Principal Component Analysis

Algorithm

The Principal component analysis operation results in a linear transformation of a set of (satellite) raster maps. The map values are transformed into raster map values, called components.

The following steps apply:

  1. The covariance matrix of the input raster maps is computed.
  2. The orientation of the components is computed based on the eigenvectors and eigenvalues of the covariance matrix.
  3. The vectors in each column are normalized. The normalized values are the principal component analysis coefficients.
  4.  

    With two input raster maps the principal components analysis coefficients matrix looks like:

     

     

    where:

    a1 and a2

    =

    coefficients of the first component

    b1 and b2

    =

    coefficients of the second component.

     

    With M bands an MxM matrix of principal component analysis coefficients is calculated.

     

  5. A map list is created which contains an expression with which the transformed raster maps (factors) can be defined and calculated.
  6.  

    The expression in the map list reads:

    MapListMatrixMultiply(InputMapList, PrincipalComponentsMatrix, nr of output maps)

     

  7. When the map list is opened, the pixel values of the input maps are transformed into the new raster maps (principal component):
  8.  

     

    where:

    x and y

    =

    spectral values in the first and second component

    X and Y

    =

    spectral values in the two input raster maps

    a1 and a2

    =

    coefficients of the first component

    b1 and b2

    =

    coefficients of the second component.

References:

See also: