In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using t...In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using two types of approximation: 1) approximate the zeros in the target by the non-zeros in the loadings, and 2) approximate the non-zeros in the target by the non-zeros in the loadings. The central issue of Procrustes rotation considered in the article is that it equally treats the two types of approximation, while the former is more important for simplifying the loading matrix. Furthermore, a well-known issue of Simplimax is the computational inefficiency in estimating the sparse target matrix, which yields a considerable number of local minima. The research proposes a new rotation procedure that consists of the following two stages. The first stage estimates sparse target matrix with lesser computational cost by regularization technique. In the second stage, a loading matrix is rotated to the target, emphasizing on the approximation of non-zeros to zeros in the target by least squares criterion with generalized weighing that is newly proposed by the study. The simulation study and real data examples revealed that the proposed method surely simplifies loading matrices.展开更多
This paper proposes a framework for human action recognition based on procrustes analysis and Fisher vector coding(FVC).Firstly,we applied a pose feature extracted from silhouette image by employing Procrustes analysi...This paper proposes a framework for human action recognition based on procrustes analysis and Fisher vector coding(FVC).Firstly,we applied a pose feature extracted from silhouette image by employing Procrustes analysis and local preserving projection(LPP).Secondly,the extracted feature can preserve the discriminative shape information and local manifold structure of human pose and is invariant to translation,rotation and scaling.Finally,after the pose feature was extracted,a recognition framework based on FVC and multi-class supporting vector machine was employed to classify the human action.Experimental results on benchmarks demonstrate the effectiveness of the proposed method.展开更多
In order to study correlations between sensory properties and acceptance, regular and gluten-free carrot cakes (sweetened with sucrose and sucralose) were evaluated. Appearance, aroma, flavor, texture and overall liki...In order to study correlations between sensory properties and acceptance, regular and gluten-free carrot cakes (sweetened with sucrose and sucralose) were evaluated. Appearance, aroma, flavor, texture and overall liking were analyzed by 120 carrot cake consumers using a 9-cm hedonic scale. Quantitative Descriptive Analysis (QDA) was carried out with 11 assessors among 16 attributes. Data were analyzed by ANOVA, Tukey test (p < 0.05), Internal Preference Map and Cluster analysis. Also texture parameters were analyzed by Partial Least Square (PLS) to be able to show the instrumental parameters influence. Generalized Procrustes Analysis (GPA) was used before an Ex-ternal Preference Mapping to reduce the scale effects and to obtain a consensus configuration. According to PLS correlation, the attributes hardness, fracturability, adhesiveness, chewiness and gumminess interfered on characteristics considered undesirable for texture acceptance and smoothness, elasticity, cohesiveness and water activity interfered as desirable features. It was noted that all cakes were well accepted, except cake sweetened with sucralose and mix done using cornmeal, rice flour, potato starch and corn starch (2:3:3:2). As for the instrumental aspects, cohesiveness and elasticity influenced positively the cake’s acceptance. Instead, smoothness and adhesion parameters weren’t so significant.展开更多
In order to realize high precision industrial operations,based on the POE formula,an effective approach to calibrate the robot's actual base frame(ABF) is proposed. Due to the existence of manufacturing errors,the...In order to realize high precision industrial operations,based on the POE formula,an effective approach to calibrate the robot's actual base frame(ABF) is proposed. Due to the existence of manufacturing errors,the ABF deviates slightly from nominal base frame( NBF). Using external precision measurement,the ABF can be established only through the three dimension(3D) position of the robot's end-effector.To ensure the orthonormal constraints of rotation matrix as well as the precise solutions,Procrustes Analysis is introduced,where an optimal orthogonal matrix is solved out by the Lagrange Multiplier method and Singular Value Decomposition(SVD). Furthermore,calibration experiment on a serial 6-DOF robot is performed,where a FARO laser tracker is utilized to measure the 3D position. Finally, calibration result indicates that the positioning accuracy has been significantly improved after calibration. The calibration method is also applicable to other similar problems,such as multi-robot coordination and robot hand-eye system calibration.展开更多
This paper is intended to study the volume-preserving procrustes problem arising from practical areas. The corresponding solution should satisfy a matrix equation which is solved by the singular value decomposition me...This paper is intended to study the volume-preserving procrustes problem arising from practical areas. The corresponding solution should satisfy a matrix equation which is solved by the singular value decomposition method. Some further results are also given to characterize the solution. Using these results, a numerical algorithm is introduced and some numerical results are provided to illustrate the effectiveness of the algorithm. Key words volume-preserving - procrustes problems - singular value decomposition MSC2000 65F30 - 65K10 Project supported by NNSFC (Grant No. 10371076), E-Institutes of Shanghai Municipal Education Commission (Grant No. N. E03004)展开更多
文摘In factor analysis, a factor loading matrix is often rotated to a simple target matrix for its simplicity. For the purpose, Procrustes rotation minimizes the discrepancy between the target and rotated loadings using two types of approximation: 1) approximate the zeros in the target by the non-zeros in the loadings, and 2) approximate the non-zeros in the target by the non-zeros in the loadings. The central issue of Procrustes rotation considered in the article is that it equally treats the two types of approximation, while the former is more important for simplifying the loading matrix. Furthermore, a well-known issue of Simplimax is the computational inefficiency in estimating the sparse target matrix, which yields a considerable number of local minima. The research proposes a new rotation procedure that consists of the following two stages. The first stage estimates sparse target matrix with lesser computational cost by regularization technique. In the second stage, a loading matrix is rotated to the target, emphasizing on the approximation of non-zeros to zeros in the target by least squares criterion with generalized weighing that is newly proposed by the study. The simulation study and real data examples revealed that the proposed method surely simplifies loading matrices.
