semi supervised learning

In semi-supervised learning you are given a few labeled points. You can make use of the whole dataset to do your learning.
Picture to have in your head: there are two clusters of unlabeled data. On the one cluster, you have a few red points, on the other you have a few blue. The reasonable thing to do would be to color the whole of one cluster as red and the other as blue. This is the main idea.

1. thoughts

there's a technique mentioned in this justin solomon lecture in which semi-supervised learning is done by finding a labeling function that minimizes the dirichlet energy. That is, you want your function to be a smooth interpolation over the few labeled points you have. This seems similar in spirit to the inference you can do using Markov Chain Monte Carlo over the Ising model. There, you have a few labeled spin up/down atoms and you want to find the labeling for the rest of the atoms that minimizes the energy.