We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold i...We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.展开更多
Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex ...Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex geometries, and we compare several concepts and results for arbitrary （that is, not necessarily finite） aligned, topological and Higgs spaces.展开更多
In the traditional unscented Kalman filter（UKF）,accuracy and robustness decline when uncertain disturbances exist in the practical system.To deal with the problem,a robust UKF algorithm based on an H-infinity norm i...In the traditional unscented Kalman filter（UKF）,accuracy and robustness decline when uncertain disturbances exist in the practical system.To deal with the problem,a robust UKF algorithm based on an H-infinity norm is proposed.In Krein space,a robust element is added in the simplified UKF so as to improve the algorithm.The filtering gain is adjusted by the robust element and in this way the performance of the robustness of the filtering algorithm is promoted.In the initial alignment process of the large heading misalignment angle of the strapdown inertial navigation system（SINS）,comparative studies are conducted on the robust UKF and the simplified UKF.The simulation results illustrate that compared with the simplified UKF,the robust UKF is more accurate,and the estimation error of heading misalignment decreases from 16.9＇ to 4.3＇.In short,the robust UKF can reduce the sensitivity to the system disturbances resulting in better performance.展开更多
Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated ...Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated to aligned spaces which is similar to the one we have given for switching functions associated to finite topological spaces.展开更多
The research on positioning system and spatial alignment is a big topic. In this paper, we proposed a design (that) studies two issues. One is the study of range positioning algorithm based on ZigBee communication sys...The research on positioning system and spatial alignment is a big topic. In this paper, we proposed a design (that) studies two issues. One is the study of range positioning algorithm based on ZigBee communication system. The other one is spatial alignment platform which is controlled with two servos. Hardware and software control system was realized, which also consists of two parts, ZigBee network positioning system and automatic orientation platform.展开更多
Considering gravity change from ground alignment to space applications, a fuzzy proportional-integral-differential(PID)control strategy is proposed to make the space manipulator track the desired trajectories in diffe...Considering gravity change from ground alignment to space applications, a fuzzy proportional-integral-differential(PID)control strategy is proposed to make the space manipulator track the desired trajectories in different gravity environments. The fuzzy PID controller is developed by combining the fuzzy approach with the PID control method, and the parameters of the PID controller can be adjusted on line based on the ability of the fuzzy controller. Simulations using the dynamic model of the space manipulator have shown the effectiveness of the algorithm in the trajectory tracking problem. Compared with the results of conventional PID control,the control performance of the fuzzy PID is more effective for manipulator trajectory control.展开更多
Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In thi...Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In this paper, based on combination of modified maximum margin criterion and ILTSA, a novel feature extraction method named orthogonal discriminant improved local tangent space alignment (ODILTSA) is proposed. ODILTSA can preserve local geometry structure and maximize the margin between different classes simultaneously. Based on ODILTSA, a novel face recognition method which combines augmented complex wavelet features and original image features is developed. Experimental results on Yale, AR and PIE face databases demonstrate the effectiveness of ODILTSA and the feature fusion method.展开更多
文摘We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
文摘Aligned spaces generalize topological spaces and generate Higgs spaces. We give a necessary and sufficient condition for a finite aligned space to be a topological space, we prove the existence of two kinds of convex geometries, and we compare several concepts and results for arbitrary （that is, not necessarily finite） aligned, topological and Higgs spaces.
基金The National Basic Research Program of China (973 Program) (No. 613121010202)
文摘In the traditional unscented Kalman filter（UKF）,accuracy and robustness decline when uncertain disturbances exist in the practical system.To deal with the problem,a robust UKF algorithm based on an H-infinity norm is proposed.In Krein space,a robust element is added in the simplified UKF so as to improve the algorithm.The filtering gain is adjusted by the robust element and in this way the performance of the robustness of the filtering algorithm is promoted.In the initial alignment process of the large heading misalignment angle of the strapdown inertial navigation system（SINS）,comparative studies are conducted on the robust UKF and the simplified UKF.The simulation results illustrate that compared with the simplified UKF,the robust UKF is more accurate,and the estimation error of heading misalignment decreases from 16.9＇ to 4.3＇.In short,the robust UKF can reduce the sensitivity to the system disturbances resulting in better performance.
文摘Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated to aligned spaces which is similar to the one we have given for switching functions associated to finite topological spaces.
文摘The research on positioning system and spatial alignment is a big topic. In this paper, we proposed a design (that) studies two issues. One is the study of range positioning algorithm based on ZigBee communication system. The other one is spatial alignment platform which is controlled with two servos. Hardware and software control system was realized, which also consists of two parts, ZigBee network positioning system and automatic orientation platform.
基金supported by National High Technology Research and Development Program of China(863 Program)(No.2011AA)
文摘Considering gravity change from ground alignment to space applications, a fuzzy proportional-integral-differential(PID)control strategy is proposed to make the space manipulator track the desired trajectories in different gravity environments. The fuzzy PID controller is developed by combining the fuzzy approach with the PID control method, and the parameters of the PID controller can be adjusted on line based on the ability of the fuzzy controller. Simulations using the dynamic model of the space manipulator have shown the effectiveness of the algorithm in the trajectory tracking problem. Compared with the results of conventional PID control,the control performance of the fuzzy PID is more effective for manipulator trajectory control.
基金the National Natural Science Foundation of China(No.61004088)the Key Basic Research Foundation of Shanghai Municipal Science and Technology Commission(No.09JC1408000)
文摘Improved local tangent space alignment (ILTSA) is a recent nonlinear dimensionality reduction method which can efficiently recover the geometrical structure of sparse or non-uniformly distributed data manifold. In this paper, based on combination of modified maximum margin criterion and ILTSA, a novel feature extraction method named orthogonal discriminant improved local tangent space alignment (ODILTSA) is proposed. ODILTSA can preserve local geometry structure and maximize the margin between different classes simultaneously. Based on ODILTSA, a novel face recognition method which combines augmented complex wavelet features and original image features is developed. Experimental results on Yale, AR and PIE face databases demonstrate the effectiveness of ODILTSA and the feature fusion method.
