Determination of class-specific variables in nonparametric multiple-class classification

As technology advanced, collecting data via automatic collection devices become popular, thus we commonly face data sets with lengthy variables, especially when these data sets are collected without specific research goals beforehand. It has been pointed out in the literature that the difficulty of high-dimensional classification problems is intrinsically caused by too many noise variables useless for reducing classification error, which offer less benefits for decision-making, and increase complexity, and confusion in model-interpretation. A good variable selection strategy is therefore a must for using such kinds of data well; especially when we expect to use their results for the succeeding applications/studies, where the model-interpretation ability is essential. hus, the conventional classification measures, such as accuracy, sensitivity, precision, cannot be the only performance tasks. In this paper, we propose a probability-based nonparametric multiple-class classification method, and integrate it with the ability of identifying high impact variables for individual class such that we can have more information about its classification rule and the character of each class as well. The proposed method can have its prediction power approximately equal to that of the Bayes rule, and still retains the ability of "model-interpretation." We report the asymptotic properties of the proposed method, and use both synthesized and real data sets to illustrate its properties under different classification situations. We also separately discuss the variable identification, and training sample size determination, and summarize those procedures as algorithms such that users can easily implement them with different computing languages.