I’m trying to answer several questions about properties of randomly uniform generated SDR with sparsesness of “s”.
Let me know if I’m correct !
First question : given TWO SDRs of lengths “n” bits.
- what is the probability that they don’t overlap at all ?
- what is the probability that they match 100% ?
- what is the probability that they overlap by “q” percent of “s” ?
Here is my thinking : the probability that bit at any position is 1 for both vectors is “s*s” i.e.
From this it follows that the probability of full match is :
Then the probability of partial match of q% is of s%*nbits is :
For example if we have : n=100, s=0.02 , q=0.50
the probability of partial match is :
-> (0.02^2)^(0.5*0.02*100) = 0.0004
from this it follows that : the probability of no overlap is : 1 - x => 0.9996
m’I correct ?
Next very important question how do I calculate those for “M” SDRs, not just TWO ?
Experimentally I’m getting max 8-9bits overlap when : n=2000, sparsity=0.02 and up 5000 random-samples full comparison i.e. 9/40= max 22.5% overlap