Factor analysis

Algorithm

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

The following steps apply:

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

    Looking at two input raster maps the factor analysis coefficients matrix looks like:

     

     

    where:

    a1 and a2

    =

    coefficients of the first factor (factor loadings)

    b1 and b2

    =

    coefficients of the second factor (factor loadings)

     

    If M bands are used, an MxM matrix of factor analysis coefficients is computed.

     

  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, FactorAnalysisMatrix, 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 (factors):
  8.   

      

    where:

    x and y

    =

    spectral values in the first and second factor (output maps)

    X and Y

    =

    spectral values in the two input raster maps

    a1 and a2

    =

    coefficients of the first factor

    b1 and b2

    =

    coefficients of the second factor.

References:

See also: