Alternating least squares in nonlinear principal components
Alternating least squares in nonlinear principal components
复制标题
非线性主成分中的交替最小二乘法
DOI：
10.1002/wics.1279
复制
发表时间：
2013
影响因子：
1.3
通讯作者：
M
中科院分区：
文献类型：
--
作者：
Kuroda;M.;Mori;Y.;Iizuka;M. and Sakakihara;M
主成分分析（PCA）可能是最流行的描述性多变量方法，用于分析具有比率和区间尺度测量的定量数据。当将PCA应用于标称和有序数据时，数据通过诸如最优缩放的方法进行处理，该方法将标称和有序数据非线性地转换为定量数据。因此，具有最佳尺度的PCA被称为非线性PCA。非线性主成分分析揭示了不同测量水平变量之间的非线性关系，因此提供了一种比普通主成分分析更灵活的选择。非线性主成分分析采用交替最小二乘算法。该算法交替之间的最佳尺度量化的名义和有序的数据和普通的PCA分析最佳尺度的数据。本文讨论了两种非线性PCA算法，即PRINCIPALS和PRINCALS。WIRES COMPUT STAT 2013，5：456-464。土井：10.1002/wics.1279这篇文章分类下：算法和计算方法>算法数据分析的统计和图形方法>多元分析算法和计算方法>数值方法统计模型>非线性模型算法和计算方法>最小二乘法
Principal components analysis (PCA) is probably the most popular descriptive multivariate method for analyzing quantitative data with ratio and interval scale measures. When applying PCA to nominal and ordinal data, the data are processed by a method such as optimal scaling, which nonlinearly transforms nominal and ordinal data into quantitative data. Therefore, PCA with optimal scaling is called nonlinear PCA. Nonlinear PCA reveals nonlinear relationships among variables with different measurement levels and therefore presents a more flexible alternative to ordinary PCA. The alternating least squares algorithm is utilized for nonlinear PCA. The algorithm alternates between optimal scaling for quantifying nominal and ordinal data and ordinary PCA for analyzing optimally scaled data. This article discusses two nonlinear PCA algorithms, namely, PRINCIPALS and PRINCALS.WIREs Comput Stat2013, 5:456–464. doi: 10.1002/wics.1279This article is categorized under:Algorithms and Computational Methods > AlgorithmsStatistical and Graphical Methods of Data Analysis > Multivariate AnalysisAlgorithms and Computational Methods > Numerical MethodsStatistical Models > Nonlinear ModelsAlgorithms and Computational Methods > Least Squares