503
0.917
0.474
0.553
0.502
1.614
0.195
0.129
0.619
1.509
0.275
-0.259
0.535
0.499
0.653

MF
Fl.
Re.
1.713
0.674
1.873
0.906
0.527
0.844
1.296
1.006
0.470
0.679
1.522
0.470
0.721
0.545
1.633
1.255
-0.047
0.575
0.723
0.733

Fl.: Fluctuation, Re.: Residual

•
•
•
•

{Item1 ~ Item4} ≥ 3 → 1{ Item1 ~ Item4} ≤ 2 → 0
Preference≥6→1
Preference≤5→0~
S (i ,k ) = (a1 ,  , a5 )

HF
Fl.
Re.
1.777
0.394
1.706
0.369
2.472
0.409
1.706
0.404
2.115
0.406
1.004
0.316
2.903
0.463
1.515
0.399
2.705
0.517
1.658
0.507

2.4.1. Feeling Impression Vector (FIV)This subsection, we describe the FIVs.
First, we define the evaluation S (i, k) of examinee k as Eq.
(6). i and e 1 , …, e 5 are the music number and theevaluation of Item1 ~ Preference, respectively.

S (i ,k ) = (e1 , ..., e5 )(6)Then, we convert the evaluation (Item1 ~ Item4) and(7)

Hence, the vector S i * of the sum of evaluation r people
is FIV which is defined by Eq. (8). Z 1 , …, Z 5 are thesum of evaluation Item1 ~ Preference of r people,
respectively.
r~*
Si = (Z1 , ..., Z 5 ) = ∑ S (i ,k )

(8)

k =1

That is, we apply Eq. (6) ~ Eq. (9) to each group, which
is divided by using clustering analysis, and we perform
PCA of the each group.
Subsequent sections, we define u n (n=1, 2) and v m (m=1,…, 5) in the principal component axis of set of vectors
on PQS and FAS, respectively.
Additionally, we define f i and x i in the vectors of music
number i (i= 1, …, 10) on PQS and FAS, respectively.
So we can express f i and x i on the coordinate axes u n
and v m respectively as follows.

( f u , f u ), ( x v , , x v ) (9)iTable 3. Fluctuation and Residual.17
No.

Preference as same as Section 2.2. And we define theconverting processed vector, as Eq. (7). a 1 , …, a 5 arezero or one in Eq. (7). That is;

1

i

2

i

1

i

5

2.5. Correlation of the principal component axis
Subsequently, we investigate the correspondence ofprincipal component axes of PQS and principal
component axes of FAS. Let C u and C v be thecoefficient matrix which is calculated by PCA of PQS
and the coefficient matrix which is calculated by PCAof FAS, respectively. And we can describe the basis
vectors u n and v m by using p n (the basis vectors on
PQS) and i m (the basis vectors on FAS), as shown in Eq.
(10) and (11).

Cu12  δ n1 C (n = k ) 1, δ nk = 
un ≡ C u pn =  u11(n ≠ k ) 0
Cu 21 Cu 22  δ n 2 (10)

Cv11  Cv15  δ m1  (m = k ) 1 (11)v m ≡ C v im =       , δ mk = (m ≠ k ) 0Cv 51  Cv 55  δ m 5 

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From Eq. (9) ~ (11), correspondence between u n and v mcan be judged by the correlation coefficient R between
f i unandR=xi v m . R is defined by Eq. (12).

∑ f u
i

∑ f u
i

n

n

2

xi v m∑xv
i

examinees (G2 and G3) are not clear, because there areindividual differences. From Fig. 6(a), we consider thatexaminees of group G1 prefer “Believe_you”.
G3

(12)

