Fusion Refinement Research Articles

High-dimensional semi-supervised learning via a fusion-refinement procedure

This paper develops a sufficient dimension reduction (SDR) approach for the high-dimensional semi-supervised learning (SSL) problem. In the proposed technique, we first modify the fusion-refinement (FR) procedure, which was proposed in [1], to extract the essential features for a lower-dimensional representation. We then apply an SSL algorithm (e.g., the low density separation (LDS)) in the lower-dimensional feature space to tackle the SSL problem. Numerical experiments are conducted on some widely-used data sets. We carry out a comparison between the proposed procedure and some recently proposed semi-supervised learning approaches (including greedy gradient Max-Cut (GGMC), semi-supervised extreme learning machines (SS-ELM)) and dimension reduction procedures (such as the semi-supervised local Fisher discriminant analysis (SELF), the trace ratio based flexible semi-supervised discriminant analysis (TR-FSDA), and trace ratio relevance feedback (TRRF)). In extensive numerical simulations, the new technique outperforms its competitors in many cases, demonstrating its effectiveness.

Dimension reduction with missing response at random

When there are many predictors, how to efficiently impute responses missing at random is an important problem to deal with for regression analysis because this missing mechanism, unlike missing completely at random, is highly related to high-dimensional predictor vectors. In sufficient dimension reduction framework, the fusion-refinement (FR) method in the literature is a promising approach. To make estimation more accurate and efficient, two methods are suggested in this paper. Among them, one method uses the observed data to help on missing data generation, and the other one is an ad hoc approach that mainly reduces the dimension in the nonparametric smoothing in data generation. A data-adaptive synthesization of these two methods is also developed. Simulations are conducted to examine their performance and a HIV clinical trial dataset is analyzed for illustration.

Fusion-Refinement Procedure for Dimension Reduction With Missing Response at Random

Dimension reduction methods are useful for handling high-dimensional data. It is a common situation that responses of some subjects are not observed in practice. Generally, the missingness carries additional information about the central subspace. Here we propose a two-stage procedure known as the fusion-refinement (FR) procedure. In the first stage, we obtain a subspace including the central subspace by fusing information on regression and missingness. In the second stage, we refine the obtained subspace to recover the central subspace by imputation method. We use sliced inverse regression to illustrate the FR procedure. We conduct simulation studies, and suggest a data-driven procedure to choose from the complete-case analysis and the FR procedure for a purpose of a real application. A real data analysis is used to illustrate our methods.