Simon Burton <simon at arrowtheory.com> writes: > Oh, that should probably read: > > exp( -1/2\sigma^{2} ||x1_{i} - x2_{j}||_{2}^{2}) > > And when we vectorize this operation: > > ||x1_i - x2_j||^2 = ||x1_i||^2 + ||x2_i||^2 + 2*(x1_i,x2_j) > > and the last term is the ip matrix. > > It seems that this expression satisfies the linear operator > requirement (it's invarient under linear isometries).
I am looking again, and it appears to be the normalized graph laplacian. This is indeed a linear operator which we need to support. Matt > Simon. > > > On Thu, 18 Aug 2005 23:12:21 -0500 (CDT) > Barry Smith <bsmith at mcs.anl.gov> wrote: > >> >> In terms of exp( -1/2\sigma^{2} ||x_{i} - x_{j}||_{2}^{2}) >> what are they? >> >> Thanks >> >> Barry >> >> >> On Fri, 19 Aug 2005, Simon Burton wrote: >> >> > On Thu, 18 Aug 2005 22:49:29 -0500 (CDT) >> > Barry Smith <bsmith at mcs.anl.gov> wrote: >> > >> > > >> > > What is x1, x2 and ip? >> > > >> > > Barry >> > >> > x1 and x2 are 2-arrays; their rows are the 'sample' vectors. >> > ip is the matrix of all inner products from x1 and x2. >> > >> > Simon. >> > >> > >> > >> > > > -- > Simon Burton, B.Sc. > Licensed PO Box 8066 > ANU Canberra 2601 > Australia > Ph. 61 02 6249 6940 > http://arrowtheory.com > > > -- "Failure has a thousand explanations. Success doesn't need one" -- Sir Alec Guiness