Assume having several numerical, multidimensional time-series. As preprocessing of further Analysis, I firstly check for relevance and then for redundany of all dimensions/Features.
1) Check for relevance: I will exclude all dimensions with a variance of 0 over the whole dataset - since this specific Dimension does not contain Information that helps to classify/distinguish the time-series from each other.
2) Check for redundancy: I compute the correlation of all dimensions/Features with each other and my Intuition says (here is my question) that those Features-pairs which correlate by either -1 or +1 are redundant. Whereas a high correlation such as 0,99 seems to be redundant, it is not. Only a correlation of either -1 or +1 means redundancy. Therefore i will randomly exclude on the two dimensions/Features which correlate by +1 or -1.
I am yet sceptical whether or not this is a correct assumption. Are there any leads that could prove / disproves my intuiton of the Connection between redundancy and correlation?