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Published byMelina Wade Modified over 8 years ago
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Stanford Synchrotron Radiation Lightsource Principal Component Analysis Apurva Mehta
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1D dataset?
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Apurva Mehta A new Pebble Pattern
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Apurva Mehta 2D dataset? Two Eigenvectors
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Apurva Mehta EXAFS dataset… Two Components/distinct phases
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Apurva Mehta EXAFS dataset… Is this a new phase? Or a linear combination of the others two?
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Apurva Mehta World is certainly 2D But is it higher dimensional?
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Apurva Mehta With Better Data… Maybe 3D. But 11D? We need better data than Google Earth.
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Apurva Mehta So it is true for other datasets too
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Apurva Mehta
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OK, now we know the number of components/phases/eigenvectors So what are they?
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Apurva Mehta 2D dataset
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Apurva Mehta 2D dataset Eigen 1 Eigen 2 Why not these?
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Apurva Mehta PCA is just Math Knows nothing about your samples. Therefore, It picks component 1 to take up the largest variation, component 2 to take up the largest of the remainder, etc….
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Apurva Mehta What about orthogonality?
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Apurva Mehta What about orthogonality? PCA eigenvectors
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Apurva Mehta What about orthogonality? Another Alternate eigenset Component 1 negative
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Apurva Mehta What about orthogonality? Another Alternate eigenset All samples = +ve sum of components
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Apurva Mehta What about orthogonality? Another Alternate eigenset Why not these?
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Apurva Mehta Questions? Comments?
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Apurva Mehta Example : Decomposition of a Cu+2 compound Ceramic Body Reaction layer
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Apurva Mehta MicroXAS maps Cu 0 EB Cu M Cu X Ca K
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