Dimensionality reduction is very important in pattern recognition, machine learning, and image recognition. In this paper, we propose a novel linear dimensionality reduction technique using trace ratio criterion, name...Dimensionality reduction is very important in pattern recognition, machine learning, and image recognition. In this paper, we propose a novel linear dimensionality reduction technique using trace ratio criterion, namely Discriminant Neighbourhood Structure Embedding Using Trace Ratio Criterion (TR-DNSE). TR-DNSE preserves the local intrinsic geometric structure, characterizing properties of similarity and diversity within each class, and enforces the separability between different classes by maximizing the sum of the weighted distances between nearby points from different classes. Experiments on four image databases show the effectiveness of the proposed approach.展开更多
We are concerned with the maximization of tr(VTAV)/tr(VT BV)+ tr(VT CV)over the Stiefel manifold {V ∈ Rm×| V T V = It}(t < m), where B is a given symmetric and positive definite matrix, A and C are symmetric ...We are concerned with the maximization of tr(VTAV)/tr(VT BV)+ tr(VT CV)over the Stiefel manifold {V ∈ Rm×| V T V = It}(t < m), where B is a given symmetric and positive definite matrix, A and C are symmetric matrices, and tr() is the trace of a square matrix. This is a subspace version of the maximization problem studied in Zhang(2013), which arises from real-world applications in, for example,the downlink of a multi-user MIMO system and the sparse Fisher discriminant analysis in pattern recognition.We establish necessary conditions for both the local and global maximizers and connect the problem with a nonlinear extreme eigenvalue problem. The necessary condition for the global maximizers offers deep insights into the problem, on the one hand, and, on the other hand, naturally leads to a self-consistent-field(SCF)iteration to be presented and analyzed in detail in Part II of this paper.展开更多
Abstract The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr(VTAV)/tr(VTBV)+tr(VTCV)over the Stiefel manifold{V∈Rm×l |VTV=Il}(l<m),natura...Abstract The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr(VTAV)/tr(VTBV)+tr(VTCV)over the Stiefel manifold{V∈Rm×l |VTV=Il}(l<m),naturally leads to a self-consistent-field(SCF)iteration for computing a maximizer.In this part,we analyze the global and local convergence of the SCF iteration,and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF iteration.This is one of the advantages of the SCF iteration over optimization-based methods.Preliminary numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.展开更多
An one-year of sampling aerosol program was carried out during the period of April 1995 to April 1996 at coastal region, Cape D′Aguilar, in Hong Kong. The trace element composition of aerosol particles(TSP and PM ...An one-year of sampling aerosol program was carried out during the period of April 1995 to April 1996 at coastal region, Cape D′Aguilar, in Hong Kong. The trace element composition of aerosol particles(TSP and PM 10 ) were measured and analyzed by using the Instrumental Neutron Activation Analysis(INAA) and Inductive Couple Plasma-Mass Spectrometry(ICP-MS) techniques. The results showed that the polluted elements such as: V, Zn, As, Pb, Cd, Sb, I, Se, Bi, with high enrichment factor(E.F) values, are derived from anthropogenic sources, while Sc, Al, Fe, Mn, Sm, La, Sr are less than 10 in E.F, these elements are related the crust and soil. The concentration of the trace elements are present seasonal variation i.e. summer low and winter high, whereas the V or noncrustal V(V *) present summer high and winter low, this phenomenon might be explained by local or regional oil combustion sources. Use three type of elemental ratio, e.g. La/Sm, Mn */V * and Bi/Al indicate that both TSP and PM 10 of La/Sm ratios are mainly related to soil and dust, Mn */V * are probably represent fossil combustion and Bi/Al are possibly associated with refuse incineration, ferromanganese alloys and aluminum production. The varimax rotation factor analysis for trace elements was performed. By means of the absolute principal component analysis(APCA) and multiple regression, the contribution of trace elements to possible sources and overall means of trace elements were estimated. The results showed that the present station is impacted by the anthropogenic species, although the quantities are different during the summertime and wintertime.展开更多
Reagents are optimized for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in zinc sulfate solution, which contains an extremely large excess of Zn^(2+). First, the reagents and their d...Reagents are optimized for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in zinc sulfate solution, which contains an extremely large excess of Zn^(2+). First, the reagents and their doses for the experiment are selected according to the characteristics of the zinc sulfate solution. Then, the reagent doses are optimized by analyzing the influence of reagent dose on the polarographic parameters(i.e. half-wave potential E_(1/2) and limiting diffusion current I_p). Finally, the optimization results are verified by simultaneously determining trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in the presence of an extremely large excess of Zn^(2+). The determination results indicate that the optimized reagents exhibit wide linearity, low detection limits, high accuracy and good precision for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in the presence of an extremely large excess of Zn^(2+).展开更多