2
m

G2

3. Results of Feeling Impression and Discussion

G1

3.1. Clustering analysis
Fig. 4 shows the result of clustering analysis and its
statistical test. As shown in Fig. 4, 34-person examinees
are divided 3 groups. The names of groups (G1, G2, and
G3) are given in descending order of head-count.
Examinees belonging to A, B, and C are 19 person(55.9% of total), 8 person (23.5% of total), and 7 person(20.6% of total), respectively. Table 4 a lso shows theresults of the aggregate of evaluation items that ispreprocessed describing in Section 2.3.
3.2. PCA
Table 5 a nd Fig. 5 show the results of PCA on PQS(Physical Quantity Space). The plotted marks in Fig. 5
indicate endpoints of the vectors from origin. F rom
Table 5 a nd Fig. 5, we consider that the music that isused in the investigation of this paper, the weight ofFluctuation and the Residual are same degree. Because
the components of the Fluctuation and Residual arecontained in u 1 and u 2 approximately equal proportions.
The other hand, Table 6 and Fig. 6 show the results of
PCA on FAS (Feeling Adjective Space). In the space,
we do not consider principal component v 3 , because thecumulative contribution ratio of principal component v 1
and v 2 are about 94.7% in minimum of each groups.
From Table 6 and Fig. 6, we understand as follows;••In group G1, v 2 is Preference, and thecorrespondence between v 1 and Item2(Lightness) or Item3 (Artificial) are also strong.
In group G2 and G3, the correspondence
between v 1 and Item4, v 2 and Item1 are strong
respectively.

That is, 56% of examinees (G1) prefer light andartificial music in which have used this paper. However
tendency of music to suit the taste of the remaining ofFig. 4. Dendrogram of clustering result by using questionnaire
results of examinees.17

Table 4. Results of feeling impression questionnaire.17(a) Group G1
Music# *.wav
1 Another_Sky
2 Londonderry_Air
3 Blieve_you
4 Drafting
5 Down_by_the_Riverside
6 Space_Odessey3_Revelation
7 Tomorrow
8 Old_French_Song
9 Freedom
10 Red_River_Valley (brass)

Item1(Quick)

3
1
3
0
18
1
12
1
19
9

Item2
Item3
Item4
Preference(Llight) (Artificial (Positive)
14
17
15
7
6
3
8
9
5
2
18
10
3
3
0
7
18
15
19
5
11
6
1
5
12
18
19
13
7
7
1
3
15
15
18
8
17
15
18
6

(b) Group G2
Music# *.wav
1 Another_Sky
2 Londonderry_Air
3 Blieve_you
4 Drafting
5 Down_by_the_Riverside
6 Space_Odessey3_Revelation
7 Tomorrow
8 Old_French_Song
9 Freedom
10 Red_River_Valley (brass)

Item1(Quick)

1
0
0
0
6
0
7
0
8
4

Item2
(Llight)(c) Group G3
Music# *.wav
1 Another_Sky
2 Londonderry_Air
3 Blieve_you
4 Drafting
5 Down_by_the_Riverside
6 Space_Odessey3_Revelation
7 Tomorrow
8 Old_French_Song
9 Freedom
10 Red_River_Valley (brass)

Item1(Quick)

0
0
0
2
1
1
2
5
4
5

Item2
(Llight)

4
0
2
0
7
2
6
0
7
8

Item3
Item4
Preference(Artificial (Positive)
5
8
8
0
4
7
0
8
8
2
0
7
6
8
7
1
0
8
8
8
8
2
0
8
5
8
7
7
8
8

Item3
Item4
Preference(Artificial (Positive)
5
4
7
7
1
4
3
6
3
4
4
5
2
4
2
6
4
5
6
6
4
4
2
4
1
4
4
7
4
5
3
4
3
5
5
3
5
6
6
5

3.3. Correlation of the principal component axis
We have calculated the correlation coefficient between
principal component axes of PQS (u n ) and FAS (v m )based on the results of PCA on each space, in eachfrequency domains (AF, LF, MF, and HF).
Table 7 and Fig. 7 show the results of correlation

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307

0.05

0.8

Residual

RRV

0.03

0.4
OFS

0.02

0.2

SO3R

0.01

u2

DR

Londonderry _Air

-0.01

-0.2
Tomorrow

Another_Sky

-0.02
-0.03

Believe_y ou

-0.04
0.0

0.1

0.0

Freedom

Drafting

0.00

0.2

0.3

3.0

0.6

0.4

-0.4

Fluctuation

0.5

0.6

0.7

2.0
1.5
1.0

-0.6

0.0

-0.8

-0.5

0.8

u1

0.6

RRV

0.4

Another_Sky

0.05

0.2

DR
Drafting

u 2 0.00
-0.05

0.0

Londonderry _Air

-0.2

-0.10

-0.4

-0.15
OFS

-0.20
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.0
-0.2
-0.4

Another_Sky

SO3R

Fluctuation
0.1

0.2

5.0

6.0

7.0

8.0

9.0

OFS

SO3R
Londonderry_Air
Believe_you

Pref.

