# What does it tell you when PCA cannot reduce the dimensionality of your dataset

I'm new to PCA and I'm trying to apply it to a dataset I have with 15 different features. I normalized my dataset before applying PCA and used the PCA method in the decomposition function from sklearn. I was hoping that a few PCAs (probably less than 10) would be able to explain 90% of the variance of the data matrix. But the cumulative variance I got is

 [0.21  0.323 0.413 0.486 0.555 0.619 0.681 0.74  0.794 0.844 0.89  0.922
0.953 0.981 0.9998]


which means that I need at least 12 PCs to explain 90% of the variance and 15 PCs to explain 100%. So it seems like PCA does not reduce the dimensionality of my dataset. Does it mean that the 15 features I have are not redundant? like there is no redundancy in my dataset and it's better not to eliminate any of the 15 features I currently have?

Below is my features correlation heatmap.

• Hard to say withouth looking to all factor loadings. Perhaps two or three variables are highly correlated. You could check a correlation matrix of your variables to see if it is the case: towardsdatascience.com/… Nov 20 '20 at 1:35
• Thanks for the input! I added the correlation heatmap. Nov 20 '20 at 12:50
• Most of those correlations are quite small in magnitude so your PCA results are not surprising. Nov 20 '20 at 13:05
• Take it to the extreme and consider what PCA does when your observed variables are uncorrelated (so a diagonal (empirical) covariance matrix).
– Dave
Nov 20 '20 at 13:09