Background: Type 2 Diabetes Mellitus (T2DM) is a chronic polymetabolic disorder characterized by chronic hyperglycemia resulting from resistance to insulin action or inadequacy of insulin secretion. Role of the micro ...Background: Type 2 Diabetes Mellitus (T2DM) is a chronic polymetabolic disorder characterized by chronic hyperglycemia resulting from resistance to insulin action or inadequacy of insulin secretion. Role of the micro & macro nutrients in the pathogenesis of T2DM has not been studied thoroughly. The aim of this study was to evaluate the status of calcium, magnesium, zinc and chromium in relation to HbA1c in a group of subjects with T2DM patients. Methodology: The study comprised of seventy three patients with T2DM, attending the OP of a tertiary care medical college hospital. Thirty four individuals were with HbA1c < 7% (group 1) and thirty nine with HbA1c ≥ 7% (group 2). Cation concentrations were determined using Atomic Absorption Spectroscopy and HbA1c by ion exchange chromatography. Results: The individual cation concentrations were not significantly different between the groups. Association of these serum ion concentrations with the glycemic control in group 2 (HbA1c 7%) was noted. Significant association of cation ratios with glycemic control was noted. Conclusion: The concentration of magnesium, zinc and chromium were low in subjects with poor glycemic control (HbA1c > 7%). Cation ratios were significantly associated with the glycemic control in T2DM.展开更多
A topographic target light scattering-differential optical absorption spectroscopy （＇IbTaL-DOA~） system is de- veloped for measuring average concentrations along a known optical path and studying surface-near distr...A topographic target light scattering-differential optical absorption spectroscopy （＇IbTaL-DOA~） system is de- veloped for measuring average concentrations along a known optical path and studying surface-near distributions of atmospheric trace gases. The telescope of the ToTaL-DOAS system points to targets which are located at known dis- tances from the measurement device and illuminated by sunlight. Average concentrations with high spatial resolution can be retrieved by receiving sunlight reflected from the targets, A filed measurement of NO2 concentration is performed with the ToTaL-DOAS system in Shijiazhuang in the autumn of 2011. The measurement data are compared with con- centrations measured by the point monitoring technique at the same site. The results show that the ToTaL-DOAS system is sensitive to the variation of NO2 concentrations along the optical path.展开更多
文摘Dimensionality reduction is very important in pattern recognition, machine learning, and image recognition. In this paper, we propose a novel linear dimensionality reduction technique using trace ratio criterion, namely Discriminant Neighbourhood Structure Embedding Using Trace Ratio Criterion (TR-DNSE). TR-DNSE preserves the local intrinsic geometric structure, characterizing properties of similarity and diversity within each class, and enforces the separability between different classes by maximizing the sum of the weighted distances between nearby points from different classes. Experiments on four image databases show the effectiveness of the proposed approach.
基金supported by National Natural Science Foundation of China(Grant Nos.11101257 and 11371102)the Basic Academic Discipline Program+3 种基金the 11th Five Year Plan of 211 Project for Shanghai University of Finance and Economicsa visiting scholar at the Department of Mathematics,University of Texas at Arlington from February 2013 toJanuary 2014supported by National Science Foundation of USA(Grant Nos.1115834and 1317330)a Research Gift Grant from Intel Corporation
文摘We are concerned with the maximization of tr(VTAV)/tr(VT BV)+ tr(VT CV)over the Stiefel manifold {V ∈ Rm×| V T V = It}(t < m), where B is a given symmetric and positive definite matrix, A and C are symmetric matrices, and tr() is the trace of a square matrix. This is a subspace version of the maximization problem studied in Zhang(2013), which arises from real-world applications in, for example,the downlink of a multi-user MIMO system and the sparse Fisher discriminant analysis in pattern recognition.We establish necessary conditions for both the local and global maximizers and connect the problem with a nonlinear extreme eigenvalue problem. The necessary condition for the global maximizers offers deep insights into the problem, on the one hand, and, on the other hand, naturally leads to a self-consistent-field(SCF)iteration to be presented and analyzed in detail in Part II of this paper.
基金Acknowledgements The first author was supported by National Natural Science Foundation of China(Grant Nos.11101257 and 11371102)the Basic Academic Discipline Program,the 11th Five Year Plan of 211 Project for Shanghai University of Finance and Economics+1 种基金supported by National Science Foundation of USA(Grant Nos.1115834and 1317330)a Research Gift Grant from Intel Corporation
文摘Abstract The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max V tr(VTAV)/tr(VTBV)+tr(VTCV)over the Stiefel manifold{V∈Rm×l |VTV=Il}(l<m),naturally leads to a self-consistent-field(SCF)iteration for computing a maximizer.In this part,we analyze the global and local convergence of the SCF iteration,and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF iteration.This is one of the advantages of the SCF iteration over optimization-based methods.Preliminary numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.
