The Principal Component Analysis operation is mathematical method to uncover relationships among many variables (as found in a set of raster maps in a map list) and to reduce the amount of data needed to define the relationships. With Principal Component Analysis each variable is transformed into a linear combination of orthogonal common components (output raster maps) with decreasing variation. The linear transformation assumes the components will explain all of the variance in each variable. Hence each component (output raster map) carries different information which is uncorrelated with other components.
The input for Principal components analysis consists of a map list with raster maps from which the covariance matrix will be calculated.
The output of the principal component analysis operation is:
The output raster maps are listed in decreasing order of variance. This enables a reduction of output maps because the last number of transformed maps have little or no variation left (may be virtually constant maps). The 'last' components thus do not add significance and may hence be discarded. During the operation, the number of output bands can be directly reduced by specifying a parameter.
The additional information of the output matrix contains furthermore the amount of variance accounted for by each component.
Note:
Just as Principal Component Analysis uses the covariance matrix to calculate the map transformations, Factor analysis uses the correlation matrix (standardized variance-covariance matrix). The difference in approach is that Principal Component Analysis is more of a mathematical manipulation whilst Factor analysis is regarded as a statistical technique (Davis, 1986).
Principal components analysis can be used for several purposes, e.g.:
Input requirements:
The operation requires a map list that contains at least 2 raster maps (bands) and, when using the dialog box, a maximum of 99 raster maps. On the command line, the maximum number of bands in the input map list is not limited.
All raster maps in the map list must use the Image domain or the same value domain, and all raster maps should have the same georeference. Undefined values in the input raster maps are ignored.
Output objects of this operation:
Domain and georeference of output raster maps:
The output raster maps use the system Value domain and have the same georeference as the input raster maps.
See also:
Principal Component Analysis: dialog box
Principal Component Analysis: command line