Related methods
There are some methods rather similar or actually equal to recurrence plots
developed in several scientic fields:
Close returns plot
(recurrence of a state after certain time)
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time series analysis, UPOs, financial markets
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G. M. Mindlin, R. Gilmore:
Topological analysis and synthesis of chaotic time series,
Physica D, 58(1-4), 1992, 229-242.
DOI:10.1016/0167-2789(92)90111-Y
C. G. Gilmore:
A new test for chaos,
Journal of Economic Behavior & Organization, 22(2), 1993, 209-237.
DOI:10.1016/0167-2681(93)90064-V |
Contact map
(map of contacts of protein sequences)
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investigation of protein folding
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H. S. Chan, K. A. Dill:
Intrachain loops in polymers: Effects of excluded volume,
The Journal of Chemical Physics, 90(1), 1989, 492-509.
DOI:10.1063/1.456500
H. S. Chan, K. A. Dill:
Origins of Structure in Globular Proteins,
Proceedings of the National Academy of Sciences, 87, 1990, 6388-6392.
WWW:www.pnas.org/cgi/content/abstract/87/16/6388
L. Holm, Chr. Sander:
Protein Structure Comparison by Alignment of Distance Matrices,
Journal of Molecular Biology,
233(1), 1993, 123-138.
DOI:10.1006/jmbi.1993.1489
E. L. L. Sonnhammer and J. C. Wootton:
Dynamic contact maps of protein structures, Journal of Molecular Graphics and Modelling, 16(1), 1998, 1-5.
DOI:10.1016/S1093-3263(98)00009-6
E. Domany:
Protein folding in contact map space, Physica A, 288(1-4), 2000, 1-9.
DOI:10.1016/S0378-4371(00)00410-6 |
Dot plot, Dot matrix, Graphic matrix, Link plot, Sequence matrix
(recurrence of symbols)
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genome sequence alignment, structures of
proteins (cp. contact maps!), structures in text and
computer code
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J. V. Maizel, R. P. Lenk:
Enhanced Graphic Matrix Analysis of Nucleic Acid and Protein Sequences,
Proceedings of the National Academy of Sciences, 78(12), 1981, 7665-7669.
WWW:pnas.org/cgi/content/abstract/78/12/7665
J. B. Kruskal:
An overview of sequence comparison,
In: Time Warps, String Edits, and Macromolecules: The Theory and
Practice of Sequence Comparison,
Eds.: D. Sankoff and J. B. Kruskal, Addison-Wesley,
Reading, Mass., 1983, 1-44.
G. Krishnan, R. K. Kaul, P. Jagadeeswaran:
DNA sequence analysis: a procedure to find homologies among many
sequences, Nucleic Acids Research, 14(1), 1986, 543-550.
WWW:nar.oupjournals.org/cgi/content/abstract/14/1/543
M. Vihinen:
An algorithm for simultaneous comparison of several sequences,
Computer applications in the biosciences: CABIOS, 4(1), 1988, 89-92.
WWW:bioinformatics.oupjournals.org/cgi/content/abstract/4/1/89
W. R. Pearson, D. J. Lipman:
Improved Tools for Biological Sequence Comparison,
Proceedings of the National Academy of Sciences, 85(8), 1988, 2444-2448.
WWW:pnas.org/cgi/content/abstract/85/8/2444
M. Bernstein, J. D. Bolter, M. Joyce, E. Mylonas:
Architectures for volatile hypertext,
In: Proceedings of the third annual ACM conference on Hypertext, San Antonio, USA, 1991, 243-260.
DOI:10.1145/122974.122999
WWW:imagebeat.com/dotplot
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Dynamic time warping
(matching or alignment of two sequences)
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speech recognition
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H. Sakoe, S. Chiba:
Dynamic programming algorithm optimization for spoken word recognition,
IEEE Trans. Acoustics, Speech and Signal Proc.,
26, 1978, 43-49.
