Anyway, recall one definition of simm:

simm(w,f,g) = \Sum_k w[k] min(f[k],g[k]) / max(w*f,w*g)If we ignore the max(w*f,w*g) denominator, here is a MatSumSig version of simm:

[ r ] = [ sigmoid[x1] ] [ w1 w2 w3 w4 ] [ pos[x1] ] [ 1 -1 -1 0 0 0 0 0 0 0 0 0 ] [ pos[x1] ] [ 1 1 0 0 0 0 0 0 ] [ f1 ] [ pos[x2] ] [ 0 0 0 1 -1 -1 0 0 0 0 0 0 ] [ pos[x2] ] [ 1 -1 0 0 0 0 0 0 ] [ g1 ] [ pos[x3] ] [ 0 0 0 0 0 0 1 -1 -1 0 0 0 ] [ pos[x3] ] [ -1 1 0 0 0 0 0 0 ] [ f2 ] [ pos[x4] ] [ 0 0 0 0 0 0 0 0 0 1 -1 -1 ] [ pos[x4] ] [ 0 0 1 1 0 0 0 0 ] [ g2 ] [ pos[x5] ] [ 0 0 1 -1 0 0 0 0 ] [ f3 ] [ pos[x6] ] [ 0 0 -1 1 0 0 0 0 ] [ g3 ] [ pos[x7] ] [ 0 0 0 0 1 1 0 0 ] [ f4 ] [ pos[x8] ] [ 0 0 0 0 1 -1 0 0 ] [ g4 ] [ pos[x9] ] [ 0 0 0 0 -1 1 0 0 ] [ pos[x10] ] [ 0 0 0 0 0 0 1 1 ] [ pos[x11] ] [ 0 0 0 0 0 0 1 -1 ] [ pos[x12] ] [ 0 0 0 0 0 0 -1 1 ]where it is assumed w_k >= 0.

If we extract out the intersection component, see last post, we have:

[I1,I2,I3,I4] = 2* [min(f1,g1), min(f2,g2), min(f3,g3), min(f4,g4)] [ r ] = [ sigmoid[x1] ] [ w1 w2 w3 w4 ] [ I1 ] [ I2 ] [ I3 ] [ I4 ]Now, the above can be considered a space based simm. We can also do a time based one. I think it goes like this, though I haven't given this much thought in a long, long time!

[ r ] = [ sum[x1,t2] ] [ sigmoid[x1,t1] ] [ 1 -1 -1 ] [ pos[x1] ] [ 1 1 ] [ f ] [ pos[x2] ] [ 1 -1 ] [ g ] [ pos[x3] ] [ -1 1 ]where [ sum[x1,t2] ] is the time based equivalent of [ w1 w2 w3 w4 ]

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updated: 19/12/2016

by Garry Morrison

email: garry -at- semantic-db.org