Another_Sky

-0.25

I3

-0.50

I1

I4
I2

RRV
Tomorrow
DR-0.75

Freedom

-1.00
0.0

0.5

1.0

1.5

2.0

2.5

v1

3.0

3.5

4.0

(b) Group G2

-0.6

-0.15
0.0

u 2 (Fluctuation, Reidua

0.2

OFS

Londonderry _Air

-0.10

v1

0.00

0.8

Tomorrow

-0.05

4.0

0.50

0.4
Drafting

3.0

v 2 0.25

DR

u 2 0.00

2.0

Drafting

0.75

0.6

RRV

1.0

1.25

0.8

Believe_y ou

0.05

DR

1.50

-0.8

Residual

Freedom

Freedom

1.00(b) LF (Low Frequency domain)

0.10

RRV

SO3R

(a) Group G1

u1

0.15

I2
OFS
I1

I3

0.0

-0.6

Fluctuation

SO3R

-0.25

Another_Sky

-2.0

0.8

Tomorrow
Believe_y ou

0.10

Tomorrow
Drafting

I4-1.5

u 2 (Fluctuation, Residua

0.15

Pref.

-1.0

Residual

Freedom

0.20

Londonderry_Air

v 2 0.5(a) AF (All Frequency domain)
0.25

Believe_you

2.5

u 2 (Fluctuation, Residua

0.04

0.3

0.4

0.5

0.6

0.7

-0.8

0.8

0.8

u1

0.6

(c) MF (Middle Frequency domain)

Londonderry_Air

Pref.

0.4
0.08

0.8

Residual

OFS

0.02

0.2
Draftingu2

Londonderry _Air

0.00

0.0

Another_Sky

DR

-0.02

-0.2
Freedom-0.4
Believe_y ou-0.04

Fluctuation

Tomorrow

-0.06
0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

u 2 (Fluctuation, Residual

0.4

SO3R

0.04

Believe_you

0.2

0.6

RRV

0.06

-0.4
-0.6

-0.6

-0.8

-0.8

-1.0

0.8

Freedom
OFS

I1
0.0

u1

SO3R

I3

I2

-0.2

Tomorrow
DR

Drafting

I4

0.0

v2

Another_Sky(d) HF (High Frequency domain)

0.5

1.0

1.5

v1

2.0

RRV

2.5

3.0

(c) Group G3
17

Fig. 5. PCA results on Physical Quantity Space (PQS).

DR: Down_by_the_Riverside, SO3R: Space_Odessey3_Reveration,
OFS: Old_French_Song, RRV: Red_River_Valley (brass)

Fig. 6. PCA results on Feeling Adjective Space (FAS).17

DR: Down_by_the_Riverside, SO3R: Space_Odessey3_Reveration,
OFS: Old_French_Song, RRV: Red_River_Valley (brass),
I1: Item1 (Quick), I2: Item2 (Light), I3: Item3 (Artificial),
I4: Item4 (Positive), Pref.: Preference (Like)

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308

Table 5. PCA results on Physical Quantity Space (PQS).

1.000(a) Music vector

AF
LF
MF
HF
<f i | u 1> <f i | u 2> <f i | u 1> <f i | u 2> <f i | u 1> <f i | u 2> <f i | u 1> <f i | u 2>
1 Another_Sky
0.2959 -0.0139 0.2379 0.0757 0.3567 -0.0907 0.2856 0.0093
2 Londonderry_Air
0.2826 -0.0112 0.3402 -0.0256 0.4235 -0.0659 0.2707 0.0054
3 Believe_you
0.3492 -0.0319 0.2437 0.0802 0.2354 0.0978 0.3454 -0.0390
4 Drafting
0.2904 0.0027 0.3163 -0.0115 0.3679 0.0292 0.2838 0.0186
5 Down_by_the_Riverside
0.3082 -0.0032 0.2604 0.0625 0.1955 0.0726 0.3162 -0.0127
6 Space_Odessey3_Revelation 0.1994 0.0206 0.3514 -0.2257 0.2915 -0.1062 0.1965 0.0404
7 Tomorrow
0.3937 -0.0158 0.2220 0.1759 0.2017 0.0132 0.3991 -0.0523
8 Old_French_Song
0.2736 0.0211 0.3582 -0.1814 0.4610 0.0343 0.2671 0.0315
9 Freedom
0.3966 0.0042 0.1259 0.2185 0.1072 0.1195 0.4039 -0.0168
10 Red_River_Valley (brass)0.3164 0.0419 0.2992 0.1210 0.2390 0.0502 0.3187 0.0609

