We propose a nonlinear time series method for characterizing two layers of regularity simultaneously. The key of the method is using the recurrence plots hierarchically, which allows us to preserve the underlying regularities behind the original time series. We demonstrate the proposed method with musical data. The proposed method enables us to visualize both the local and the global musical regularities or two different features at the same time. Furthermore, the determinism scores imply that the proposed method may be useful for analyzing emotional response to the music.

1.
J.-P.
Eckmann
,
S. O.
Kamphorst
, and
D.
Ruelle
,
Europhys. Lett.
4
,
973
(
1987
).
2.
N.
Marwan
,
M. C.
Romano
,
M.
Thiel
, and
J.
Kurths
,
Phys. Rep.
438
,
237
(
2007
).
3.
Y.
Hirata
,
E.-J.
Lang
, and
K.
Aihara
, “
Recurrence plots and the analysis of multiple spike trains
,” in
Springer Handbook of Bio-/Neuroinformatics
, edited by
K.
Nikola
(
Springer
,
Berlin
,
2014
), pp.
735
744
.
4.
J. S.
Iwanski
and
E.
Bradley
,
Chaos
8
,
861
(
1998
).
5.
J. P.
Bello
,
IEEE/ACM Trans. Audio Speech Lang. Process.
19
,
2013
(
2011
).
6.
J.
Serra
,
X.
Serra
, and
R. G.
Andrzejak
,
New J. Phys.
11
,
093017
(
2009
).
7.
K.
Iwayama
,
Y.
Hirata
,
K.
Takahashi
,
K.
Watanabe
,
K.
Aihara
, and
H.
Suzuki
,
Sci. Rep.
2
,
423
(
2012
).
9.
M.
Goto
, “
Development of the RWC music database
,” in
Proceedings of the 18th International Congress on Acoustics
(ICA
2004
), Vol.
I
, pp.
553
556
.
10.
D.
Chelidze
, “
Statistical characterization of nearest neighbors to reliably estimate minimum embedding dimension
,” in
Proceedings of the International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
(ASME
2014
), Vol.
8
, p.
V008T11A015
.
11.
H.
Helmholtz
,
On the Sensations of Tone as a Physiological Basis for the Theory of Music
(
Dover Publications
,
New York
,
1877
).
12.
Y.
Ushakov
,
A.
Dubkov
, and
B.
Spagnolo
,
Phys. Rev. Lett.
107
,
108103
(
2011
).
13.
J. E.
LeDoux
,
Annu. Rev. Neurosci.
23
,
155
(
2000
).
14.
A.
Damasio
,
The Feeling of What Happens: Body and Emotion in the Making of Consciousness
(
Mariner Books
,
New York
,
2000
).
15.
Y.
Hirata
,
S.
Horai
, and
K.
Aihara
,
Eur. Phys. J. Spec. Top.
164
,
13
22
(
2008
).
17.
S.-H.
Cha
,
Math. Models Methods Appl. Sci.
1
,
300
307
(
2007
).
18.
J. F.
Donges
,
H. C. H.
Schultz
,
N.
Marwan
,
Y.
Zou
, and
J.
Kurths
,
Eur. Phys. J. B
84
,
635
651
(
2011
).
19.
S.
Suzuki
,
Y.
Hirata
, and
K.
Aihara
,
Int. J. Bifurcation Chaos
20
,
3699
(
2010
).
20.
Y.
Hirata
and
K.
Aihara
,
Chaos
25
,
123117
(
2015
).
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