12PrincipalComponentsAnalysisLectureNotes

12PrincipalComponentsAnalysisLectureNotes - 1 Geo 4037c...

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1 Geo 4037c Digital Image Analysis The Principal Components Analysis Principal components analysis (PCA)is a multivariate statistical technique that can be used to dramatically reduce the size of the data set. Suppose a study area overlapped with four TM images. Each image contains 7 bands and consumes approximately half a gigabyte of storage space. PCA can be used to reduce the file size and consequently processing time by removing redundant information. The way that PCA works is that the bands are plotted in multidimensional spectral space, and a regression line (or vector, in this case, called an eigenvector) is regressed to the best fit for the data. Optimum coefficients are derived for each band. These coefficients find the best fitting of the eigenvector to the spread of data. Thus, they maximize the ability of the regression eigenvector to explain the spread of data points. A single file is created, called PC1, and this new file is an image of eigenvector 1, which typically accounts for over 90% of the variability in the data set. PC1 is now an image that contains, say, 91% of all the information of the 7 band scene.
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12PrincipalComponentsAnalysisLectureNotes - 1 Geo 4037c...

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