作　　者： ; ; ; ;

机构地区： 空军工程大学理学院

出　　处： 《纳米技术与精密工程》 2013年第6期557-561,共5页

摘　　要： 为探索因子分析中因子旋转的性能和提升因子分析计算的效率,研究因子分析的原理并提出基于最大方差旋转的因子分析算法.从线性表示的角度分析,因子分析模型与稀疏表示情况下的独立分量分析相似,独立分量分析模型是忽略了噪声因子的因子分析模型,目标函数关系分析表明,传统的因子旋转方法,如最大方差方法和一般直交法,与独立分量分析的峭度估计方法条件等价,但并不再适用于源信号中既包括超高斯源又包括次高斯源的情况.基于以上分析,提出了一种基于最大方差旋转的因子分析算法,其中的源信号可以是混合类型,而不限定单纯的次高斯源或者超高斯源.此外,这种算法还可以作为Fastica算法的简单模式并适用于高阶统计分析.仿真结果表明,在混合矩阵为稀疏的情况下,所提出的基于最大方差旋转的因子分析算法具有简易高效等优异性能.和独立分量分析的Fastica算法比较,新算法的估计精度相近,平均值达到0.975 3,但是效率高得多,时耗仅占25%. To explore the performance of factor rotation in factor analysis and improve its computing effi ciency, the principle of factor analysis is investigated and a Varimaxbased rotation algorithm is presen ted. From the aspect of linear representation, factor analysis is proved to be a similar form of independent component analysis （ICA） in the case of sparse representation, and ICA model is essentially a specialized factor analysis model when noise factor is neglected. In detail, from the relationship between object functions, it is convinced that conventional factor rotation, such as Varimax and Orthomax, is con ditionally equivalent to kurtosisbased estimation for ICA, but no longer suitable for the case that both su perGaussian sources and subGaussian sources are included. Based on the above conclusions, a Vari maxbased rotation algorithm is presented for factor analysis in which the sources may be hybrid, and not limited to superGanssian or subGaussian. Moreover, the algorithm can be regarded as a simplified form of Fastica algorithm and be available for highorder statistical analysis. Simulation results show the out standing performance of Varimaxbased rotation algorithm, such as convenience and high efficiency, when the mixing matrix is sparse. Compared with Fastica algorithm for ICA, the proposed algorithm achieves similar high estimation accuracy with the mean value 0. 975 3, but much better efficiency with only 25% time cost.

关 键 词： 因子分析 因子旋转 最大方差 独立分量分析 峭度

领　　域： [电子电信]