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I have a high dimensionality data set (20k rows, 50 variables). when running PCA on it, PC1 is about 20%, PC2 is 16%, etc etc. I have to go up to PC30 to get 90% explained variance.

What I'm trying to do is to perform PCA on my data, do K-means clustering, and be able to say PC1 is mostly "gender" related, PC2 is mostly about "income" related, etc, using the eigen vectors (from my research online, that's how to interpret PCs?)

So what i'm getting is this: low PC1 and PC2s. when I look at the PC1 eigen values, the highest value is like .2. when I look at something like PC 24(which has an extremely low variance explained), I do see one eigenvalue that is .6.

So in terms of interpretability, I'm not sure how to proceed.

  1. can I rely on a low eigen value on PC1 which has .2 variance explained?
  2. can I rely on a fairly high eigen value, but with a PC that has a very very low variance explained?
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PCA is a good technique for data dimension reduction. Based on what you shared, few thoughts as suggestions:

  1. Eigen values measure the variability for each component. You should choose the components with eigen values greater or equal to one.

  2. The sum of all eigen values produces a measure of variability in your data. If your eigen values are close to zero, variability is to low and using only two components as input for clustering will not produce a robust scheme for groups.

  3. What to do in this case. You can scale your data ($(x_j-mean_j)/\sigma_j$). Apply that for all your variables and the results must change. In case you decided not scaling, your should take all components that accumulate at least 90% of variability in data, in this situation as you mentioned 30 components.

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