How to reduce an unknown size data into a fixed size data? Please read details
My approach would be using the Moments.
Using moments is a cool way trowing any arbitrary set of points into space, and it is used for both probability and mass calculations.
Since you have not stated what are you going to do with this vector representation I guess that a generalized "shape" like representation might work for you. 

If you are using Python, then this can help.