# If almost all variance is explained by the few first principal components, what can we say about the dataset?

What can we say about a dataset if we apply PCA and observe that there is a high percentage of variance in the first principal component(s)?

Can we say that this dataset has linear structure? Can we say that most of the features in this dataset are highly correlated?

For example, I extracted PC1 and PC2 for two high-dimensional datasets $A$ and $B$. For data set $A$, 95% of variance is explained by PC1 and PC2. Whereas for data set $B$, we only observed 40% of variance explained by PC1 and PC2. What can we infer about datasets $A$ and $B$?

• Welcome to Cross Validated. In order to allow our users to help you, you need to add more details to your post. Can you post some of your output here so that we know what you're dealing with? A screengrab is fine. – Marquis de Carabas May 3 '16 at 23:11
• @amoeba, the question has since been edited to add information about what the OP meant by "high percentage." I also didn't understand the "linearly separable" part. – Marquis de Carabas May 4 '16 at 15:59
• @amoeba : Some data-sets have non-linear structure (like swiss-roll researchgate.net/figure/…). Th linear dimension reduction techniques (like PCA) does not work well for them. My question is this: if first PCA components provides high explained variance, does it mean the data has linear structure? – JBJT May 4 '16 at 16:04
• @amoeba That's right. I mean "linear Structure". I may need to edit my post. – JBJT May 5 '16 at 0:55