I have a data frame with about 500 observations and 8 variables that I'd like to run through PCA in order to try and reduce the number of variables to only those with the most variance.
From here, I want to find the [Euclidean] distance between each observation.
Here's my question: should I use every Principal Component to calculate the distances? Or should I just use (by the general rule of thumb) the Principal Components that describe, in total, about 90% of the variance (here, the first 6)?
Here's the importance of components (from R) if you're curious:
Importance of components: PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 Standard deviation 1.4652 1.1997 1.0477 0.9630 0.9103 0.87524 0.75321 0.47645 Proportion of Variance 0.2683 0.1799 0.1372 0.1159 0.1036 0.09576 0.07092 0.02838 Cumulative Proportion 0.2683 0.4482 0.5855 0.7014 0.8050 0.90071 0.97162 1.00000
Any ideas? I'd appreciate any insight.