The relation of eigenvalue and PCs in PCA

In R, I got the result of PCA and eigenvalues and vectors and three eigenvalues above 1 were checked.

If so, is it valid data from PCA results to PC1 ~ 3?

Here is my eigen values and vectors,

eigen() decomposition
$values [1] 2.3502254 1.4170606 1.2658360 0.8148231 0.5608698 0.3438629 0.2473222$vectors
[,1]        [,2]        [,3]        [,4]        [,5]         [,6]         [,7]
[1,]  0.2388621  0.46839043  0.37003850  0.47205027 -0.58802244 -0.133939151 -0.009233395
[2,]  0.1671739 -0.71097984 -0.14062597  0.25083439 -0.26726985 -0.502411130 -0.244983436
[3,]  0.2132841 -0.19677142  0.64662974  0.34508779  0.61416969 -0.003950736  0.036814153
[4,]  0.1697817 -0.24468987  0.55631886 -0.69016805 -0.34039757  0.039899816  0.089531675
[5,]  0.4857016  0.36681570 -0.09905329 -0.31456085  0.26225761 -0.344919726 -0.577088755
[6,] -0.5359245  0.20164924  0.17958243 -0.13144417  0.11755661 -0.748885304  0.218966481
[7,]  0.5635252  0.03619081 -0.27131854 -0.05105919  0.08439733 -0.219629096  0.741315659


and, Here is my PCA result

Importance of components:
PC1    PC2    PC3    PC4     PC5     PC6     PC7
Standard deviation     1.5330 1.1904 1.1251 0.9027 0.74891 0.58640 0.49732
Proportion of Variance 0.3357 0.2024 0.1808 0.1164 0.08012 0.04912 0.03533
Cumulative Proportion  0.3357 0.5382 0.7190 0.8354 0.91554 0.96467 1.00000


but, in PC3 Cumulative Proportion is only 71.9%. Still, since the eigenvalue is 3, should I say that data only valid up to PC3?

for the comment, I added my scree plot.

migrated from stackoverflow.comApr 24 at 7:52

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• What do you mean by the word "valid"? – jkpate Apr 24 at 9:46

Your question is not very clear. But mostly, PCA is used to do denoise a dataset or reduce its dimensionality. What are you using PCA for? Secondly, although there are rules of thumb people use to derive how many principal components to take, there is no right or wrong here. People tend to look at a so-called elbow-plot which looks at the cumulative variance explained for every number of principal components and then look for that number of principal components before a large drop, i.e. the elbow.

• I added my scree plot. – S. Oh Apr 24 at 8:46