I am working on analysing and visualizing a dataset having 12 features and came across PCA. I reduced the dataset to 2 principal components which together explain a variance of 18%. I was able to plot the data and see if there is a tendency to form natural clusters within the data. But I could not understand what to conclude where the first two principal components only explain 18% of the variance in the whole data.
So, what could be concluded in general when:
- The variance suggested by the first two principal components is very high as being close 90%
- The variance suggested by the first two principal components is very low as 18% as has happened in my case
Thinking about the above 2 questions also makes me think about the assumptions PCA makes about data? What data would not be a good fit for PCA / or when should I avoid using PCA?
Edit:
Following is the loadings table, which I computed using python's scikit as :
pca.components_.T * np.sqrt(pca.explained_variance_)
Loadings:
[[ 0.8616755 -0.15340052]
[-0.42014373 0.38166004]
[ 0.81644887 -0.21071762]
[ 0.25729266 0.37770332]
[ 0.37376327 0.205526 ]
[-0.0636729 0.71293634]
[ 0.04151499 0.79056501]
[ 0.69621113 0.32425081]
[-0.77222693 0.00931596]
[ 0.42778107 -0.05213256]
[-0.19940009 -0.53609858]]
Also, here are the first 2 principal components created from the dataset:
[[ 0.48931422 -0.23858436 0.46363166 0.14610715 0.21224658 -0.03615752
0.02357485 0.39535301 -0.43851962 0.24292133 -0.11323207]
[-0.11050274 0.27493048 -0.15179136 0.27208024 0.14805156 0.51356681
0.56948696 0.23357549 0.00671079 -0.03755392 -0.38618096]]