文摘An one-year of sampling aerosol program was carried out during the period of April 1995 to April 1996 at coastal region, Cape D′Aguilar, in Hong Kong. The trace element composition of aerosol particles(TSP and PM 10 ) were measured and analyzed by using the Instrumental Neutron Activation Analysis(INAA) and Inductive Couple Plasma-Mass Spectrometry(ICP-MS) techniques. The results showed that the polluted elements such as: V, Zn, As, Pb, Cd, Sb, I, Se, Bi, with high enrichment factor(E.F) values, are derived from anthropogenic sources, while Sc, Al, Fe, Mn, Sm, La, Sr are less than 10 in E.F, these elements are related the crust and soil. The concentration of the trace elements are present seasonal variation i.e. summer low and winter high, whereas the V or noncrustal V(V *) present summer high and winter low, this phenomenon might be explained by local or regional oil combustion sources. Use three type of elemental ratio, e.g. La/Sm, Mn */V * and Bi/Al indicate that both TSP and PM 10 of La/Sm ratios are mainly related to soil and dust, Mn */V * are probably represent fossil combustion and Bi/Al are possibly associated with refuse incineration, ferromanganese alloys and aluminum production. The varimax rotation factor analysis for trace elements was performed. By means of the absolute principal component analysis(APCA) and multiple regression, the contribution of trace elements to possible sources and overall means of trace elements were estimated. The results showed that the present station is impacted by the anthropogenic species, although the quantities are different during the summertime and wintertime.
基金Projects(61533021,61321003,61273185)supported by the National Natural Science Foundation of ChinaProject(2015CX007)supported by the Innovation-driven Plan in Central South University,ChinaProject(13JJ8003)supported by the Joint Fund of Hunan Provincial Natural Science Foundation of China
文摘Reagents are optimized for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in zinc sulfate solution, which contains an extremely large excess of Zn^(2+). First, the reagents and their doses for the experiment are selected according to the characteristics of the zinc sulfate solution. Then, the reagent doses are optimized by analyzing the influence of reagent dose on the polarographic parameters(i.e. half-wave potential E_(1/2) and limiting diffusion current I_p). Finally, the optimization results are verified by simultaneously determining trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in the presence of an extremely large excess of Zn^(2+). The determination results indicate that the optimized reagents exhibit wide linearity, low detection limits, high accuracy and good precision for the simultaneous determination of trace amounts of Cu^(2+), Cd^(2+) and Co^(2+) in the presence of an extremely large excess of Zn^(2+).
文摘Background: Type 2 Diabetes Mellitus (T2DM) is a chronic polymetabolic disorder characterized by chronic hyperglycemia resulting from resistance to insulin action or inadequacy of insulin secretion. Role of the micro & macro nutrients in the pathogenesis of T2DM has not been studied thoroughly. The aim of this study was to evaluate the status of calcium, magnesium, zinc and chromium in relation to HbA1c in a group of subjects with T2DM patients. Methodology: The study comprised of seventy three patients with T2DM, attending the OP of a tertiary care medical college hospital. Thirty four individuals were with HbA1c < 7% (group 1) and thirty nine with HbA1c ≥ 7% (group 2). Cation concentrations were determined using Atomic Absorption Spectroscopy and HbA1c by ion exchange chromatography. Results: The individual cation concentrations were not significantly different between the groups. Association of these serum ion concentrations with the glycemic control in group 2 (HbA1c 7%) was noted. Significant association of cation ratios with glycemic control was noted. Conclusion: The concentration of magnesium, zinc and chromium were low in subjects with poor glycemic control (HbA1c > 7%). Cation ratios were significantly associated with the glycemic control in T2DM.
基金Project supported by the National High Technology Research and Development of China (Grant No.2009AA063006)the National Natural Science Foundation of China (Grant No. 40905010)the Special Project of Environmental Nonprofit Industry Research,China (Grant No. 201109007)
文摘A topographic target light scattering-differential optical absorption spectroscopy （＇IbTaL-DOA~） system is de- veloped for measuring average concentrations along a known optical path and studying surface-near distributions of atmospheric trace gases. The telescope of the ToTaL-DOAS system points to targets which are located at known dis- tances from the measurement device and illuminated by sunlight. Average concentrations with high spatial resolution can be retrieved by receiving sunlight reflected from the targets, A filed measurement of NO2 concentration is performed with the ToTaL-DOAS system in Shijiazhuang in the autumn of 2011. The measurement data are compared with con- centrations measured by the point monitoring technique at the same site. The results show that the ToTaL-DOAS system is sensitive to the variation of NO2 concentrations along the optical path.
