Hi,
I am working on hyperspectral image analysis. I want to apply PCA on my hyperspectral dataset to reduce spectral dimensions. My question is Why do we need to center the hyperspectral data(mean subtraction) before applying Principal component analysis(PCA)? Is this step is mandatory? What will happen if we did not center the hyperspectral data before applying PCA.
When i googled about this I got following links.
https://www.quora.com/Why-is-it-beneficial-to-center-and-normalize-the-data-before-running-Principal-Component-Analysis-on-it
https://www.quora.com/Why-do-we-need-to-center-the-data-for-Principle-Components-Analysis
From these links, I feel data centering is required to maintain same scale for all features before applying PCA. But coming to hyperspectral data cube, generally all spectral bands will be in same scale.
So, Do we need to center the hyperspectral data before applying Principal component analysis(PCA)?? What will happen if we did not center the hyperspectral data?
Thanks.
Actually, it is a baffling question. Some peoples believe that the mean-centering is necessary. For example, take a look at " Article Remote sensing of burned areas via PCA, Part 1; centering, s...
". They mentioned, " Principal components analysis (PCA) is based conventially on the eigenvector decomposition (EVD). Mean-centering the input data prior to the eigenanalysis is treated as an integral part of the algorithm. It ensures that the first principal component is proportional to the maximum variance of the input data. Equivalent to EVD, but numerically more robust, is the singular value decomposition (SVD). Mean-centered data subjected to SVD, yield transformation coefficients identical to EVD. Nevertheless, mean-centering is optional in SVD. "On the other hand, you may find some opinions which oppose the above idea. For instance take a look at: " https://sebastianraschka.com/faq/docs/pca-scaling.html " and " https://www.researchgate.net/post/Does_PCA_require_mean_corrected_data."
I am personally of mind that the mean-centering at least facilitates the calculation and results to a more robust results. Therefore, it would be better to do the mean-centering (No matter you're working with a Hyper spectral image or something) as the well-known built-in PCA function in MATLAB does it in default.
In addition to Sayyed Hamed Alizadeh Moghaddam's post, two complementary references of interest on this topic by following:
- Alexandris et al., " Remote sensing of burned areas via PCA, Part 2: SVD-based PCA using MODIS and Landsat data ", 2017 -
Article Remote sensing of burned areas via PCA, Part 2: SVD-based PC...
- P. Honeine, " An eigenanalysis of data centering in machine learning ", 2014 - https://arxiv.org/pdf/1407.2904.pdf
The second reference covers a larger applicative scope (extension to ML).
Please explain what you want to do afterwards i.e. what is your research question. Then its much easier to help. As PCA is just a brute force decomposition, it is not the best tool to process non linear mixed signals.
Cheerrs, Chris
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