Stanford Synchrotron Radiation Lightsource Principal Component Analysis Apurva Mehta.

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Presentation transcript:

Stanford Synchrotron Radiation Lightsource Principal Component Analysis Apurva Mehta

1D dataset?

Apurva Mehta A new Pebble Pattern

Apurva Mehta 2D dataset? Two Eigenvectors

Apurva Mehta EXAFS dataset… Two Components/distinct phases

Apurva Mehta EXAFS dataset… Is this a new phase? Or a linear combination of the others two?

Apurva Mehta World is certainly 2D But is it higher dimensional?

Apurva Mehta With Better Data… Maybe 3D. But 11D? We need better data than Google Earth.

Apurva Mehta So it is true for other datasets too

Apurva Mehta

OK, now we know the number of components/phases/eigenvectors So what are they?

Apurva Mehta 2D dataset

Apurva Mehta 2D dataset Eigen 1 Eigen 2 Why not these?

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….

Apurva Mehta What about orthogonality?

Apurva Mehta What about orthogonality? PCA eigenvectors

Apurva Mehta What about orthogonality? Another Alternate eigenset Component 1 negative

Apurva Mehta What about orthogonality? Another Alternate eigenset All samples = +ve sum of components

Apurva Mehta What about orthogonality? Another Alternate eigenset Why not these?

Apurva Mehta Questions? Comments?

Apurva Mehta Example : Decomposition of a Cu+2 compound Ceramic Body Reaction layer

Apurva Mehta MicroXAS maps Cu 0 EB Cu M Cu X Ca K