1. Data Mining / Information Extraction Techniques: Principal Component Images Don Hillger NOAA/NESDIS/RAMMT CIRA / Colorado State University hillger@cira.colostate.edu 20-21 August 2003

2. Principal Component Image (PCI) transformation of multi-spectral imagery Terminology/Definitions:  PCI = Principal Component Image – a new image combination  Eigenvectors = transformation vectors to create PCIs from multi-spectral imagery  Eigenvalues = explained variances (weights) of the principal component images

3. Why transform imagery? To simplify multi-spectral imagery by reducing redundancy to obtain the independent information A new set of images that are optimal combinations of the original spectral-band images for extracting the variance in the available imagery Important image combinations for detection of atmospheric and surface features in multi- spectral data

4. GOES Imager bands GOES-8/11 band Central Wavelength Spatial Resolution Purpose 10.7 um1 kmCloud cover 23.9 um4 km Low clouds, hot spots 36.7 um8 kmWater vapor 410.7 um4 km Surface or cloud-top temperature 512.0 um4 kmDirty window

5. General Case band(N)  PCI(N)  The number of component images resulting from a PCI transformation is equal to the number of spectral- band images input.  The sum of the explained variances of the component images is equal to the sum of the explained variances of the original images (the same information content as the original imagery expressed in a new form)

6. General Case PCI = E @ B where:  PCI = transformed set of N images, at M horizontal locations (pixels)  E = N by N transformation matrix. The rows of E are the eigenvectors of the symmetric matrix with elements determined by the covariance of each band with every other band (summed over M pixels)  B = set of imagery from N bands, viewing a scene at M horizontal locations (pixels)

7. Two-dimensional Case pci1 = e1 @ band1 + e2 @ band2 pci2 = f1 @ band1 + f2 @ band2 where: pci1 and pci2 = Principal Component Images (PCIs) band1 and band2 = band images e and f = linear transformation vectors (eigenvectors, or rows in the eigenvector matrix E). In the two-dimensional case: pci1 usually contains the information that is common to the band1 and band2 images pci2 contains the information that is different between the band1 and band2 images.

8. 2-dimensional case – Montserrat / Soufriere Hills volcano 2 PCIs2 bands

9. 2-dimensional case – Montserrat / Soufriere Hills volcano Comparison to ash- cloud analysis

10. GOES 5-band Imager Covariance Matrix band12345 11. 2-0.6221. 3-0.6030.6531. 4-0.7600.9200.7981. 5-0.7580.9000.8160.9981.

11. GOES 5-band Principal Component Matrix Band 12345 PCI 1-0.3200.3600.1270.6180.608 20.9130.3650.0090.1390.120 3-0.2410.784-0.422-0.141-0.359 4-0.0790.3240.895-0.207-0.211 50.028-0.1310.0620.732-0.665

12. 5-band transform (GOES Imager)

14. 5 bands5 PCIs

15. 5 bands (GOES Imager)

16. 5 PCIs (GOES Imager)

17. Signal-to-Noise (GOES Imager)  5 bands 5 PCIs 

18. 19-band transform (GOES Sounder) 19 bands 19 PCIs

19. 19-band transform (GOES Sounder)

21. 19 bands (GOES Sounder)

22. 19 PCIs (GOES Sounder)

23. Signal-to-Noise (GOES Sounder)  19 bands 19 PCIs 

24. Analysis of MODIS

26. Northeast UT fog/status: 7 Dec 2002 18 UTC

27. Northeast UT fog/status: 12 Dec 2002 18 UTC

28. Arizona fires – 21 June 2002 1806 UTC (MODIS) Principal Component Images of fire hot spots and smoke rings of fire smoke clouds

29. Arizona fires – 23 June 2002 1754 UTC (MODIS) Principal Component Images of fire hot spots and smoke rings of fire smoke

30. In conclusion: Why transform imagery? To simplify multi-spectral imagery by reducing redundancy to obtain the independent information A new set of images that are optimal combinations of the original spectral-band images for extracting the variance in the available imagery Important image combinations for detection of atmospheric and surface features in multi- spectral data