| 讲座简介： | Big data are becoming increasingly common in our modern digital society and business world. More and more data are being collected with ever-increasing volume, dimensionality, and complexity. Efficient dimension reduction techniques are essential for analyzing such data. Principal component analysis (PCA) is a ubiquitous technique for dimension reduction of classical multivariate data. Regularization of PCA becomes necessary for high dimensionality, for example, in techniques such as functional PCA and sparse PCA. I shall introduce a general framework that enables flexible regularization of PCA, and leads to alternative approaches for its regularized siblings. I will illustrate its applicability using business analytics applications, including workforce management of labor-intensive service systems and yield curve forecasting. If time permits, I shall conclude with a general asymptotic framework for studying consistency properties of PCA. The framework includes several existing domains of asymptotics as special cases, and furthermore enables one to investigate interesting connections and transitions among the various domains. |
