On classification with incomplete data

We address the incomplete-data problem in which feature vectors to be classified are missing data (features). A (supervised) logistic regression algorithm for the classification of incomplete data is developed. Single or multiple imputation for the missing data is avoided by performing analytic inte-gration with an estimated conditional density function (conditioned on the observed data). Conditional density functions are estimated using a Gaussian mixture model (GMM), with parameter estimation performed using both Expectation-Maximization (EM) and Variational Bayesian EM (VB-EM). The proposed supervised algorithm is then extended to the semi-supervised case by incorporating graph-based regularization. The semi-supervised algorithm utilizes all available data — both incomplete and complete, as well as labeled and unlabeled. Experimental results of the proposed classification algorithms are shown. I