0.800

Title (*.wav)

Physicalparameter
Fluctuation
Residual(b) Bases vector

AF
u10.70710.7071

LF

u2-0.70710.7071

u1
0.70710.7071

u2-0.70710.7071

0.600

Correlation coefficient

No.

0.400
0.200
0.000
-0.200-0.400-0.600MF

u10.70710.7071

u2-0.70710.7071HF
u1
0.70710.7071-0.800u2-0.70710.7071

1

2

3

4

1

2

AF

3

4

1

2

LF

3

4

1

2

MF

3

4

3

4

3

4

HF

(a) Group G1

Table 6. PCA results on Feeling Adjective Space (FAS).

1.000(a) Music vector

0.800

G1
G2
G3
<x i | v 1> <x i | v 2> <x i | v 1> <x i | v 2> <x i | v 1> <x i | v 2>
1 Another_Sky
6.0797 0.3689 2.8965 0.3500 2.5807 0.5734
2 Londonderry_Air
2.7105 1.4754 1.4441 1.0455 1.6698 0.5723
3 Believe_you
4.0316 2.5531 2.2330 0.8974 1.8146 0.3734
4 Drafting
1.1179 0.6379 1.1369 1.0948 1.7465 0.1387
5 Down_by_the_Riverside
7.9547 -1.3869 3.4447 -0.6613 2.4187 0.2587
6 Space_Odessey3_Revelation 2.4144 -0.3028 1.3663 1.1635 1.5952 -0.0153
7 Tomorrow
7.6395 0.6232 3.7316 -0.6296 2.0180 0.3437
8 Old_French_Song
1.9509 -0.4201 1.2753 1.2671 2.0279 -0.7724
9 Freedom
7.7726 -1.0138 3.4965 -0.8230 1.9809 -0.6257
10 Red_River_Valley (brass)7.0231 -0.2201 3.6188 -0.4069 2.6909 -0.6853
Title (*.wav)

Feeling
impression
Item1 (Quick)
Item2 (Light)
Item3 (Artificial)
Item4 (Positive)
Preference (Like)

G1
v1
0.366
0.482
0.477
0.570
0.285

G2

v1
0.296
0.382
0.367
0.518
0.603

0.400
0.200
0.000
-0.200-0.400-0.600-0.800(b) Bases vectorv2-0.520-0.249-0.269
0.460
0.619

0.600

Correlation coefficient

No.

1

G3
v2
-0.474-0.348-0.243-0.175
0.751

v1
0.227
0.364
0.495
0.483
0.581

2

3

4

1

2

AF

v2
-0.801-0.209-0.174
0.078
0.527

3

4

1

2

LF

3

4

1

2

MF

HF

(b) Group G2
1.000
0.900

17

Table 7. Correlation coefficient between principal.
AF
Principal
u1
u2
axis
v1
0.926 0.028
v2
0.216 -0.579(a) Group G1
LF
MF
u1
u2
u1
u2
0.774 0.547 0.704 0.351
0.230 0.068 0.288 -0.080

AF
Principal
u1
u2
axis
v1
0.956 0.049
v2
0.251 0.000(b) Group G2
LF
MF
u1
u2
u1
u2
0.827 0.506 0.761 0.341
0.528 -0.660 0.611 -0.351

AF
Principal
u1
u2
axis
v1
0.976 0.115
v2
0.024 -0.784(c) Group G3
LF
MF
u1
u2
u1
u2
0.945 0.280 0.911 0.226
0.031 0.083 0.075 -0.425

HF
u1
u2
0.931 -0.059
0.203 -0.294

Correlation coefficient

0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
1

HF
u1
u2
0.960 -0.015
0.233 0.371

2

3
AF

4

1

2

3

4

1

LF

2

3

4

1

MF

2
HF

(c) Group G3

Fig. 7. Correlation coefficient between principal axes.

