Latent factor(LF) models are highly effective in extracting useful knowledge from High-Dimensional and Sparse(HiDS) matrices which are commonly seen in various industrial applications. An LF model usually adopts itera...Latent factor(LF) models are highly effective in extracting useful knowledge from High-Dimensional and Sparse(HiDS) matrices which are commonly seen in various industrial applications. An LF model usually adopts iterative optimizers,which may consume many iterations to achieve a local optima,resulting in considerable time cost. Hence, determining how to accelerate the training process for LF models has become a significant issue. To address this, this work proposes a randomized latent factor(RLF) model. It incorporates the principle of randomized learning techniques from neural networks into the LF analysis of HiDS matrices, thereby greatly alleviating computational burden. It also extends a standard learning process for randomized neural networks in context of LF analysis to make the resulting model represent an HiDS matrix correctly.Experimental results on three HiDS matrices from industrial applications demonstrate that compared with state-of-the-art LF models, RLF is able to achieve significantly higher computational efficiency and comparable prediction accuracy for missing data.I provides an important alternative approach to LF analysis of HiDS matrices, which is especially desired for industrial applications demanding highly efficient models.展开更多
Based on the fixed-point theory, we study the existence and the uniqueness of the maximal Hermitian positive definite solution of the nonlinear matrix equation X＋A^＊X^-2A=Q, where Q is a square Hermitian positive de...Based on the fixed-point theory, we study the existence and the uniqueness of the maximal Hermitian positive definite solution of the nonlinear matrix equation X＋A^＊X^-2A=Q, where Q is a square Hermitian positive definite matrix and A＊ is the conjugate transpose of the matrix A. We also demonstrate some essential properties and analyze the sensitivity of this solution. In addition, we derive computable error bounds about the approximations to the maximal Hermitian positive definite solution of the nonlinear matrix equation X＋A^＊X^-2A=Q. At last, we further generalize these results to the nonlinear matrix equation X＋A^＊X^-nA=Q, where n≥2 is a given positive integer.展开更多
Simulated photo-degradation of fluorescent dissolved organic matter(FDOM) in Lake Baihua(BH) and Lake Hongfeng(HF) was investigated with three-dimensional excitationemission matrix(3 DEEM) fluorescence combined with t...Simulated photo-degradation of fluorescent dissolved organic matter(FDOM) in Lake Baihua(BH) and Lake Hongfeng(HF) was investigated with three-dimensional excitationemission matrix(3 DEEM) fluorescence combined with the fluorescence regional integration(FRI),parallel factor(PARAFAC) analysis,and multi-order kinetic models.In the FRI analysis,fulvic-like and humic-like materials were the main constituents for both BH-FDOM and HF-FDOM.Four individual components were identified by use of PARAFAC analysis as humic-like components(C1),fulvic-like components(C2),protein-like components(C3) and unidentified components(C4).The maximum 3 DEEM fluorescence intensity of PARAFAC components C1-C3 decreased by about 60%,70% and 90%,respectively after photo-degradation.The multi-order kinetic model was acceptable to represent the photo-degradation of FDOM with correlation coefficient(Radj2)(0.963-0.998).The photo-degradation rate constants(kn) showed differences of three orders of magnitude,from 1.09 × 10-6 to 4.02 × 10-4 min-1,and half-life of multi-order model(T1/2n)ranged from 5.26 to 64.01 min.The decreased values of fluorescence index(FI) and biogenic index(BI),the fact that of percent fluorescence response parameter of Region I(PⅠ,n) showed the greatest change ratio,followed by percent fluorescence response parameter of Region II(PⅡ,n,while the largest decrease ratio was found for C3 components,and the lowest T1/2n was observed for C3,indicated preferential degradation of protein-like materials/components derived from biological sources during photodegradation.This research on the degradation of FDOM by 3 DEEM/FRI-PARAFAC would be beneficial to understanding the photo-degradation of FD OM in natural environments and accurately predicting the environmental behaviors of contaminants in the presence of FDOM.展开更多
