Abstract. With uncorrelated Gaussian factors extended to mutually independent factors beyond Gaussian, the conventional factor analysis is extended to what is recently called independent factor analysis. Typically, it is called binary factor analysis (BFA) when the factors are binary and called non-Gaussian factor analysis (NFA) when the factors are from real non-Gaussian distributions. A crucial issue in both BFA and NFA is the determination of the number of factors. In the literature of statistics, there are a number of model selection criteria that can be used for this purpose. Also, the Bayesian Ying-Yang (BYY) harmony learning provides a new principle for this purpose. This paper further investigates BYY harmony learning in comparison with existing typical criteria, including Akaik_s information criterion (AIC), the consistent Akaike_s information criterion (CAIC), the Bayesian inference criterion (BIC), and the cross-validation (CV) criterion on selection of the number of factors. This comparative study is made via experiments on the data sets with different sample sizes, data space dimensions, noise variances, and hidden factors numbers. Experiments have shown that for both BFA and NFA, in most cases BIC outperforms AIC, CAIC, and CV while the BYY criterion is either comparable with or better than BIC. In consideration of the fact that the selection by these criteria has to be implemented at the second stage based on a set of candidate models which have to be obtained at the first stage of parameter learning, while BYY harmony learning can provide not only a new class of criteria implemented in a similar way but also a new family of algorithms that perform parameter learning at the first stage with automated model selection, BYY harmony learning is more preferred since computing costs can be saved significantly. (2000): 68Q10, 62H25, 68T05, 65C10, 68Q32. Mathematical Subject Classifications
Metaproteomic analyses, including two-dimensional polyacrylamide gel electrophoresis (2D-PAGE) separation and matrix-assisted laser desorption/ionization (MALDI)-time-of-flight (TOF)/TOF mass spectrometer (MS) detection, were used to trace and identify biocake proteins on membranes in a bench-scale submerged membrane bioreactor (MBR). 2D-PAGE images showed that proteins in the biocake (S3) at a low transmembrane pressure (TMP) level (i.e., before the TMP jump) had larger gray intensities in the pH 5.5–7.0 region regardless of the membrane flux, similar to soluble microbial product (SMP) proteins. However, the biocake (S2 and S4) at a high TMP level (i.e., after the TMP jump) had many more proteins in the pH range of 4.0–5.5, similar to extracellular polymeric substance (EPS) proteins. Such similarities between biocake proteins and SMP or EPS proteins can be useful for tracing the sources of proteins resulting in membrane fouling. In total, 183 differentially abundant protein spots were marked in the three biocakes (S2, S3, and S4). However, only 32 protein spots co-occurred in the 2D gels of the three biocakes, indicating that membrane fluxes and TMP evolution levels had significant effects on the abundance of biocake proteins. On the basis of the MS and MS/MS data, 23 of 71 protein spots were successfully identified. Of the 23 proteins, outer membrane proteins (Omp) were a major contributor (60.87%). These Omps were mainly from potential surface colonizers such as Aeromonas, Enterobacter, Pseudomonas, and Thauera. Generally, the metaproteomic analysis is a useful alternative to trace the sources and compositions of biocake proteins on the levels of molecules and bacteria species that can provide new insight into membrane fouling.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.