论文部分内容阅读
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%.
In order to explore the performance of factor rotation in factor analysis and enhance the efficiency of factor analysis and calculation, the principle of factor analysis is studied and the factor analysis algorithm based on maximum variance rotation is proposed. From the perspective of linear representation, the independence between factor analysis model and sparse representation Component analysis is similar, independent component analysis model is to ignore the noise factor factor analysis model, the objective function of the relationship between the analysis shows that the traditional factor rotation methods, such as the maximum variance method and the general orthogonal method, independent component analysis kurtosis estimation method conditions But it is no longer suitable for the case where the source signal includes both super-Gaussian and sub-Gaussian sources.Based on the above analysis, a factor analysis algorithm based on maximum variance rotation is proposed, in which the source signal can be mixed type, But not limited to purely sub-Gaussian source or super-Gaussian source.In addition, this algorithm can also be used as a simple mode of Fastica algorithm and suitable for high-order statistical analysis.The simulation results show that in the mixed matrix is sparse, the proposed The factor analysis algorithm based on the maximum variance rotation has excellent performance such as simple and high efficiency, Fastica comparative analysis algorithm, similar to the estimated accuracy of the new algorithm, the average reached 0.975 3, but much higher efficiency, while consumption accounted for only 25%.