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I have a dataset with 1228 peaks and 15 features, and I am trying to use PCA analysis to reduce dimensionality and discover the most useful features describing the dataset.

When I ran PCA analysis using R's prcomp, I found that no principle component explains the majority of the variance in my dataset.

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The second plot shows that the first 9 PCs together explain 90% of the variance in the dataset.

What I can see is that this means that PCA is probably useless for analysis of this dataset. But can I make any other observations about the nature of this data? What does it mean if none of the PCs explain the majority of the variance in the dataset?

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    $\begingroup$ It means that the data are not close to being one-dimensional. Why did you expect it in the first place? $\endgroup$
    – amoeba
    Dec 22, 2015 at 1:50
  • $\begingroup$ Are you expecting "one principal component to explain the majority of the variance" as "one principal to explain more than 50% (or 90%) of the variance"? There's no expectation that PCA will explain a majority of the variance with a single component, only that you can usually represent a high % of the variance with less components. $\endgroup$
    – David Waterworth
    Apr 19, 2021 at 2:29

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The first principal component will always account for the majority of the variance in the original matrix relative to the other PCs. This appears to be your case. To be sure, the first PC accounts for only about 40% of the variance, so your data are not really one-dimensional; however, it nonetheless does account for (and will always account for) more variance than any other PC.

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