Structured Regularized Dimensionality Reduction on Two Real Applications

Abstract

Datasets with a large number of observations and variables, called large datasets, become ubiquitous as a consequence of the development of technology. To deal with large datasets, data scientists face challenges such as the overfitting problem and the computational problem. Particularly, an important issue when analyzing large datasets is to study the structural information of observations and features. This dissertation focuses on a currently popular strategy called the structured regularized dimensionality reduction to analyze large datasets, which utilizes dimensionality reduction and regularization techniques to incorporate structural information into the model. We build new machine learning models of structured regularized dimensionality reduction for two real applications. In the first application, we propose a regularized spatially varying coefficient model to select important variables and estimate spatially clustered coefficients simultaneously in the spatial regression problem. In the second application, we build a regularized matrix decomposition model to solve the biclustering problem with a complex layout of latent biclusters in the data matrix.