On the usage of joint diagonalization in multivariate statistics
本文综述了基于联合对角化的多种多变量数据分析方法，涵盖无监督的坐标选择和盲源分离，以及有监督的判别分析和切片逆回归，并包括处理时间序列或空间数据的方法。
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also encompass methods that handle dependent data such as time series or spatial data.