L. Rabiner, B.-H. Juang:
Fundamentals of Speech Recognition, Prentice Hall, PTR, 1993,
ISBN: 0-13-015157-2.
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First return map
(plot of times when states recur)
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time series analysis
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D. P. Lathrop, E. J. Kostelich:
Characterization of an experimental strange attractor by periodic orbits,
Physical Review A, 40(7), 1989, 4028-4031.
DOI:10.1103/PhysRevA.40.4028 |
Order matrix
(pair-wise rank order test)
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ordinal time series analysis
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Chr. Bandt:
Ordinal time series analysis, Ecological Modelling, 182(3-4), 2004, 229-238.
DOI:10.1016/j.ecolmodel.2004.04.003 |
Recurrence time statistics
(statistics of times between recurrent states)
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time series analysis
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J. B. Gao:
Recurrence Time Statistics for Chaotic Systems and Their Applications,
Physical Review Letters, 83(16), 1999, 3178-3181.
DOI:10.1103/PhysRevLett.83.3178
V. Balakrishnan, G. Nicolis, C. Nicolis:
Recurrence time statistics in deterministic and stochastic dynamical
systems in continuous time: A comparison,
Physical Review E, 61(3), 2000, 2490-2499.
DOI:10.1103/PhysRevE.61.2490
E. G. Altmann, E. C. da Silva, I. L. Caldas:
Recurrence time statistics for finite size intervals,
Chaos, 14(4), 2004, 975-981.
DOI:10.1063/1.1795491 |
SDC plots
(scale-dependent correlations)
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time series analysis
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X. Rodó , M.-À. Rodríguez-Arias:
A new method to detect transitory signatures and local
time/space variability structures in the climate
system: the scale-dependent correlation analysis,
Climate Dynamics, 27(5), 2006, 441-458.
DOI:10.1007/s00382-005-0106-4 |
Self-similarity matrix, IXEGRAM
(recurrence/distance of features, e.g. frequencies or histogrammes)
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music structure recognition
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J. Foote:
Visualizing Music and Audio using Self-Similarity,
In: Proceedings of ACM Multimedia '99, Orlando, Florida.
M. A. Casey, W. Westner:
Separation of Mixed Audio Sources by Independent Subspace Analysis,
In: Proceedings of the International Computer Music Conference (ICMC), 2000.
WWW:www.merl.com/papers/TR2001-31
M. A. Casey:
Sound Classification and Similarity Tools,
in B.S. Manjunath, P. Salembier and T. Sikora, (Eds),
Introduction to MPEG-7: Multimedia Content Description Language,
J. Wiley, 2002, 309-323.
WWW:musicstructure.com
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Similarity plot
(distance plot between dynamical changing images)
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2D image analysis (images change over time)
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R. Cutler and L. Davis:
Robust Periodic Motion and Motion Symmetry Detection,
In: Proceedings of the Conference on Computer Vision and Pattern Recognition, South Carolina, USA, 2000.
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Space time-index plot
(another statistics of times between recurrent states)
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time series analysis (detecting of nonstationarity)
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D. Yu, W. Lu, R. G. Harrison:
Space time-index plots for probing dynamical nonstationarity,
Physics Letters A, 250(4-6), 1998, 323-327.
DOI:10.1016/S0375-9601(98)00767-1 |
Space time separation plot
(yet another statistics of times between recurrent states)
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time series analysis (detecting of nonstationarity)
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A. Provenzale, L. A. Smith, R. Vio, G. Murante:
Distinguishing between low-dimensional dynamics and randomness in measured time series,
Physica D, 58(1-4), 1992, 31-49.
DOI:10.1016/0167-2789(92)90100-2 |
Further examples can also be found at the
self-similarity analysis web page.
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(www.recurrence-plot.tk)
as well as N. Marwan: Encounters With Neighbours -
Current Developments Of Concepts Based On Recurrence Plots
And Their Applications, Ph.D. Thesis, University of Potsdam,
ISBN 3-00-012347-4.
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