I have a data set, all the vectors are ranging from 0-1, positive skewed, I used PCA to reduce the dimension and find importance features, I tried by using the original data and the data after Z-score scaled, the features identified by using the original data seem more sensible to me, but re-scaling the data before PCA seems like a standard procedure, can I just use PCA on my positive skewed data?
I also tried to transform the data but cannot find a way to transform them into normal distribution.
Hello Lu,
The conversion of scores to z-scores doesn't change the shape of a distribution, nor will it affect the relationships of scores with those of any other variable (e.g., it's a linear transformation).
I suspect that, the reason you are unable to "fix" the positive skew is because your data are in the interval of 0..1. Ordinarily, transforms like root (e.g., Y' = sqr root(Y)) or log work just fine, so long as your data are all above 1.0. So, add a constant first, then try the (nonlinear) transform. Alternatively, you could multiply by a constant (e.g., 10 or 100) to get the values all above 1 and to expand the scale. Arc sin transforms are frequently used when data are expressed as proportions (and therefore in the interval of 0..1).
Finally, to answer your question: Of course you can analyze data any way you wish, regardless of symmetry/skew...the numbers will NOT leap off the page and shout in protest!
Good luck with your work.
Dear Lu Liu
I strongly recommended David Morse answer. However, I would like to ask if you standardized (normalized) your data during the analysis with PCA. Skewed result could be caused by a sample set not standardize. Please check this fact out. if you did, then follow David Morse suggestion. If you did not, please normalize your data.
All the best
David Morse Edenio Olivares Diaz Hi thanks for the answer, my data is actually generated from subtitles and trained by a neural network model, and has been L1-normalised, that’s why it’s positive skewed, I feel like it would make more sense if I perform PCA without doing transformation as it might lose some information of my data, but on the other hand, I need to be careful about the ‘outliers’, I’ll try arc sin transformation and compare the result to see which one is more reasonable.
Dear Lu Liu ,
Please check the mean of each variable of your data. If there is a significant difference among the variable means, I strongly recommend you to standardize your data by multiplying each variable wit the inverse of the standard deviation SD of the corresponding variable (1/SD). As a result, each standardized variable will get the same variance and when you carry out PCA any variable will dominate over another thus influence the model.
All the best
Hi Lu Liu
Please check if the variable with the higher number explained the higher variance in previous PCA analysis. This will help you to understand also if the data need to be standardize.
Also, check if the range is similar among those small numbers. Anyway, if one of them is significant higher with respect to the other, you need to standardize your data while carrying out the PCA analysis.
Remember PCA is an exploratory analysis, therefore after you are able to preprocess the data set for carrying out the machine learning algorithm.
Have a great weekend,
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