基金supported in part by the National Natural Science Foundation of China (6177249391646114)+1 种基金Chongqing research program of technology innovation and application (cstc2017rgzn-zdyfX0020)in part by the Pioneer Hundred Talents Program of Chinese Academy of Sciences
文摘Latent factor(LF) models are highly effective in extracting useful knowledge from High-Dimensional and Sparse(HiDS) matrices which are commonly seen in various industrial applications. An LF model usually adopts iterative optimizers,which may consume many iterations to achieve a local optima,resulting in considerable time cost. Hence, determining how to accelerate the training process for LF models has become a significant issue. To address this, this work proposes a randomized latent factor(RLF) model. It incorporates the principle of randomized learning techniques from neural networks into the LF analysis of HiDS matrices, thereby greatly alleviating computational burden. It also extends a standard learning process for randomized neural networks in context of LF analysis to make the resulting model represent an HiDS matrix correctly.Experimental results on three HiDS matrices from industrial applications demonstrate that compared with state-of-the-art LF models, RLF is able to achieve significantly higher computational efficiency and comparable prediction accuracy for missing data.I provides an important alternative approach to LF analysis of HiDS matrices, which is especially desired for industrial applications demanding highly efficient models.
文摘Based on the fixed-point theory, we study the existence and the uniqueness of the maximal Hermitian positive definite solution of the nonlinear matrix equation X＋A^＊X^-2A=Q, where Q is a square Hermitian positive definite matrix and A＊ is the conjugate transpose of the matrix A. We also demonstrate some essential properties and analyze the sensitivity of this solution. In addition, we derive computable error bounds about the approximations to the maximal Hermitian positive definite solution of the nonlinear matrix equation X＋A^＊X^-2A=Q. At last, we further generalize these results to the nonlinear matrix equation X＋A^＊X^-nA=Q, where n≥2 is a given positive integer.
基金financially supported by the National Natural Science Foundation of China(No.41573130)BNU Interdisciplinary Research Foundation for First-Year Doctoral Candidates(No.BNUXKJC1802)
文摘Simulated photo-degradation of fluorescent dissolved organic matter(FDOM) in Lake Baihua(BH) and Lake Hongfeng(HF) was investigated with three-dimensional excitationemission matrix(3 DEEM) fluorescence combined with the fluorescence regional integration(FRI),parallel factor(PARAFAC) analysis,and multi-order kinetic models.In the FRI analysis,fulvic-like and humic-like materials were the main constituents for both BH-FDOM and HF-FDOM.Four individual components were identified by use of PARAFAC analysis as humic-like components(C1),fulvic-like components(C2),protein-like components(C3) and unidentified components(C4).The maximum 3 DEEM fluorescence intensity of PARAFAC components C1-C3 decreased by about 60%,70% and 90%,respectively after photo-degradation.The multi-order kinetic model was acceptable to represent the photo-degradation of FDOM with correlation coefficient(Radj2)(0.963-0.998).The photo-degradation rate constants(kn) showed differences of three orders of magnitude,from 1.09 × 10-6 to 4.02 × 10-4 min-1,and half-life of multi-order model(T1/2n)ranged from 5.26 to 64.01 min.The decreased values of fluorescence index(FI) and biogenic index(BI),the fact that of percent fluorescence response parameter of Region I(PⅠ,n) showed the greatest change ratio,followed by percent fluorescence response parameter of Region II(PⅡ,n,while the largest decrease ratio was found for C3 components,and the lowest T1/2n was observed for C3,indicated preferential degradation of protein-like materials/components derived from biological sources during photodegradation.This research on the degradation of FDOM by 3 DEEM/FRI-PARAFAC would be beneficial to understanding the photo-degradation of FD OM in natural environments and accurately predicting the environmental behaviors of contaminants in the presence of FDOM.
