## Related methods

There are some methods rather similar or actually equal to recurrence plots developed in several scientic fields:

Method | Application | References |
---|---|---|

Close returns plot
(recurrence of a state after certain time) |
time series analysis, UPOs, financial markets |
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) |
investigation of protein folding |
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) |
genome sequence alignment, structures of proteins (cp. contact maps!), structures in text and computer code |
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 |

Dynamic time warping
(matching or alignment of two sequences) |
speech recognition |
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. |

First return map
(plot of times when states recur) |
time series analysis | 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) |
ordinal time series analysis | 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) |
time series analysis |
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) |
time series analysis | 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) |
music structure recognition |
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 |

Similarity plot
(distance plot between dynamical changing images) |
2D image analysis (images change over time) | 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. |

Space time-index plot
(another statistics of times between recurrent states) |
time series analysis (detecting of nonstationarity) | 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) |
time series analysis (detecting of nonstationarity) | 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 |

Variogram cloud/ madogram
(spatial distance in fields) |
spatial statistics (geostatistics) | N. A. C. Cressie: Statistics for spatial data, J. Wiley, 1993, ISBN 9780471002550. |

Further examples can also be found at the
self-similarity analysis web page.

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