基金National Natural Science Foundation of China(No.61602148)Natural Science Foundation of Fujian Province,China(No.2016J01040)Xiamen University of Technology High Level Talents Project,China(No.YKJ15018R)
文摘This paper proposes a framework for human action recognition based on procrustes analysis and Fisher vector coding(FVC).Firstly,we applied a pose feature extracted from silhouette image by employing Procrustes analysis and local preserving projection(LPP).Secondly,the extracted feature can preserve the discriminative shape information and local manifold structure of human pose and is invariant to translation,rotation and scaling.Finally,after the pose feature was extracted,a recognition framework based on FVC and multi-class supporting vector machine was employed to classify the human action.Experimental results on benchmarks demonstrate the effectiveness of the proposed method.
文摘In order to study correlations between sensory properties and acceptance, regular and gluten-free carrot cakes (sweetened with sucrose and sucralose) were evaluated. Appearance, aroma, flavor, texture and overall liking were analyzed by 120 carrot cake consumers using a 9-cm hedonic scale. Quantitative Descriptive Analysis (QDA) was carried out with 11 assessors among 16 attributes. Data were analyzed by ANOVA, Tukey test (p < 0.05), Internal Preference Map and Cluster analysis. Also texture parameters were analyzed by Partial Least Square (PLS) to be able to show the instrumental parameters influence. Generalized Procrustes Analysis (GPA) was used before an Ex-ternal Preference Mapping to reduce the scale effects and to obtain a consensus configuration. According to PLS correlation, the attributes hardness, fracturability, adhesiveness, chewiness and gumminess interfered on characteristics considered undesirable for texture acceptance and smoothness, elasticity, cohesiveness and water activity interfered as desirable features. It was noted that all cakes were well accepted, except cake sweetened with sucralose and mix done using cornmeal, rice flour, potato starch and corn starch (2:3:3:2). As for the instrumental aspects, cohesiveness and elasticity influenced positively the cake’s acceptance. Instead, smoothness and adhesion parameters weren’t so significant.
基金Sponsored by the Applied Major Research Program of Science and Technology Commission Foundation of Beijing(Grant No.141100003514003)
文摘In order to realize high precision industrial operations,based on the POE formula,an effective approach to calibrate the robot's actual base frame(ABF) is proposed. Due to the existence of manufacturing errors,the ABF deviates slightly from nominal base frame( NBF). Using external precision measurement,the ABF can be established only through the three dimension(3D) position of the robot's end-effector.To ensure the orthonormal constraints of rotation matrix as well as the precise solutions,Procrustes Analysis is introduced,where an optimal orthogonal matrix is solved out by the Lagrange Multiplier method and Singular Value Decomposition(SVD). Furthermore,calibration experiment on a serial 6-DOF robot is performed,where a FARO laser tracker is utilized to measure the 3D position. Finally, calibration result indicates that the positioning accuracy has been significantly improved after calibration. The calibration method is also applicable to other similar problems,such as multi-robot coordination and robot hand-eye system calibration.
文摘This paper is intended to study the volume-preserving procrustes problem arising from practical areas. The corresponding solution should satisfy a matrix equation which is solved by the singular value decomposition method. Some further results are also given to characterize the solution. Using these results, a numerical algorithm is introduced and some numerical results are provided to illustrate the effectiveness of the algorithm. Key words volume-preserving - procrustes problems - singular value decomposition MSC2000 65F30 - 65K10 Project supported by NNSFC (Grant No. 10371076), E-Institutes of Shanghai Municipal Education Commission (Grant No. N. E03004)
