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There is a larger matrix (1500 rows x 40 columns), 1500 observations x 40 variables. then I follow the procedures of PCA(Principle components analysis), 1. find correlation 2. find eigenvalues 3. find Eigenvectors I have got the result (Mathematica)

dataCorrEigenvalues/Total@dataCorrEigenvalues

{0.647833, 0.128731, 0.0843738, 0.0519215, 0.0246577, 0.018331, \
0.0100494, 0.00657219, 0.0054721, 0.00373078, 0.00310175, 0.00244999, \
0.0022292, 0.00190861, 0.00166728, 0.00124446, 0.00113064, \
0.00093684, 0.000673087, 0.000579798, 0.00049716, 0.000425554, \
0.000371012, 0.000261027, 0.000225517, 0.000173631, 0.000133479, \
0.000128954, 0.000103792, 0.0000853669}

FoldList[Plus, dataCorrEigenvalues/Total@dataCorrEigenvalues]

{0.647833, 0.776564, 0.860938, 0.91286, 0.937517, 0.955848, 0.965898, \
0.97247, 0.977942, 0.981673, 0.984775, 0.987225, 0.989454, 0.991362, \
0.99303, 0.994274, 0.995405, 0.996342, 0.997015, 0.997595, 0.998092, \
0.998517, 0.998888, 0.999149, 0.999375, 0.999548, 0.999682, 0.999811, \
0.999915, 1.}

As I know the first 6 components explain about 95% of the variability, However, I don't understand how to use these components for data analysis.

The projection Matrix "w" as the following

w = dataCorrEigenvectors[[All, 1 ;; 4]];

I try to calculate the dot product of W against data, however, it seems the result is not same as expectation.

PC5 = data.w;

Please feel free to command and advise what I should do. Thank you.

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    $\begingroup$ Interpreting PCs depends a lot on what your initial data is. Also, what is the question you want to answer? Remember, by itself, each PC is really just the vector which explains the greatest proportion of variance in the dataset. You may want to tell is there is a variable that maps onto the PCs (i.e. a variable that provides structure within the data) or if two groups cluster separately, but this depends on what you actually want to know. $\endgroup$
    – Jautis
    Jan 21, 2016 at 17:34

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