Principal Components and Independent Component Analysis of Solar and Space Data

Abstract Principal components analysis (PCA) and independent component analysis (ICA) are used to identify global patterns in solar and space data. PCA seeks orthogonal modes of the two-point correlation matrix constructed from a data set. It permits the identification of structures that remain coherent and correlated or that recur throughout a time series. ICA seeks for maximally independent modes and takes into account all order correlations of the data. We apply PCA to the interplanetary magnetic field polarity near 1 AU and to the 3.25R⊙ source-surface fields in the solar corona. The rotations of the two-sector structures of these systems vary together to high accuracy during the active interval of solar cycle 23. We then use PCA and ICA to hunt for preferred longitudes in northern hemisphere Carrington maps of magnetic fields.

[1]  C. Chatfield,et al.  Fourier Analysis of Time Series: An Introduction , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  James V. Stone.  Independent Component Analysis: A Tutorial Introduction , 2007 .

[3]  Chris Chatfield,et al.  The Analysis of Time Series: An Introduction , 1981 .

[4]  A. Ruzmaikin,et al.  The solar magnetic field and the solar wind: Existence of preferred longitudes , 2000 .

[5]  J. Wilcox,et al.  A model of interplanetary and coronal magnetic fields , 1969 .

[6]  Alexander Ruzmaikin,et al.  Principal Component Analysis of the Solar Magnetic Field I: The Axisymmetric Field at the Photosphere , 2004 .

[7]  M. Altschuler,et al.  Magnetic fields and the structure of the solar corona , 1969 .

[8]  J. Harvey,et al.  Phase Coherence Analysis of Solar Magnetic Activity , 2002, astro-ph/0612606.

[9]  J. Elsner,et al.  Singular Spectrum Analysis: A New Tool in Time Series Analysis , 1996 .

[10]  P. Scherrer,et al.  Rotation of the Coronal Magnetic Field , 1986 .

[11]  G. Newkirk,et al.  Magnetic fields and the structure of the solar corona , 1970 .

[12]  Erkki Oja,et al.  Independent component analysis for artefact separation in astrophysical images , 2003, Neural Networks.

[13]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[14]  A. Pevtsov,et al.  Large-scale Structures and their Role in Solar Activity , 2005 .

[15]  J. Edward Jackson,et al.  A User's Guide to Principal Components. , 1991 .

[16]  A. Ruzmaikin,et al.  Independent Global Modes of Solar Magnetic Field Fluctuations , 2005 .

[17]  N. Sheeley,et al.  The quasi-rigid rotation of coronal magnetic fields , 1988 .

[18]  A. Ruzmaikin,et al.  Preferred solar longitudes with signatures in the solar wind , 2001 .

[19]  J. E. Jackson.  A User's Guide to Principal Components , 1991 .

[20]  J. Kruskal.  TOWARD A PRACTICAL METHOD WHICH HELPS UNCOVER THE STRUCTURE OF A SET OF MULTIVARIATE OBSERVATIONS BY FINDING THE LINEAR TRANSFORMATION WHICH OPTIMIZES A NEW “INDEX OF CONDENSATION” , 1969 .