HF
u1
u2
0.975 0.166
0.016 -0.482

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1: Correlation between <f i | u 1 > and <x i | v 1 >,2: Correlation between <f i | u 1 > and <x i | v 2 >,3: Correlation between <f i | u 2 > and <x i | v 1 >,4: Correlation between <f i | u 2 > and <x i | v 2 >.

coefficient in each group (G1, G2, and G3). The colored
portion of Table 7 indicates that the absolute value ofthe correlation coefficient is 0.700 or higher.
3.3.1. Group G1
From Table 7 (a) and Fig. 7 (a), the correlation
coefficient on AF and HF between u 1 and v 1 are 0.926
and 0.931 respectively, so they have strong positive
correlation.
We refer Fig. 5(a) and (d), increase in Fluctuation and
Residual are tendency in response to increase of u 1 .
Also from Fig. 6(a), increase in Item2 (Lightness) andItem3 (Artificial) are tendency in response to increase ofv1.
Similarly, the correlation coefficient on LF and MF
between u 1 and v 1 are 0.774 and 0.704 respectively, sothey have positive correlation.
We refer Fig. 5(a) ~ (c), Fluctuation and Residual on LF
of all music are lower than AF. And the music which
Fluctuation and Residual are small on AF, there aretendency they increase on MF.
Therefore, we consider the music become light andartificial impression by increasing Fluctuation and
Residual, on AF, MF, and HF.
3.3.2. Group G2
From Table 7 (b) and Fig. 7 (b), we understand that G2
have tendency same as G1. And, the correlation
coefficient of each domain between u 1 and v 1 are higher
than 0.761, so they have positive correlation. Besides,
we refer Fig. 6(b), increase in Item4 (Positive) is
tendency in response to increase of v 1 .
Therefore, we consider the music become positive
impression by increasing Fluctuation and Residual.
3.3.3. Group G3
From Table 7 (c) and Fig. 7 (c), we understand that thecorrelation coefficient of each domain of G3 between u 1
and v 1 are higher than 0.911, so they have strong
positive correlation. Especially the correlation
coefficient of AF between u 2 and v 2 is -0.784, so they
have negative correlation.
We refer Fig. 6(c), increase in Item4 (Positive) is
tendency in response to increase of v 1 . And from Fig 5(a) ~ (d), increase in Fluctuation and Residual aretendency in response to increase of u 1 . Furthermore,decreasing Fluctuation and increasing Residual aretendency in response to decrease of v 2 .
Therefore, we consider the music become positive
impression by increasing Fluctuation and Residual.
Especially, by increasing Fluctuation and Residual on
AF, the music become fast impression.
3.3.4. Overall tendency
We understand that 56% of examinees (Group G1) feellight and artificial impression from the music which
both of Fluctuation and Residual are high, and they havetendency that they prefer the music which Fluctuation
and Residual are high and low, respectively. We also
understand that rest of 44% examinees (Group G2 andG3) feel positive impression, but they don’t.
We can judge that the sensitivity of the music
impression is strong influence by Fluctuation and
Residual of HF, because the above tendencies arecommon to AF and HF.
4. Conclusion
In this paper, we have investigated the effects between
feature quantity of sound signal and feeling impression
by using Principal Component Analysis (PCA). Asfeature quantity, we have used Fluctuation and Residual.
As for the feeling impression questionnaire, we havepresented 10 piece of music to examinees and theyevaluated 5 items, i.e. quickness, lightness, artificial,
positiveness, and preference (like or dislike). Then, we
performed clustering analysis using Ward method basedon the evaluation results, and we understood that theexaminees feeling impression could be divided into 3
groups.
Next, we have performed PCA in the Physical Quantity
Spaces of the each frequency domain (AF, LF, MF, andHF) and performed PCA in the Feeling Adjective
Spaces of each group. Furthermore, we also investigatedcorrelation between the principal component axes.
As the results, we have understood that 56% of
examinees feel light and artificial impression from themusic in which both values of Fluctuation and Residual
are high. And we have also found that they prefer such
music.
Although there were not seen such correlativity about
the rest 44% of examinees, we were able to understandthat they feel positive impression from the music in
which the both values of Fluctuation and Residual arehigh.

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310

Moreover, we have found that the high frequency
feature quantity of sound has the strongest influence topeople’s feeling impression.

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