Semi-supervised Support Vector Machines (S3VM)
When we discussed the cluster assumption, we also defined the low-density regions as boundaries and the corresponding problem as low-density separation. A common supervised classifier which is based on this concept is a Support Vector Machine (SVM), the objective of which is to maximize the distance between the dense regions where the samples must be. For a complete description of linear and kernel-based SVMs, please refer to Bonaccorso G., Machine Learning Algorithms, Packt Publishing; however, it's useful to remind yourself of the basic model for a linear SVM with slack variables ξi:
This model is based on the assumptions that yi can be either -1 or 1. The slack variables ξi or soft-margins are variables, one for each sample, introduced to reduce the strength imposed by the original condition (min ||w||), which is based on a hard margin that misclassifies all the samples that are on the wrong side. They are defined by the Hinge loss, as follows...
