# Spatial Modeler Tutorials

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### Description:

Derive the Factor Loadings of each input band to each Principal Component as part of Principal Component Analysis. Factor Loadings are described in Jensen, John R, "Introductory Digital Image Processing" Third Edition, p297 - 299. They can also be described as the degree of correlation between each input band and each principal component. As such they are useful for determining which input bands contribute most to the higher order Principal Components.

The screenshots and tables shown in this article were derived from a Landsat 8, 7-band image of northern Georgia, USA.

 Landsat 8 image (5,4,3) on the left, derived Principal Components (PC1, PC2, PC3) on the right

This model simply takes the input multispectral image, derives the Factor Loadings and sends them to a Report text file (e.g. for loading into Excel).

The output is a matrix organised such that the columns are the Principal Components (in ascending order, left to right) and the rows are the input Bands (in ascending order, top to bottom), like this:

 PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 Band 1 0.613 0.473 -0.599 -0.013 0.199 -0.023 -0.037 Band 2 0.637 0.513 -0.558 -0.025 0.131 -0.008 0.035 Band 3 0.762 0.410 -0.471 -0.073 -0.078 0.135 -0.004 Band 4 0.730 0.582 -0.338 -0.018 -0.092 -0.069 -0.001 Band 5 0.506 -0.861 -0.045 0.012 -0.002 -0.002 0.000 Band 6 0.949 0.242 0.190 -0.074 0.011 -0.002 0.000 Band 7 0.852 0.501 0.075 0.136 0.002 0.010 0.000

For example in the table above, Principal Component 1 has a correlation of 0.613 with input Band 1, a correlation of 0.730 with Band 4 and a correlation of 0.852 with Band 7. Principal Component 2 is most highly correlated with Bands 5 (in an inverse fashion), 4 and 2. Etc.

This model does not calculate a Principal Components image. But if desired this model could be easily combined with other Principal Component Analysis models, such as the one described here (https://community.hexagongeospatial.com/t5/Spatial-Recipes/Calculate-Principal-Components-and-Report...) to offer one model which generates several derivative PCA products, including a PC image.

### Input parameters:

Input MS Image:  Filename for the input multispectral image to have Principal Components Analysis performed on it and Loading Factors derived

Skip Factor: Enter an integer statistics sampling factor.  Larger numbers will increase processing speed at the expense of some accuracy. 1 uses all pixel values, 4 uses every fourth row and column value, etc.