This would have the effect of reducing the The image with just the first one or several principal components. In Landsat data, to give an example, one might perform PCA analysis on all seven bands, then reconstruct PCA analysis is often performed, for example, on multispectral image data sets. Not explained by the first vector, and so on.ĭepending on the purpose of your analysis, you can reconstruct or transform your data, using one or more (or all) Of the differences in your data, the vector with the next largestĮigenvalue is called the second principal component and explains most of the differences Largest eigenvalue is called the first principal component of the differences and explains most These vectors and values are also called the principal components of the differences in your data. Of how much of the difference between your data sets can be explained by its corresponding vector. Matching eigenvector.) The magnitude of these eigenvalues is a measure (Be sure when you order them you also order the corresponding or These eigenvaluesĬan be ordered from largest to smallest. You will also get a set of matching numbers,Ĭalled the eigenvalues. I hope you have read lots of science fiction! Note that if you are comparing more than three data sets, you willīe on your own visualizing higher dimensional orthogonal spaces.
You will have as many eigenvectors as you have data sets you are comparing.
That describe the differences in your data. In the end, you will get a set of orthogonal, or completely uncorrelated, vectors Variances or differences (also called the covariances) Ok, so Principal Components Analysis is a technique for analysing the This is a practical tutorial, not a theoretical one. What the terms standard deviation, variance, covariance matrix, eigenvectors, and eigenvalues mean, don't you? And I'll bet for the first time in your life you understand How to work the examples in Lindsay Smith's tutorial in IDL, show you why I think some of Smith's examplesĪre wrong, and maybe a few other things that will be useful to you.
Smith's marvelous PCA tutorial, entitled, naturally enough, Stop reading this nonsense for an hourĪnd go read Lindsay I. Or you are not sure what it is, or if you are like me and your eyes glaze over when confronted with theĪrcane symbolism of mathematical formulas, do yourself a favor. Images and other data in IDL, but I don't know the first thing about it.Ĭan you help me learn how to do this in IDL?ĪNSWER: If you are just coming to Principal Components Analysis (PCA) for the first time, QUESTION: I hear a lot of people talking about Principal Components Analysis (PCA) with respect to
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