How best to reduce dimensionality of a dataset composed of events and trials? I'm trying to reduce dataset dimensionality. PCA is a good metric but that gives me new dataset. My goal is to determine from number of events (e.g. 60) and number of trials (e.g. 6) which events are more relevant.  
For example:


*

*1st, 3rd, 21st, 45th ... (N total) events are good enough to approximate behavior of dataset.
That will allow me to discard  60-N events, and to deal with only N.


For now, I'm calculating covariance matrix, and take events for which correlation is smaller than some threshold.
Is there some official metric or math function for this?
 A: What you are describing is not dimensionality reduction, but rather sampling. If your data is labeled (which I couldn't understand from your question), then most probably you would want to perform stratified sampling - a random sampling that ensures that each label is sampled with a probability that approximately equals to that in the original data set.
See this Wikipedia article on sampling techniques. It provides a list of good reading material on this matter
A: I think that any answer depends heavily on your notion of 'relevant' and also on the question why you want to do this.
Anyway, an approach that might work for you is sth like 'stemming'. This originates from natural language processing, where the events 'played' and 'playing' are both mapped to the equivalence class 'play'.
A way to do this for arbitrary real valued data is to use a clustering method (eg K-Means) with as many centroids as you want items in your new dataset. After fitting K-Means, you keep those centroids as the new dataset.
