Alternating Poisson Regression for fitting CP to sparse count data
Contents
Set up a sample problem
We follow the general procedure outlined by E. C. Chi and T. G. Kolda, On Tensors, Sparsity, and Nonnegative Factorizations, arXiv:1112.2414 [math.NA], December 2011 (http://arxiv.org/abs/1112.2414).
% Pick the size and rank sz = [100 80 60]; R = 5; % Generate factor matrices with a few large entries in each column; this % will be the basis of our soln. A = cell(3,1); for n = 1:length(sz) A{n} = rand(sz(n), R); for r = 1:R p = randperm(sz(n)); nbig = round( (1/R)*sz(n) ); A{n}(p(1:nbig),r) = 100 * A{n}(p(1:nbig),r); end end lambda = rand(R,1); S = ktensor(lambda, A); S = normalize(S,'sort',1); % Create sparse test problem based on provided solution. nz = prod(sz) * .05; info = create_problem('Soln', S, 'Sparse_Generation', nz); % Extract data and solution X = info.Data; M_true = info.Soln;
Call CP-APR
% Compute a solution M = cp_apr(X, R, 'printitn', 10); % Score the solution factor_match_score = score(M, M_true, 'greedy', true)
CP_PQNR (alternating Poisson regression using quasi-Newton) Precomputing sparse index sets...done 10. Ttl Inner Its: 648, KKT viol = 2.32e-02, obj = -8.28190514e+03, nz: 301 20. Ttl Inner Its: 240, KKT viol = 9.81e-05, obj = -8.28188887e+03, nz: 302 =========================================== Final log-likelihood = -8.281889e+03 Final least squares fit = 5.784574e-01 Final KKT violation = 9.8085093e-05 Total inner iterations = 20238 Total execution time = 5.85 secs factor_match_score = 0.9609