Research Article

Fast Nonnegative Matrix Factorization Algorithms Using Projected Gradient Approaches for Large-Scale Problems

Table 1

Mean-SIRs [dB] obtained with 100 samples of Monte Carlo analysis for the estimation of sources and columns of mixing matrix from noise-free mixtures of signals in Figure 1. Sources 𝐗 are estimated with the projected pseudoinverse. The number of inner iterations for updating 𝐀 is denoted by 𝑘 , and the number of layers (in the multilayer technique) by 𝐿 . The notation best or worst in parenthesis that follows the algorithm name means that the mean-SIR value is calculated for the best or worst sample from Monte Carlo analysis, respectively. In the last column, the elapsed time [in seconds] is given for each algorithm with 𝑘 = 1 and 𝐿 = 1 .

AlgorithmMean- S I R 𝐴 [dB]Mean- S I R 𝑋 [dB]Time
𝐿 = 1 𝐿 = 3 𝐿 = 1 𝐿 = 3
𝑘 = 1 𝑘 = 5 𝑘 = 1 𝑘 = 5 𝑘 = 1 𝑘 = 5 𝑘 = 1 𝑘 = 5

M-NMF (best)2122.142.637.326.627.344.740.71.9
M-NMF (mean)13.113.826.723.114.715.228.927.6
M-NMF (worst)5.55.75.36.35.86.555.5
OPL(best)22.925.346.54223.923.555.8511.9
OPL(mean)14.71425.527.215.314.823.925.4
OPL(worst)4.84.84.85.04.64.64.64.8
Lin-PG(best)36.323.678.6103.734.233.378.592.88.8
Lin-PG(mean)19.718.340.961.218.518.238.455.4
Lin-PG(worst)14.413.117.540.113.913.818.134.4
GPSR-BB(best)18.222.77.3113.822.854.39.4108.12.4
GPSR-BB(mean)11.220.2753.11120.55.153.1
GPSR-BB(worst)7.417.36.824.94.614.7223
PSESOP(best)21.222.671.1132.223.455.556.5137.25.4
PSESOP(mean)15.22029.457.315.934.527.465.3
PSESOP(worst)8.315.86.928.78.216.67.230.9
IPG(best)20.622.252.184.335.728.654.281.42.7
IPG(mean)20.118.235.344.119.719.133.836.7
IPG(worst)10.513.49.421.210.213.58.915.5
IPN(best)20.822.659.965.853.552.468.667.214.2
IPN(mean)19.417.338.222.522.819.136.621
IPN(worst)11.715.27.57.15.721.52
RMRNSD(best)24.721.622.257.930.243.525.562.43.8
RMRNSD(mean)14.319.28.333.81721.58.433.4
RMRNSD(worst)5.515.93.68.44.713.813.9
SCWA(best)12.120.410.624.56.325.611.934.42.5
SCWA(mean)11.216.39.320.95.318.69.421.7
SCWA(worst)7.311.46.912.83.8103.310.8