Let me introduce the second topic of my research interests:
Consider a situation in which we wish to select items or variables so as to delete the redundant variables or to make a small dimensional rating scale to measure latent traits, variable selection in principal component analysis (PCA) is necessary to identify a subset of variables that represents all variables as much as possible.
In the figure below, the left-hand plot is a scatter plot of the 1st and 2nd principal components (PCs) obtained based on all 19 original variables, and the right-hand plot is based on seven selected variables. Little difference exists between the two configurations of PCs. This illustrates the meaningfulness of variable selection in PCA since selected variables can provide almost the same result as the original variables if the goal of the analysis is to observe the configuration of the PCs.

We can perform the variable selection in PCA as a prior analysis in big data analysis, and apply the proposed selection procedures to other multivariate methods such as factor analysis and correspondence analysis.In this topic, we also study on how to deal with categorical/qualitative data (for the first topic), and how to improve the computation effectively (for the third topic).