Alternating Poisson Regression for fitting CP to sparse count data

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Reference: E. C. Chi, T. G. Kolda, On Tensors, Sparsity, and Nonnegative Factorizations, SIAM J. Matrix Analysis and Applications, 33:1272-1299, 2012, https://doi.org/10.1137/110859063.

Contents

Set up a sample problem

We follow the general procedure outlined by Chi and Kolda (2013).

rng('default') %<- Setting random seed for reproducibility of this script

% 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: 1576, KKT viol = 2.00e-01, obj = 1.43584130e+04, nz: 291
  20. Ttl Inner Its: 336, KKT viol = 6.45e-03, obj = 1.25598428e+04, nz: 279
===========================================
 Final log-likelihood = -1.255984e+04 
 Final least squares fit = 5.232259e-01 
 Final KKT violation = 9.5452289e-05
 Total inner iterations = 36709
 Total execution time = 4.78 secs

factor_match_score =

    0.9745

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