svd - How do I generate data from a similarity matrix? -

suppose there 14 objects, each of have or not have 1000 binary features. have 14x14 similarity matrix, not raw 14x1000 data. there way reconstruct or generate similar raw data, given similarity matrix?

i tried monte carlo simulations, unconstrained take way time achieve low level of consistency original similarity matrix.

i saw relevant question: similarity matrix -> feature vectors algorithm?. however, wanted reduce not increase dimensionality. also, not sure (1) matrix or matrices use, , (2) how convert binary matrix.

it's impossible sure unless describe how similarity scores computed.

in general, usual kind of similarity scoring not possible: information has been lost in transformation individual features aggregate statistics. best can hope arrive @ set of features consistent similarity scores.

i think talking when "similar to" original. problem pretty interesting. suppose similarity computed dot-product of 2 feature vectors (ie count of features pair of objects both have value = 1/true). not choice: consistent value of 0 (false) meaning no information. may generalize other similarity measures.

in such case, problem linear programming problem: naive approach exhaustively search space of possible objects - not randomly, guided constraints. example, suppose sim(a,b) := similarity of object , object b. define order on these vectors.

if sim(a,b) = n, choose a=b minimal (like (1,....,1 (n times), 0, .... 0 (1000-n times)), , choose minimum c s.t. (a,c), (b,c) have given values. once find inconsistency, backtrack, , increment.

this find consistent answer, although complexity high (but better monte carlo).

finding better algorithm interesting problem, more can't in post - that's topic cs thesis!