Multiclass Laplacian support vector machine with functional analysis of variance decomposition

In classification problems, acquiring a sufficient amount of labeled samples sometimes proves expensive and time-consuming, while unlabeled samples are relatively easier to obtain. The Laplacian Support Vector Machine (LapSVM) is one of the successful methods that learn better classification functions by incorporating unlabeled samples. However, since LapSVM was originally designed for binary classification, it can not be applied directly to multiclass classification problems commonly encountered in practice. Thus we derive an extension of LapSVM to multiclass classification problems using an appropriate multiclass formulation. Another problem with LapSVM is that irrelevant variables easily degrade classification performance. The irrelevant variables can increase the variance of predicted values and make the model difficult to interpret. Therefore, this paper also proposes the multiclass LapSVM with functional analysis of variance decomposition to identify relevant variables. Through comprehensive simulations and real-world datasets, we demonstrate the efficiency and improved classification performance of the proposed methods.