为了解决增量流形学习中的噪声干扰,以及对不同分布状态下的新数据进行流形降维问题,本文提出一种数据流形边界及其分布条件的增量式降维算法(incremental dimensionality reduction algorithm based on data manifold boundaries and d...为了解决增量流形学习中的噪声干扰,以及对不同分布状态下的新数据进行流形降维问题,本文提出一种数据流形边界及其分布条件的增量式降维算法(incremental dimensionality reduction algorithm based on data manifold boundaries and distribution state,IDR-DMBDS)。该算法首先分析噪声概率分布同时对数据降噪,确定降噪数据的流形形态为主流形,并在主流形上表征出噪声的分布形式,以此获得近似的原数据流形边界,然后基于流形边界判别新数据的分布状态,最后将分布于原流形形态之上以及之外的新数据分别映射至低维空间。实验表明,该算法能够有效实现基于流形的增量式高维含噪数据的低维特征挖掘。展开更多
This article is devoted to the numerical solution of a projected generalized Sylvester equation with relatively small size. Such an equation arises in stability analysis and control problems for descriptor systems inc...This article is devoted to the numerical solution of a projected generalized Sylvester equation with relatively small size. Such an equation arises in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. The algebraic formula of the solution of the projected generalized continuous-time Sylvester equation is presented. A direct method based on the generalized Schur factorization is proposed. Moreover, its low-rank version for problems with low-rank right-hand sides is also proposed. The computational cost of the direct method is estimated. Numerical simulation show that this direct method has high accurncv展开更多
文摘为了解决增量流形学习中的噪声干扰,以及对不同分布状态下的新数据进行流形降维问题,本文提出一种数据流形边界及其分布条件的增量式降维算法(incremental dimensionality reduction algorithm based on data manifold boundaries and distribution state,IDR-DMBDS)。该算法首先分析噪声概率分布同时对数据降噪,确定降噪数据的流形形态为主流形,并在主流形上表征出噪声的分布形式,以此获得近似的原数据流形边界,然后基于流形边界判别新数据的分布状态,最后将分布于原流形形态之上以及之外的新数据分别映射至低维空间。实验表明,该算法能够有效实现基于流形的增量式高维含噪数据的低维特征挖掘。
基金supported by the National Natural Science Foundation of China(Nos.10801048,10926150,11101149)the Natural Science Foundation of Hunan Province(No.09JJ6014)+4 种基金the Key Program of the Scientific Research Foundation from Education Bureau of Hunan Province(No.09A033)the Scientific Research Foundation of Education Bureau of Hunan Province for Outstanding Young Scholars in University(No.10B038)the Science and Technology Planning Project of Hunan Province(No.2010JT4042)the Young Core Teacher Foundation of Hunan Province in Universitythe Fundamental Research Funds for the Central Universities
文摘This article is devoted to the numerical solution of a projected generalized Sylvester equation with relatively small size. Such an equation arises in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. The algebraic formula of the solution of the projected generalized continuous-time Sylvester equation is presented. A direct method based on the generalized Schur factorization is proposed. Moreover, its low-rank version for problems with low-rank right-hand sides is also proposed. The computational cost of the direct method is estimated. Numerical simulation show that this direct method has high accurncv
