Assessment of phytoplankton class abundance using fluorescence excitation-emission matrix by parallel factor analysis and nonnegative least squares

The feasibility of using fluorescence excitation-emission matrix(EEM) along with parallel factor analysis(PARAFAC) and nonnegative least squares(NNLS) method for the differentiation of phytoplankton taxonomic groups was investigated. Forty-one phytoplankton species belonging to 28 genera of five divisions were studied. First, the PARAFAC model was applied to EEMs, and 15 fluorescence components were generated. Second, 15 fluorescence components were found to have a strong discriminating capability based on Bayesian discriminant analysis(BDA). Third, all spectra of the fluorescence component compositions for the 41 phytoplankton species were spectrographically sorted into 61 reference spectra using hierarchical cluster analysis(HCA), and then, the reference spectra were used to establish a database. Finally, the phytoplankton taxonomic groups was differentiated by the reference spectra database using the NNLS method. The five phytoplankton groups were differentiated with the correct discrimination ratios(CDRs) of 100% for single-species samples at the division level. The CDRs for the mixtures were above 91% for the dominant phytoplankton species and above 73% for the subdominant phytoplankton species. Sixteen of the 85 field samples collected from the Changjiang River estuary were analyzed by both HPLC-CHEMTAX and the fluorometric technique developed. The results of both methods reveal that Bacillariophyta was the dominant algal group in these 16 samples and that the subdominant algal groups comprised Dinophyta, Chlorophyta and Cryptophyta. The differentiation results by the fluorometric technique were in good agreement with those from HPLC-CHEMTAX. The results indicate that the fluorometric technique could differentiate algal taxonomic groups accurately at the division level.

EFFICIENT NONNEGATIVE MATRIX FACTORIZATION VIA MODIFIED MONOTONE BARZILAI-BORWEIN METHOD WITH ADAPTIVE STEP SIZES STRATEGY

In this paper,we develop an active set identification technique.By means of the active set technique,we present an active set adaptive monotone projected Barzilai-Borwein method(ASAMPBB)for solving nonnegative matrix factorization(NMF)based on the alternating nonnegative least squares framework,in which the Barzilai-Borwein(BB)step sizes can be adaptively picked to get meaningful convergence rate improvements.To get optimal step size,we take into account of the curvature information.In addition,the larger step size technique is exploited to accelerate convergence of the proposed method.The global convergence of the proposed method is analysed under mild assumption.Finally,the results of the numerical experiments on both synthetic and real-world datasets show that the proposed method is effective.

Nonnegative tensor factorizations using an alternating direction method

The nonnegative tensor （matrix） factorization finds more and more applications in various disciplines including machine learning, data mining, and blind source separation, etc. In computation, the optimization problem involved is solved by alternatively minimizing one factor while the others are fixed. To solve the subproblem efficiently, we first exploit a variable regularization term which makes the subproblem far from ill-condition. Second, an augmented Lagrangian alternating direction method is employed to solve this convex and well-conditioned regularized subproblem, and two accelerating skills are also implemented. Some preliminary numerical experiments are performed to show the improvements of the new method.