title: Segmentation of time series with long-range fractal correlations.
abstract: Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome.
authors: Dpto. de Física Aplicada II, Universidad de Málaga, 29071 Málaga, Spain.
authors: P
authors: P
authors: Bernaola-Galván
authors: J L
authors: JL
authors: Oliver
authors: M
authors: M
authors: Hackenberg
authors: A V
authors: AV
authors: Coronado
authors: P Ch
authors: PC
authors: Ivanov
authors: P
authors: P
authors: Carpena
references: Phys Rev Lett. 2001 Jun 18;86(25):5815-8
references: 11415365
references: Lancet. 1984 Jan 21;1(8369):126-31
references: 6140442
references: Phys Rev Lett. 2000 Aug 7;85(6):1342-5
references: 10991547
references: Nature. 1996 Sep 26;383(6598):323-7
references: 8848043
references: Nature. 2002 Aug 29;418(6901):955-9
references: 12198542
references: Gene. 2002 Oct 30;300(1-2):117-27
references: 12468093
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jan;71(1 Pt 1):011104
references: 15697577
references: Phys Rev Lett. 2000 Apr 3;84(14):3197-200
references: 11019046
references: Nucleic Acids Res. 2004 Jul 1;32(Web Server issue):W287-92
references: 15215396
references: Med J Aust. 1978 Jul 15;2(2):52-3
references: 713911
references: J Mol Biol. 1987 Jul 20;196(2):261-82
references: 3656447
references: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Feb;49(2):1685-9
references: 9961383
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Apr;65(4 Pt 1):041107
references: 12005806
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Mar;75(3 Pt 1):032903
references: 17500745
references: Gene. 2001 Oct 3;276(1-2):47-56
references: 11591471
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 1):051908
references: 12059594
references: Europhys Lett. 1999 Dec 1;48(5):594-600
references: 11542917
references: BMC Bioinformatics. 2007 May 23;8:171
references: 17521423
references: Phys Rev Lett. 1995 Apr 17;74(16):3293-3296
references: 10058160
references: Mol Biol Evol. 2005 Dec;22(12):2315-7
references: 16093569
references: Mol Biol Evol. 2005 May;22(5):1260-72
references: 15728737
references: Physica A. 2011 Nov 1;390(23-24):4057-4072
references: 25392599
references: IEEE Trans Biomed Eng. 2009 May;56(5):1564-73
references: 19203874
references: Science. 1997 Mar 7;275(5305):1465-8
references: 9045609
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Jul;64(1 Pt 1):011114
references: 11461232
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Mar;83(3 Pt 1):031908
references: 21517526
references: Europhys Lett. 1998 Aug 15;43(4):363-8
references: 11542723
references: Phys Rev Lett. 2001 Oct 15;87(16):168105
references: 11690251
references: Physica A. 2004 Jun;337(1-2):307-18
references: 15759365
references: Gene. 2002 Oct 30;300(1-2):105-15
references: 12468092
references: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 May;53(5):5181-5189
references: 9964850
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Dec;66(6 Pt 1):062902
references: 12513330
references: Science. 2001 Feb 16;291(5507):1304-51
references: 11181995
references: Comput Biol Chem. 2003 Feb;27(1):5-10
references: 12798034
references: Gene. 2001 Oct 3;276(1-2):57-72
references: 11591472
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jan;75(1 Pt 1):011915
references: 17358192
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Mar;79(3 Pt 2):035102
references: 19392005
references: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 May;53(5):5445-5449
references: 9964877
references: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Jun;71(6 Pt 1):061925
references: 16089783
references: Integr Physiol Behav Sci. 1994 Jul-Sep;29(3):205-10
references: 7811641
references: BMC Bioinformatics. 2006 Oct 12;7:446
references: 17038168
references: Nat Struct Biol. 1999 Apr;6(4):346-9
references: 10201403
references: IEEE Eng Med Biol Mag. 2007 Nov-Dec;26(6):33-7
references: 18189085