Multiset canonical correlations analysis and multispectral, truly multitemporal remote sensing data

This paper describes two- and multiset canonical correlations analysis (CCA) for data fusion, multisource, multiset, or multitemporal exploratory data analysis. These techniques transform multivariate multiset data into new orthogonal variables called canonical variates (CVs) which, when applied in remote sensing, exhibit ever-decreasing similarity (as expressed by correlation measures) over sets consisting of 1) spectral variables at fixed points in time (R-mode analysis), or 2) temporal variables with fixed wavelengths (T-mode analysis). The CVs are invariant to linear and affine transformations of the original variables within sets which means, for example, that the R-mode CVs are insensitive to changes over time in offset and gain in a measuring device. In a case study, CVs are calculated from Landsat Thematic Mapper (TM) data with six spectral bands over six consecutive years. Both Rand T-mode CVs clearly exhibit the desired characteristic: they show maximum similarity for the low-order canonical variates and minimum similarity for the high-order canonical variates. These characteristics are seen both visually and in objective measures. The results from the multiset CCA R- and T-mode analyses are very different. This difference is ascribed to the noise structure in the data. The CCA methods are related to partial least squares (PLS) methods. This paper very briefly describes multiset CCA-based multiset PLS. Also, the CCA methods can be applied as multivariate extensions to empirical orthogonal functions (EOF) techniques. Multiset CCA is well-suited for inclusion in geographical information systems (GIS).

[1]  A. Buja.  Remarks on Functional Canonical Variates, Alternating Least Squares Methods and Ace , 1990 .

[2]  Ed Anderson,et al.  LAPACK Users' Guide , 1995 .

[3]  S. Wold,et al.  The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses , 1984 .

[4]  Jan de Leeuw,et al.  Non-linear canonical correlation , 1983 .

[5]  Morton J. Canty,et al.  Possibilities and limits of remote sensing for the verification of international agreements: algorithms to detect changes at nuclear plants , 1998, IGARSS '98. Sensing and Managing the Environment. 1998 IEEE International Geoscience and Remote Sensing. Symposium Proceedings. (Cat. No.98CH36174).

[6]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[7]  Allan Aasbjerg Nielsen,et al.  Analysis of Regularly and Irregularly Sampled Spatial, Multivariate, and Multi-temporal Data , 1994 .

[8]  Håkan Olsson,et al.  Reflectance calibration of thematic mapper data for forest change detection , 1995 .

[9]  R. Preisendorfer,et al.  Principal Component Analysis in Meteorology and Oceanography , 1988 .

[10]  Håkan Olsson,et al.  Regression functions for multitemporal relative calibration of Thematic Mapper data over boreal forest , 1993 .

[11]  Paul Switzer,et al.  Ordering of time-difference data from multispectral imagery , 1986 .

[12]  Allan Aasbjerg Nielsen,et al.  Multi-Channel Remote Sensing Data and Orthogonal Transformations for Change Detection , 1999 .

[13]  J. Friedman,et al.  A Statistical View of Some Chemometrics Regression Tools , 1993 .

[14]  Robert G. D. Steel,et al.  Minimum Generalized Variance for a set of Linear Functions , 1951 .

[15]  Paul Horst,et al.  Relations amongm sets of measures , 1961 .

[16]  Arne Drud,et al.  CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems , 1985, Math. Program..

[17]  P. Switzer,et al.  A transformation for ordering multispectral data in terms of image quality with implications for noise removal , 1988 .

[18]  W. Dixon,et al.  BMDP statistical software , 1983 .

[19]  B. Ersbøll,et al.  Integration of multi-source data in mineral exploration , 1991 .

[20]  J. Friedman,et al.  Estimating Optimal Transformations for Multiple Regression and Correlation. , 1985 .

[21]  B. Kowalski,et al.  Partial least-squares regression: a tutorial , 1986 .

[22]  Sadao Fujimura,et al.  Method for change analysis with weight of significance using multitemporal multispectral images , 1994, Remote Sensing.

[23]  A. Höskuldsson.  PLS regression methods , 1988 .

[24]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[25]  Hans Knutsson,et al.  Learning multidimensional signal processing , 1998, Proceedings. Fourteenth International Conference on Pattern Recognition (Cat. No.98EX170).

[26]  J. B. Lee,et al.  Enhancement of high spectral resolution remote-sensing data by a noise-adjusted principal components transform , 1990 .

[27]  Jan de Leeuw,et al.  Use of the multinomial jack-knife and bootstrap in generalized non-linear canonical correlation analysis , 1988 .

[28]  B. Vinograde.  Canonical positive definite matrices under internal linear transformations , 1950 .

[29]  Winson Taam,et al.  Non-linear canonical correlation analysis with a simulated annealing solution , 1992 .

[30]  Knut Conradsen,et al.  Multivariate Alteration Detection (MAD) and MAF Postprocessing in Multispectral, Bitemporal Image Data: New Approaches to Change Detection Studies , 1998 .

[31]  Morton J. Canty,et al.  Unsupervised change detection techniques using multispectral satellite images , 1999, IEEE 1999 International Geoscience and Remote Sensing Symposium. IGARSS'99 (Cat. No.99CH36293).

[32]  Fusion of SPOT HRV XS and Orthophoto Data Using a Markov Random Field Model , 1998 .

[33]  Hiroshi Hanaizumi.  Change Detection From Remotely Sensed Multi-temporal Images Using Multiple Regression , 1992, [Proceedings] IGARSS '92 International Geoscience and Remote Sensing Symposium.

[34]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[35]  Chong-sun Kim.  Canonical Analysis of Several Sets of Variables , 1973 .

[36]  J. Cipar,et al.  Distinguishing vegetation land covers using hyperspectral imagery , 2003, IEEE Workshop on Advances in Techniques for Analysis of Remotely Sensed Data, 2003.