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Last Post 01 Apr 2008 03:02 AM by  anon
Covariance matrix
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anon



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01 Apr 2008 03:02 AM
    Hello forum, Generally a covariance is statistical measure of the tendency of variables to move or vary together. So I would like to ask about the meaning of values in covariance matrix that I produced for certain ROI over multispectral image.

    MariM



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    01 Apr 2008 03:02 AM
    The covariance matrix produced in ENVI (for ROIs or for entire images) represent the variance-covariance for each input variable (band) and is a standard covariance matrix which can be read about in many statistics textbooks or found on many websites. A typical matrix could look like the following: Covariance Band 1 Band 2 Band 3 Band 4 Band 5 Band 6 Band 1 8.599503 11.174737 15.494209 -8.037589 20.246167 25.925923 Band 2 11.174737 15.747146 21.785713 -7.596741 27.531285 34.383645 Band 3 15.494209 21.785713 31.914576 -13.880573 39.939858 48.719358 Band 4 -8.037589 -7.596741 -13.880573 59.225776 -22.452640 -35.318013 Band 5 20.246167 27.531285 39.939858 -22.452640 61.784982 73.710561 Band 6 25.925923 34.383645 48.719358 -35.318013 73.710561 95.427294 where the diagonal (Band1:Band1, Band2: Band2...) represents the band variance, and values above and below represent the band-to-band covariance. The matrix is symmetrical meaning that the covariance matrix 'below' the variance diagonal is the same as the covariance matrix 'above' the variance diagonal. If the bands had unit variance, than the covariance matrix would be the same as the correlation matrix. Are there specific questions you have about the covariance matrix?
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